ArticlePDF Available

Abstract and Figures

As Africa-wide malaria prevalence declines, an understanding of human movement patterns is essential to inform how best to target interventions. We fitted movement models to trip data from surveys conducted at 3–5 sites throughout each of Mali, Burkina Faso, Zambia and Tanzania. Two models were compared in terms of their ability to predict the observed movement patterns – a gravity model, in which movement rates between pairs of locations increase with population size and decrease with distance, and a radiation model, in which travelers are cumulatively “absorbed” as they move outwards from their origin of travel. The gravity model provided a better fit to the data overall and for travel to large populations, while the radiation model provided a better fit for nearby populations. One strength of the data set was that trips could be categorized according to traveler group – namely, women traveling with children in all survey countries and youth workers in Mali. For gravity models fitted to data specific to these groups, youth workers were found to have a higher travel frequency to large population centers, and women traveling with children a lower frequency. These models may help predict the spatial transmission of malaria parasites and inform strategies to control their spread.
No caption available
… 
Empirical and model-predicted travel frequencies for each survey country. Model predictions are for the gravity model with the destination population size raised to a power, τ, and radiation model B fitted to data for each country individually. Each dot represents a commune or ward, the radius of which is a monotonically increasing function of its population size. Each line represents travel frequency between communes/wards, the width of which is proportional to travel frequency. Maps were generated using Mathematica version 11 (https://www.wolfram.com/mathematica/) with political boundaries obtained from Wolfram’s Data Repository (https://datarepository.wolframcloud.com/). The survey was conducted at 3–5 sites in each country, and trips are color-coded according to the survey location. In Mali (panels a–c), purple trips originate in Bamako, the capital city and largest urban center, green trips originate in the fishing village of Baya, blue trips originate in the farming villages of Barouéli and Boidié, and red trips originate in Mopti and Fatoma, a commercial center and village respectively. In Burkina Faso (panels d–f), red trips originate in Ouagadougou, the capital and largest city, blue trips originate in Sapone, an agricultural village, and green trips originate in Boussé, a local center of agriculture and trade. In Zambia (panels g–i), blue trips originate in Lusaka, the capital and largest city, green trips originate in Samfya, a central fishing town, red trips originate in Kitwe, an urban trading town in the Copperbelt, yellow trips originate in Nakonde, a town in the north-east bordering Tanzania, and purple trips originate in Chipata, a rural town in the east bordering Malawi. In Tanzania (panels j–l), green trips originate in Dar es Salaam, the capital and largest city, red trips originate in Ifakara, a small rural town on the edge of the Kilombero valley, purple trips originate in Muheza, a small rural town near the border with Kenya, and blue trips originate in Mtwara, an agricultural town with a growing mining industry near the border with Mozambique.
… 
Content may be subject to copyright.
1
SCIENTIFIC REPORts | (2018) 8:7713 | DOI:10.1038/s41598-018-26023-1
www.nature.com/scientificreports
Mathematical models of human
mobility of relevance to malaria
transmission in Africa
John M. Marshall1,2, Sean L. Wu2, Hector M. Sanchez C.
2, Samson S. Kiware3,
Micky Ndhlovu4, André Lin Ouédraogo5,6, Mahamoudou B. Touré7, Hugh J. Sturrock8,
Azra C. Ghani1 & Neil M. Ferguson
1
As Africa-wide malaria prevalence declines, an understanding of human movement patterns is essential
to inform how best to target interventions. We tted movement models to trip data from surveys
conducted at 3–5 sites throughout each of Mali, Burkina Faso, Zambia and Tanzania. Two models
were compared in terms of their ability to predict the observed movement patterns – a gravity model,
in which movement rates between pairs of locations increase with population size and decrease
with distance, and a radiation model, in which travelers are cumulatively “absorbed” as they move
outwards from their origin of travel. The gravity model provided a better t to the data overall and
for travel to large populations, while the radiation model provided a better t for nearby populations.
One strength of the data set was that trips could be categorized according to traveler group – namely,
women traveling with children in all survey countries and youth workers in Mali. For gravity models
tted to data specic to these groups, youth workers were found to have a higher travel frequency to
large population centers, and women traveling with children a lower frequency. These models may help
predict the spatial transmission of malaria parasites and inform strategies to control their spread.
Increasing human mobility in Africa is creating highly favorable conditions for the persistence of diseases being
targeted for elimination, such as malaria1,2, and for the faster spread of emerging pathogens, such as Ebola or
Zika3. Signicant funding is currently being invested in global malaria control and elimination4 and mathematical
models are informing the most ecient use of these resources for reducing transmission5. As malaria transmis-
sion declines6, predictive models of human movement are needed to help inform how best to target interven-
tions7,8. Empirical data on human movement are available for some locations1,911; however there are invariably
biases inherent in all data sets and there are many locations for which data are not available12. Predictive move-
ment models therefore provide an opportunity to extrapolate movement patterns to locations where data is biased
or unavailable.
In recent years, two general classes of models have been proposed to describe patterns of human movement –
gravity models13,14 and radiation models15. Gravity models assume movement rates between pairs of locations
increase with the sizes of origin and destination populations and decrease with journey distance, akin to physical
gravity. ese models were used by Xia et al.14 to describe the spread of measles through populations in the UK
prior to wide-scale vaccination programs. Variants have since been proposed in which the dependence on dis-
tance is described by a function that may depend on Euclidean distance, road distance, travel cost, travel time,
or some combination of these metrics16. Radiation models take their inspiration from a simple particle diusion
model whereby travelers (the particles) are “absorbed” as they move outwards from their origin of travel, with the
probability of absorption at a given radius being proportional to the population size within that radius15. ese
models were shown to apply well to US national and state-wide travel data originating from New York county15,
1MRC Centre for Outbreak Analysis and Modelling, Department of Infectious Disease Epidemiology, Imperial College
London, London, UK. 2Divisions of Biostatistics and Epidemiology, School of Public Health, University of California,
Berkeley, California, USA. 3Environmental Health and Ecological Sciences Thematic Group, Ifakara Health Institute,
Dar es Salaam, Tanzania. 4Chainama College of Health Sciences, Lusaka, Zambia. 5Centre National de Recherche et
de Formation sur le Paludisme, Ouagadougou, Burkina Faso. 6Institute for Disease Modeling, Bellevue, Washington,
USA. 7Malaria Research and Training Center, University of Bamako, Bamako, Mali. 8Malaria Elimination Initiative,
Global Health Group, University of California, San Francisco, California, USA. Correspondence and requests for
materials should be addressed to J.M.M. (email: john.marshall@berkeley.edu)
Received: 13 October 2017
Accepted: 3 May 2018
Published: xx xx xxxx
OPEN
Content courtesy of Springer Nature, terms of use apply. Rights reserved
www.nature.com/scientificreports/
2
SCIENTIFIC REPORts | (2018) 8:7713 | DOI:10.1038/s41598-018-26023-1
and hence could be suitable for modeling the spatial spread of seasonal inuenza and other infectious diseases
in the US17. Variants have been proposed in which the spatial scale is varied, and directionality and other trip
constraints are incorporated18,19.
Comparisons of model predictions to data suggest that these families of models describe commuting patterns
in the US and UK reasonably well. However, they perform less well at capturing local movement patterns within
large population centers, such as London or New York, where movement is goal-driven14,15,18. e gravity model
provided a better overall t to commuting data in the UK; however, the radiation model provided a better t for
small populations at large distances18. Wesolowski et al.20 compared the performance of gravity and radiation
models in explaining movement patterns inferred from anonymous cell phone signal data in Kenya and suggested
that travel in Kenya, and potentially in many parts of sub-Saharan Africa, may have unique features that are not
well suited to description by these models. ey noted the variable accessibility of rural destinations, in terms of
cost, transport availability and road quality, and the rise of the mega-city, which is attractive beyond what would
be expected due to population size alone. Furthermore, they noted that movement models tend to overestimate
the number of destinations to which travelers move, and hence may overestimate the dispersal of disease.
Here, we explore the ability of gravity and radiation models to capture movement patterns from a survey
conducted at 3–5 sites throughout each of four sub-Saharan African countries – Mali, Burkina Faso, Zambia
and Tanzania10. A key feature of these data is that they were collected specically to understand movement pat-
terns of relevance to malaria transmission. Respondents were asked about trips for which they had spent at least
one night away from home, which is required for malaria transmission since the main African malaria vectors,
Anopheles gambiae and Anopheles funestus, bite at night. e surveys also asked questions about demography and
trip details, which allowed us to classify trips made by key traveler groups – women traveling with children and
youth workers – elucidated in previous analyses10. ese traveler groups are of relevance to malaria transmission,
since children are most likely to display clinical malaria incidence in high prevalence settings21, and movements
of youth workers tend to correlate with seasonal rains and hence peak mosquito densities in the Sahel22. We
therefore additionally explore the application of gravity and radiation models to describe movement patterns in
these traveler groups specically.
Methods
Data. We analyzed trip data from surveys carried out in four countries with ongoing malaria transmission –
Mali and Burkina Faso in West Africa, and Zambia and Tanzania in East/Southern Africa. e data are described
elsewhere10. In brief, participants were asked a series of questions about the last up to three trips undertaken in
the previous year, restricted to those for which they spent at least one night away from home. Information col-
lected included trip details (purpose, duration, month of departure and number of accompanying children) and
basic demographic information (age, gender and number of children under the age of ve). e surveys were
conducted at 3–5 sites per country, chosen according to a judgment/convenience sample. Models tted to these
data therefore reect the collection of sites and may only serve as proxies for the countries at large. Travel within
the ward, commune or city of origin was not recorded. Study participants were interviewed in Mali during the
rainy season of September/October 2010 and the dry season of March 2011, in Burkina Faso during the rainy
season of July 2011, in Zambia during the cool dry season of July/August 2012, and in Tanzania during the long
rainy season of March 2013.
For the purpose of model tting, only trips for which both the origin and destination were resolved at the
administrative level of commune in Mali and Burkina Faso and at the administrative level of ward in Zambia
and Tanzania were retained. is represented 96.4% of trips in Mali, 99.2% of trips in Burkina Faso, 77.0% of
trips in Zambia and 98.9% of trips in Tanzania. Trips were assigned to traveler groups based on a cluster analysis
accounting demographic and trip details10. For Mali and Burkina Faso, the population size within each commune
was estimated using WorldPop population estimates23 and the coordinates for each commune were taken as the
population-weighted centroids. For Zambia and Tanzania, the lists of wards used in the surveys and their corre-
sponding population sizes were taken from recent censuses24,25. ese lists of wards did not correspond to any one
set of shape les and so, where possible, population-weighted centroids were estimated using WorldPop23, and
otherwise coordinates were taken from GADM shape les (www.gadm.org) and the Stanford Digital Repository
(https://purl.stanford.edu/rn812zx7730). e collated data and estimates are provided in Supplementary File1.
Our surveys did not collect information on individuals who had not traveled in the last year, and so to deter-
mine whether origin population size had a signicant inuence on movement frequency, we used equivalent data
from national Demographic and Health Surveys (DHS) for each of the survey countries2629. Geocoded responses
to question V167, which measured the number of overnight trips taken by respondents in the last year, were
linked to communes/wards having the nearest centroid and used to calculate the proportion of male and female
respondents who didn’t travel and the mean number of trips taken by male and female respondents, with weight-
ings to account for dierences in demographic sampling rates. ese summary statistics were then plotted against
origin population size for each survey country. Interestingly, there was no suggestion of a relationship between
origin population size and travel frequency for either males or female respondents (Supplementary Figure1),
allowing us to explore the application of gravity and radiation models conditional upon the location of origin.
Gravity models. A gravity model was tted to the trips recorded for each country. Model tting was carried
out: (a) on the full set of trips for each country, (b) on trips subdivided according to traveler group – (i) women
traveling with children (for all survey countries), and (ii) youth workers (for Mali) – and (c) on the full set of trips
for all countries simultaneously. e gravity model was formulated conditional upon the origin, i, such that the
probability of a trip being to destination j is proportional to the population size at j, Nj, raised to a power, τ, and
proportional to a distance kernel, k(di,j), that is a function of the distance between the two locations:
Content courtesy of Springer Nature, terms of use apply. Rights reserved
www.nature.com/scientificreports/
3
SCIENTIFIC REPORts | (2018) 8:7713 | DOI:10.1038/s41598-018-26023-1
|∝ .
τ
PjiNkd() () (1)
jij,
Analyses were conducted at the national scale. Lognormal, power law and exponential distance kernels were
considered, however the power law kernel, parameterized by a scale parameter, ρ, and a power parameter, α,
provided the best t:
ρ
=
+
.
α
kd
d
() 1
(2)
ij ij
,,
Models both with and without a power, τ, on the destination population size were considered. Simplied grav-
ity models conditional upon the origin of travel were considered because: (i) the data for each country were
restricted to 3–5 origins, and (ii) data from national DHS surveys for each of the survey countries suggested no
apparent relationship between travel frequency and origin population size (Supplementary Figure1).
Radiation models. Several variants of the radiation model were also tted to the trips recorded for each
country, to trips subdivided according to traveler group, and to trips for all countries simultaneously. In the basic
radiation model, given an origin i, the probability of a journey ending at a location greater than a distance r away,
Pi(d > r), is inversely proportional to the population size living within a ring of radius r around i. Mathematically,
this may be formulated as,
>∝dr
sr
P( )
1
()
,
(3)
i
i
where si(r) represents the total population size living within a ring of radius r centered around origin i.
e basic radiation model has no free parameters. However, because we were only considering journeys
involving an overnight stay, we modied the model to generate less local journey distance distributions. We
considered two variants of this model. In the rst (model A), the origin population size, Ni, is scaled by a factor u:
>∝ −+
dr sr Nu N
P( )
1
(())/,
(4)
i
ii i
e second model variant (model B) eectively adds a xed value v to the origin population:
>∝ +.dr
sr v
P( )
1
() (5)
i
i
Parameters u and v were estimated in the model tting process.
Model tting. Model parameters were estimated using a Markov chain Monte Carlo (MCMC) algorithm.
e log likelihood of the data, D, given model parameters,
θαρτ={, ,}
for the gravity model and θ = μ or θ = v
for the radiation model, was calculated using the expected distribution of destinations for each origin given the
movement model and chosen parameter values and summing the log likelihood over trips recorded at the admin-
istrative level of ward and/or commune, i.e.:
θθ=|.
=
LPjilog()(,)
(6)
k
K
kk
1
Here, K represents the number of recorded trips resolved at the level of ward or commune and ik and jk are the ori-
gin and destination for the kth trip, respectively. e deviance information criterion (DIC) was used as a measure
for model selection30, dened as:
θ=− +.LpDIC2log()2 (7)
D
Here, the rst term represents the deviance, D(θ), dened as 2 times the log likelihood of the model, with model
parameters equal to their means from the MCMC chain at equilibrium, and pD represents the eective number of
parameters, calculated here as the mean deviance of the MCMC chain at equilibrium minus the deviance with
model parameters equal to their means from the MCMC chain at equilibrium, i.e.
θθ=−.pDD() ()
D
e rela-
tive prediction error of trip frequencies (dened as |1 (observed/predicted)|) was used as a measure to present
model t graphically.
Data availability. e data sets generated and analyzed in this study are available in Supplementary File1.
Results
e best-tting movement model for the complete set of origins and destinations for each country, and for all
countries combined, was a gravity model with a power law distance kernel and a power on the destination popu-
lation size (Table1). e estimated power on the destination population size was signicantly larger than one for
Mali and Burkina Faso (95% credible intervals (CrIs) of 1.21–1.27 and 1.30–1.38, respectively), and signicantly
less than one for Zambia and Tanzania (95% CrIs of 0.83–97 and 0.79–0.94, respectively). is can be interpreted
as large population centers being more attractive in Mali and Burkina Faso than in Zambia and Tanzania. Which
radiation model variant tted better depended on country – model A (equation4) was preferred for Mali, while
Content courtesy of Springer Nature, terms of use apply. Rights reserved
www.nature.com/scientificreports/
4
SCIENTIFIC REPORts | (2018) 8:7713 | DOI:10.1038/s41598-018-26023-1
model B (equation5) was preferred for Burkina Faso, Zambia, Tanzania and for all countries combined. Model
predictions for the best tting gravity model and radiation model B are graphically depicted alongside the empir-
ical survey data in Figs13.
e performance of both models at capturing travel to the capital city varied as, for the gravity model, the
“gravitational pull”, and for the radiation model, the absorption of the capital city, is balanced in the tting along-
side other major population centers (Table2). For Mali, the gravity model underestimated travel to the capital
(Bamako) from Barouéli/Boidié and Mopti/Fatoma; but captured it well for Baya. e radiation model, on the
other hand, underestimated travel to Bamako from all other survey sites, especially from Barouéli/Boidié and
Mopti/Fatoma. For Burkina Faso, the gravity model overestimated travel to the capital (Ouagadougou), while the
radiation model underestimated it. For Zambia, travel to the capital (Lusaka) was greatly underestimated by both
the gravity and radiation models from all survey sites except for Samfya, from which the radiation model slightly
underestimated travel while the gravity model provided a good estimate. Empirically, low frequency movement
from Samfya to Lusaka could have been due to the Democratic Republic of Congo having territory between
these two locations. For Tanzania, the radiation model provided a good prediction of travel to the capital (Dar
es Salaam) from Mtwara and Muheza, while underestimating travel from Ifakara. e gravity model slightly
underestimated travel to Dar es Salaam from Mtwara and Ifakara; but provided a good prediction from Muheza.
Another important factor in determining model t is accurately capturing travel to nearby locations. ese
destinations also have a strong gravitational attractiveness or absorption potential; however, since we are only
interested in overnight trips for malaria transmission, travelers may return home rather than sleeping nearby
and hence the attractiveness of nearby locations may be lower. Figure2 suggests that the gravity model tends
to overestimate travel from capital cities to locations within their vicinity (expected – observed travel frequen-
cies are signicantly greater than 0 for destinations within 200 km of Bamako (t-test, p-value = 0.035), Lusaka
(p-value < 105) and Dar es Salaam (p-value = 0.026)). Figure3 suggests that the radiation model provides a
closer t for travel originating at a capital city (expected – observed travel frequency is only signicantly dier-
ent from 0 for destinations within 200 km of Lusaka (t-test, p-value < 105)). Travel within 20 km of the capital
city of Mali, Bamako, is substantially underestimated by both models (t-test, p-value = 0.041 for the radiation
model and 0.0009 for the gravity model); however, the t to the Mali survey data is challenged by the high levels
of movement within the vicinity of Mopti/Fatoma and Barouéli/Boidié but not from other origins. Similarly, for
the Zambia survey data, frequent nearby movement recorded for all survey sites except the capital city, Lusaka,
was hard to reconcile with either model. Rather, the radiation model provides a superior t for travel within the
vicinity of Lusaka (error variance for the radiation model is less than that for the gravity model for destinations
within 200 km of Lusaka (F-test, p-value = 0.00002)), while the gravity model provides a superior t for travel
within the vicinity of another city – Nakonde (F-test, p-value = 0.043). Both models generally provide a good t
for travel within the vicinity of Burkina Faso and Tanzania survey sites (expected – observed travel frequencies
are not signicantly dierent from 0 for destinations within 200 km of all three survey sites in Burkina Faso and
for Ifakara, Mtwara and Muheza in Tanzania (t-tests, p-values > 0.05)).
Plots of relative prediction error (Figs4 and 5) show that both the gravity and radiation models give reasona-
ble estimates of travel frequency across the range of intermediate distances and population sizes, with large errors
oen seen at either end of the trip distance and population size spectra, where recorded numbers of journeys
are low and statistical noise is higher. For instance, for the gravity model applied to trips originating in Bamako/
Kalabancoro, some of the largest scaled errors are seen for trips to distant, large populations (e.g. Goumera,
Fanga and Tenenkou), whereas for the gravity model applied to trips originating in Mopti/Fatoma, some of the
largest relative errors are for trips to nearby, large populations (e.g. Fatoma and Bassirou). Whilst it does not
apply universally, there is a tendency for the radiation model to provide a better t than the gravity model for
trips to nearby populations. is is visually apparent in the distance distribution plots in Figs2 and 3 and is evi-
denced by the error variance for the radiation model being less than that for that for the gravity model for trips
within 200 km of nine out of 16 survey sites. is dierence in error variance is statistically signicant for trips
within 200 km of Sapone, Burkina Faso (F-test, p-value = 0.0069) and Lusaka, Zambia (F-test, p-value = 0.00002).
Conversely, there is a tendency for the gravity model to provide a better t than the radiation model for trips to
Model: Parameters: Mali: Burkina Faso: Zambia: Tanzania: All countries:
Gravity model
(Equations12) with τ
α2.00 (1.62–2.58) 1.27 (1.18–1.38) 1.70 (1.54–1.88) 3.62 (2.78–5.16) 1.91 (1.78–2.06)
log(ρ)4.98 (4.52–5.47) 0.54 (0.02–1.80) 3.65 (3.31–3.97) 5.90 (5.41–6.47) 4.29 (4.09–4.48)
τ1.239 (1.211–1.267) 1.342 (1.304–1.381) 0.91 (0.83–0.97) 0.86 (0.79–0.94) 1.22 (1.20–1.24)
DIC 12,027 8,444.4 14,593 16,762 52,206
Gravity model
(Equations12) without τ
α2.12 (1.78–2.63) 1.70 (1.48–1.99) 1.74 (1.58–1.93) 3.43 (2.71–4.64) 1.84 (1.73–1.98)
log(ρ)4.83 (4.43–5.25) 2.64 (1.47–3.32) 3.75 (3.43–4.05) 5.79 (5.33–6.29) 4.10 (3.93–4.29)
DIC 12,305 8,757.5 14,598 16,771 52,642
Radiation model A
(Equation4)
u66.2 (58.8–74.7) 34.2 (29.9–39.1) 37.8 (33.7–42.8) 210 (184–240) 68.3 (64.0–72.9)
DIC 12,149 8,653 14,719 16,931 52,860
Radiation model B
(Equation5)
v2.67 (2.37–3.00) × 1061.80 (1.58–2.06) × 1066.61 (5.80–7.60) × 1053.66 (3.24–4.19) × 1061.96 (1.84–2.10) × 106
DIC 12,222 8,649 14,657 16,886 52,761
Table 1. Movement model parameters (with 95% credible intervals) for gravity and radiation models tted to
origin-destination pairs in all survey countries.
Content courtesy of Springer Nature, terms of use apply. Rights reserved
www.nature.com/scientificreports/
5
SCIENTIFIC REPORts | (2018) 8:7713 | DOI:10.1038/s41598-018-26023-1
large populations. is is also visually apparent in the distance distribution plots in Figs2 and 3 and is evidenced
by the error variance for the gravity model being less than that for the radiation model for trips to the most pop-
ulous 25% of destinations for each country for 10 out of 16 survey sites. is dierence in error variance is statis-
tically signicant for trips from Mopti and Barouéli in Mali (F-test, p-values = 0.00017 and <105, respectively),
and Kitwe and Nakonde in Zambia (F-test, p-values = 0.019 and 9.3 × 105, respectively).
Based on the results of the countrywide analysis, we tted the gravity model with a power on the destination
population size and radiation model B to the country data sets stratied by traveler group: (i) women traveling
with children for each and all counties, and (ii) youth workers for Mali (Table3). As previously illustrated in
these data10, the “women with children” traveler group reported shorter distance trips for all survey countries.
For the gravity model in this case, we found that the power, τ, of the destination population is smaller for the
“women with children” cluster and larger for the “youth worker” cluster (Tables1 and 3). is could indicate a
Figure 1. Empirical and model-predicted travel frequencies for each survey country. Model predictions are for
the gravity model with the destination population size raised to a power, τ, and radiation model B tted to data
for each country individually. Each dot represents a commune or ward, the radius of which is a monotonically
increasing function of its population size. Each line represents travel frequency between communes/wards, the
width of which is proportional to travel frequency. Maps were generated using Mathematica version 11 (https://
www.wolfram.com/mathematica/) with political boundaries obtained from Wolfram’s Data Repository (https://
datarepository.wolframcloud.com/). e survey was conducted at 3–5 sites in each country, and trips are color-
coded according to the survey location. In Mali (panels a–c), purple trips originate in Bamako, the capital city
and largest urban center, green trips originate in the shing village of Baya, blue trips originate in the farming
villages of Barouéli and Boidié, and red trips originate in Mopti and Fatoma, a commercial center and village
respectively. In Burkina Faso (panels d–f), red trips originate in Ouagadougou, the capital and largest city, blue
trips originate in Sapone, an agricultural village, and green trips originate in Boussé, a local center of agriculture
and trade. In Zambia (panels g–i), blue trips originate in Lusaka, the capital and largest city, green trips originate
in Samfya, a central shing town, red trips originate in Kitwe, an urban trading town in the Copperbelt, yellow
trips originate in Nakonde, a town in the north-east bordering Tanzania, and purple trips originate in Chipata,
a rural town in the east bordering Malawi. In Tanzania (panels j–l), green trips originate in Dar es Salaam, the
capital and largest city, red trips originate in Ifakara, a small rural town on the edge of the Kilombero valley,
purple trips originate in Muheza, a small rural town near the border with Kenya, and blue trips originate in
Mtwara, an agricultural town with a growing mining industry near the border with Mozambique.
Content courtesy of Springer Nature, terms of use apply. Rights reserved
www.nature.com/scientificreports/
6
SCIENTIFIC REPORts | (2018) 8:7713 | DOI:10.1038/s41598-018-26023-1
smaller “gravitational pull” of large population centers for the “women with children” traveler group and a larger
“gravitational pull” for the youth worker traveler group. is is particularly apparent for the “women with chil-
dren” cluster in the Tanzania data set, for which travel frequencies to the capital and largest city, Dar es Salaam,
are signicantly smaller from Ifakara (0.12, 95% condence interval (CI): 0.06–0.23 for women with children c.f.
0.33, 95% CI 0.28–0.39 for other travelers), Mtwara (0.14, 95% CI: 0.08–0.24 for women with children c.f. 0.30,
95% CI 0.24–0.37 for other travelers) and Muheza (0.05, 95% CI: 0.02–0.12 for women with children c.f. 0.28, 95%
CI 0.22–0.34 for other travelers) (Fig.2 and Supplementary Figure2). For the radiation model applied to traveler
groups, we found that the parameter, v, is smaller for the “women with children” cluster and larger for the “youth
worker” cluster for all country data sets (Tables1 and 3). is could indicate higher “absorption” of nearby popu-
lations for the “women with children” traveler group and smaller “absorption” of nearby populations for the youth
worker traveler group. Both the gravity and radiation models provide similar overall trends for traveler groups as
seen for all trips, as indicated by the distance frequency plots for both clusters (Supplementary Figures2 and 4)
and all trips (Figs2 and 3). However, larger uctuations are seen around model predictions for traveler groups,
reected in the corresponding plots of relative predictive error (Figs4 and 5, Supplementary Figures3 and 5), as
a consequence of the smaller sample sizes in partitioned data.
Figure 2. Empirical and model-predicted distance distributions for gravity model tted to individual countries.
Predicted travel frequencies are from the gravity model with the destination population size raised to a power,
τ, and parameter values in Table1. Distance distributions are shown for trips beginning at survey sites in Mali
(panels A–D), Burkina Faso (panels E–G), Zambia (panels H–L) and Tanzania (panels M–P).
Content courtesy of Springer Nature, terms of use apply. Rights reserved
www.nature.com/scientificreports/
7
SCIENTIFIC REPORts | (2018) 8:7713 | DOI:10.1038/s41598-018-26023-1
e gravity and radiation models tted to all trips in all countries simultaneously provide a reasonable t,
despite representing a compromise between the patterns observed in each country (Supplementary Figures6 and
7 for the gravity model and Supplementary Figures8 and 9 for the radiation model). For the gravity model, the
all-country t predictions for Mali are very similar to the Mali-only predictions (Figs2 and 3), as expected given
the similarity of parameter estimates (Table1). For Burkina Faso, the all-country predictions further underesti-
mate travel from Ouagadougou to large population centers and slightly underestimate travel from Sapone and
Bousse to Ouagadougou due to a reduced τ parameter; however, the t is generally comparable (Fig.2). For
Zambia and Tanzania, the increased τ parameter from the all-country t results in a higher travel frequency to
large, distant populations and a smaller travel frequency to small, nearby populations. is results in a slightly
better t in some cases (e.g. error variance within the vicinity of Dar es Salaam is slightly reduced and trip fre-
quency from Kitwe to Lusaka is closer to the observed value) and a slightly worse t in others (e.g. error variance
within the vicinity of Lusaka is slightly increased). For the radiation model, the all-country t predictions for Mali
and Burkina Faso are very similar to the Mali-only and Burkina Faso-only predictions (Figs4 and 5), as expected
given the similarity of parameter estimates (Table1). For Zambia, the increased v parameter from the all-country
t results in slightly less travel to nearby populations, and for Tanzania, the decreased v parameter from the
all-country t results in slightly more travel to nearby populations.
Discussion
We tted human movement models to trip data from a survey conducted in Mali, Burkina Faso, Zambia and
Tanzania10. Two benets of these data were that: (i) only overnight trips were recorded – i.e. trips of relevance
to malaria transmission – and (ii) demographic and trip details were recorded, allowing trips to be categorized
according to traveler group – namely, women traveling with children in all survey countries and youth workers in
Mali. Two models were compared in terms of their ability to predict the observed movement patterns: (i) a gravity
model, in which movement rates between pairs of locations increase with population size and decrease with the
distance14, and (ii) a radiation model, in which travelers are cumulatively “absorbed” as they move outwards from
their origin of travel15. e gravity model provided the best t to the data overall, as measured by the likelihood of
the data under each model; however, neither model was uniformly superior in its predictive ability. In general, the
gravity model provided a better t for travel to large populations, while the radiation model provided a better t
for nearby populations. Signicantly dierent model parameters were obtained for two traveler groups compared
to the population as a whole, with youth workers being more attracted to large population centers, and women
traveling with children being less attracted (Table3).
A number of approaches could be explored to improve the quality of the model t to our data. For instance,
since we are interested in overnight trips, and these may be less frequent to nearby locations as travelers are able
to sleep at home, then we could consider down-weighting the distance kernel of the gravity model for shorter
distances to compensate for this. e down-weighting could also be specic to the origin, since limited travel
was observed within the vicinity of Bamako in Mali and Lusaka in Zambia; but signicant travel was observed
within the vicinity of Mopti in Mali and Nakonde in Zambia. It is dicult to generalize to the continent since
our survey only covers four countries; however, at least for these four countries, down-weighting the distance
kernel for short travel distances seems appropriate at least for capital cities. Another potential approach, given
the impressive t of the radiation model for nearby locations, would be to apply a gravity-radiation-hybrid model
for movement prediction, in which the radiation model is applied for trips up to a certain radius and the gravity
model is applied beyond this radius, with the critical radius being a free parameter to be determined through the
model tting process.
Trip origin and destination: No. observed trips to capital
city/total no. observed trips: Observed trip
frequency (95% CI): Expected trip frequency
(gravity model): Expected trip frequency
(radiation model):
Mopti & Fatoma – Bamako 32/131 0.24 (0.18–0.32) 0.140 0.042
Baya – Bamako 187/400 0.47 (0.42–0.52) 0.495 0.283
Barouéli & Boidié – Bamako 183/380 0.48 (0.43–0.53) 0.369 0.170
Sapone – Ouagadougou 157/272 0.58 (0.52–0.63) 0.675 0.429
Bousse – Ouagadougou 240/467 0.51 (0.47–0.56) 0.578 0.362
Kitwe – Lusaka 44/286 0.15 (0.12–0.20) 0.040 0.040
Nakonde – Lusaka 32/205 0.16 (0.11–0.21) 0.034 0.014
Chipata – Lusaka 46/246 0.19 (0.14–0.24) 0.039 0.022
Samfya – Lusaka 13/217 0.060 (0.035–0.100) 0.048 0.014
Ifakara – Dar es Salaam 96/320 0.30 (0.25–0.35) 0.105 0.100
Mtwara – Dar es Salaam 69/270 0.26 (0.21–0.31) 0.130 0.234
Muheza – Dar es Salaam 59/283 0.21 (0.17–0.26) 0.188 0.238
Table 2. Observed versus predicted trip frequencies to capital cities for each survey country. Here, observed
trip frequencies are the number of observed trips to the capital city divided by the total number of observed
trips. Expected trip frequencies are the equivalent quantity predicted by radiation model B and the gravity
model with the destination population size raised to a power, τ, as parameterized in Table1. 95% condence
intervals for observed trips assume a binomial distribution.
Content courtesy of Springer Nature, terms of use apply. Rights reserved
www.nature.com/scientificreports/
8
SCIENTIFIC REPORts | (2018) 8:7713 | DOI:10.1038/s41598-018-26023-1
Two other issues that could be further explored, both mentioned by Wesolowski et al.20 include: (i) the “gravi-
tational pull” of the mega-city, and (ii) the use of alternative distance metrics. Capital cities in many African coun-
tries represent unique sources of work, trade, healthcare and resources that may not be available elsewhere2,22.
Furthermore, as a growing number of people migrate to these urban centers, subsequent family-related travel also
increases31. e gravity model, with travel frequency being proportional to the destination population size raised
to a variable power, is particularly well suited to accommodating the exceptional pull of African mega-cities;
however, a consistently good t is dicult if not impossible to obtain as the gravity model over-predicts travel
to the capital city in some cases and under-predicts in others. Interestingly, travel to the capital city is generally
well predicted by the gravity model applied to Mali and Burkina Faso; but is under-predicted by the same model
applied to multiple survey sites in Zambia and Tanzania. Up-scaling of travel to the capital city could be consid-
ered in these cases; but the generalizability of this up-scaling factor is unclear.
Secondly, a major factor in determining travel frequency in Africa is road quality, availability of public transport
and travel cost. ese aspects of accessibility would potentially be better accommodated using road distance, travel
cost or travel time in the place of Euclidean distance as a distance metric. Despite this, Wesolowski et al.20 found
that Euclidean distance provided the most accurate prediction of travel frequency on a wide scale; however, this
Figure 3. Empirical and model-predicted distance distributions for radiation model tted to individual
countries. Predicted travel frequencies are from radiation model B and parameter values in Table1. Distance
distributions are shown for trips beginning at survey sites in Mali (panels A–D), Burkina Faso (panels E–G),
Zambia (panels H–L) and Tanzania (panels M–P).
Content courtesy of Springer Nature, terms of use apply. Rights reserved
www.nature.com/scientificreports/
9
SCIENTIFIC REPORts | (2018) 8:7713 | DOI:10.1038/s41598-018-26023-1
may have been due to the limited quality of road distance, travel cost and travel time data, or factors not accounted
for, such as road quality. at said; road distance provided a better model t for travel within rural areas20.
A strength of this analysis, by virtue of the data set, is that it allowed the quantication of movement patterns
of key traveler groups – women traveling with children and youth workers. Children that women travel with are
more likely to display clinical malaria incidence in high prevalence settings21, and qualitative research suggests
that youth workers tend to travel for agricultural labor during the rainy season when malaria is most prevalent
in the Sahel32,33. Further work could involve the determination of key drivers of individual travel, for instance,
dependence of travel frequency on gender, age, socio-economic status and geographical covariates34. is may
allow travel patterns to be more accurately extrapolated to other origins on the basis of their demography, with
relevance to malaria transmission being determined based on a breakdown of malaria prevalence by age, sex and
other characteristics. is is an important consideration for determining sources and sinks of malaria transmis-
sion. Further work could also explore the impact of changes in each country since these surveys were conducted.
Population growth has been consistently occurring in all countries, alongside urbanization and road develop-
ment, and in Mali there has been signicant political instability and armed conict, especially in the north of the
country, since the surveys were nished there in March 2011.
Several weaknesses of the data set should be acknowledged. For instance, the survey sites were a judgment/
convenience sample designed to capture a wide range of movement patterns, while taking advantage of existing
relationships of local researchers with these communities. Since these sites were not chosen randomly, models
Figure 4. Relative prediction error for gravity model tted to individual countries. Relative prediction error
(absolute value of the dierence between empirical and predicted travel frequency divided by the predicted
travel frequency) versus destination population size and trip distance for trips beginning at survey sites in
Mali (panels A–D), Burkina Faso (panels E–G), Zambia (panels H–L) and Tanzania (panels M–P). Predicted
travel frequencies are from the gravity model tted to individual countries with the destination population size
raised to a power, τ, and parameter values in Table1. Grid cells represent the average scaled model error for
destinations falling within the corresponding range of destination population sizes and trip distances.
Content courtesy of Springer Nature, terms of use apply. Rights reserved
www.nature.com/scientificreports/
10
SCIENTIFIC REPORts | (2018) 8:7713 | DOI:10.1038/s41598-018-26023-1
tted to these data are representative of the collection of study sites surveyed rather than of each country as a
whole. While the tted models may serve as proxies for each country, the selection of 3–5 survey sites by judg-
ment/convenience will lead to biases in model parameter estimates and likelihood measures. For instance, in
Tanzania, most of the survey sites were relatively urban, which could lead to a model and parameter values being
Figure 5. Relative prediction error for radiation model tted to individual countries. Relative prediction error
versus destination population size and trip distance for trips beginning at survey sites in Mali (panels A–D),
Burkina Faso (panels E–G), Zambia (panels H–L) and Tanzania (panels M–P). Predicted travel frequencies are
from radiation model B tted to individual countries with parameter values in Table1. Grid cells represent the
average scaled model error for destinations falling within the corresponding range of destination population
sizes and trip distances.
Model: Parameters: Mali (W&C): Mali (YW): Burkina Faso
(W&C): Zambia (W&C): Tanzania
(W&C): All countries
(W&C):
Gravity model with τ
α1.76 (1.33–2.55) 23.6 (2.8–70.6) 1.72 (1.54–2.07) 1.86 (1.60–2.19) 2.32 (1.89–2.92) 2.01 (1.83–2.23)
log(ρ)3.97 (3.05–4.87) 8.90 (6.46–9.96) 1.03 (0.05–2.75) 3.40 (2.85–3.92) 4.22 (3.59–4.85) 3.68 (3.37–4.00)
τ1.20 (1.14–1.26) 1.26 (1.21–1.31) 1.21 (1.14–1.28) 0.76 (0.62–0.90) 0.59 (0.40–0.77) 1.12 (1.08–1.16)
DIC 2,472 4,390 2,496 4,010 3,591 12,679
Radiation model B v1.95
(1.52–2.52) × 1064.99
(3.99–6.30) × 1061.13
(0.88–1.45) × 1063.55
(2.76–4.50) × 1057.66
(5.84–9.99) × 1058.56
(7.52–9.74) × 105
DIC 2,518 4,486 2,508 4,027 3,618 12,758
Table 3. Gravity model parameters (with 95% credible intervals) for models tted to origin-destination pairs
stratied by traveler group (W&C: women traveling with children; YW: youth workers) in all survey countries.
Content courtesy of Springer Nature, terms of use apply. Rights reserved
www.nature.com/scientificreports/
11
SCIENTIFIC REPORts | (2018) 8:7713 | DOI:10.1038/s41598-018-26023-1
favored that apply well for travel originating from larger population centers. In Burkina Faso, the survey sites were
in or within the vicinity of the capital city, Ouagadougou, which could have favored a model and parameter values
that accommodate capital city eects. In Zambia, several of the survey sites were border towns, and in Mali, the
survey sites were relatively rural, aside from those in Bamako and Mopti, the urban-rural balance of which could
have inuenced the favored model and parameter estimates.
Additional biases could result from the nature of the survey. For instance, in the questionnaire, respondents
were asked about their three most recent short-term and long-term trips (up to six in total). is could introduce
a bias towards trips in the months preceding the interviews in two ways – recall bias, since recent trips may be
easier to remember, and “trip clipping” since, for people who have taken many trips, only the recent ones will
be recorded. Discrepancies for travel within the vicinity of a survey site may also have been introduced as travel
within the commune/ward/city of origin was not considered travel in the survey, and there may have been some
ambiguity over what constituted the commune/ward/city of origin. Furthermore, this travel criteria led to exclu-
sion of short scale movements, the scale of exclusion for which varied depending on commune/ward/city size. A
potential selection bias against frequent travelers may also have been present, as these travelers may have been
traveling at the time of the survey. at said; there are biases in other data sources that survey data can help to
elucidate – e.g. cell phone ownership and usage patterns that lead to biases in anonymous cell phone signal data12.
Ultimately, a research agenda is needed that synergizes the strengths of multiple complementary data sets, eluci-
dating each others’ biases and obtaining an accurate picture of human movement patterns2.
Both models captured most mobility trends qualitatively well; the gravity model provided the best t to the
data overall (Table1), but neither the gravity nor radiation model was uniformly superior in its predictive ability.
e gravity model tended to provide a better t for travel to large populations (Figs2 and 4), while the radiation
model tended to provide a better t for nearby populations (Figs3 and 5). Similar trends were seen for the grav-
ity model for women traveling with children and youth workers (Supplementary Figures2 and 3), with youth
workers being more attracted to large population centers, and women traveling with children being less attracted
(Table3). Future work could address modifying gravity and radiation models to achieve a more nuanced descrip-
tion of travel to nearby locations and mega-cities, and the drivers of individual travel, such as age, gender and
socio-economic status. ese spatial coupling models could then be linked to detailed transmission models of
malaria and other diseases, to understand the role that human movement plays in their dynamics, and to better
inform strategies to control their spread.
References
1. Wesolowsi, A. et al. Quantifying the impact of human mobility on malaria. Science 338, 267–270 (2012).
2. Marshall, J. M., Bennett, A., iware, S. S. & Sturroc, H. J. W. e hitchhiing parasite: Why human movement matters to malaria
transmission and what we can do about it. Trends Parasitol. 32, 752–755 (2016).
3. Fauci, A. S. & Morens, D. M. Zia virus in the Americas: Yet another arbovirus threat. N. Engl. J. Med. 374, 601–604 (2016).
4. World Health Organization. World Malaria eport 2016 (WHO Press, Geneva, Switzerland 2016).
5. Waler, P. G. T., Grin, J. T., Ferguson, N. M. & Ghani, A. C. Estimating the most ecient allocation of interventions to achieve
reductions in Plasmodium falciparum malaria burden and transmission in Africa: A modelling study. Lancet. Global Health 4,
e474–e484 (2016).
6. Bhatt, S. et al. e eect of malaria control on Plasmodium falciparum in Af rica between 2000 and 2015. Nature 526, 207–211 (2015).
7. Bousema, T. et al. Hitting hotspots: Spatial targeting of malaria for control and elimination. PLoS Med. 9, e1001165 (2012).
8. Sturroc, H. J. W., oberts, . W., Wegbreit, J., Ohrt, C. & Gosling, . D. Tacling imported malaria: An elimination endgame. Am.
J. Trop. Med. Hyg. 93, 139–144 (2015).
9. Pindolia, D. . et al. Human movement data for malaria control and elimination strategic planning. Mal ar. J. 11, 205 (2012).
10. Marshall, J. M. et al. ey traveler groups of relevance to spatial malaria transmission: A survey of movement patterns in four sub-
Saharan African countries. Mal ar. J. 15, 200 (2016).
11. utanonchai, N. W. et al. Identifying malaria transmission foci for elimination using human mobility data. PLoS Comput. Biol. 12,
e1004846 (2016).
12. Wesolowsi, A., Eagle, N., Noor, A. M., Snow, . W. & Bucee, C. O. e impact of biases in mobile phone ownership on estimates
of human mobility. J. oy. Soc. Interface 10, 20120986 (2013).
13. Murray, G. D. & Cli, A. D. A stochastic model for measles epidemics in a multi-region setting. Institute of British Geographers 2,
158–174 (1975).
14. Xia, Y., Bjornstad, O. N. & Grenfell, B. T. Measles metapopulation dynamics: a gravity model for epidemiological coupling and
dynamics. Am. Nat. 164, 267–281 (2004).
15. Simini, F., Gonzalez, M. C., Maritan, A. & Barabasi, A. L. A universal model for mobility and migration patterns. Nature 484, 96–100
(2012).
16. Truscott, J. & Ferguson, N. M. Evaluating the adequacy of gravity models as a description of human mobility for epidemic modeling.
PLoS Comput. Biol. 8, e1002699 (2012).
17. Tizzoni, M. et al. On the use of human mobility proxies for modeling epidemics. PLoS Comput. Biol. 10, e1003716 (2014).
18. Masucci, A. P., Serras, J., Johansson, A. & Batty, M. Gravity versus radiation models: On the importance of scale and heterogeneity
in commuting ows. Phys. ev. E 88, 022812 (2013).
19. ang, C., Liu, Y., Diansheng, G. & Qin, . A generalized radiation model for human mobility: Spatial scale, searching direction and
trip constraint. PLoS ONE 10, e0143500 (2015).
20. Wesolowsi, A., O’Meara, W. P., Eagle, N., Tatem, A. J. & Bucee, C. O. Evaluating spatial interaction models for regional mobility in
sub-Saharan Africa. PLoS Comput. Biol. 11, e1004267 (2015).
21. Grin, J. T., Ferguson, N. M. & Ghani, A. C. Estimates of the changing age-burden of Plasmodium falciparum malaria disease in
sub-Saharan Africa. Nature Commun. 5, 3136 (2014).
22. Dougnon, I. Migratory trends among two Malian ethnic groups, the Songhai and the Dogon, migrating to Ghana: A comparative
study (University of Bamao, Bamao, Mali, 2010).
23. Linard, C., Gilbert, M., Snow, . W., Noor, A. M. & Tatem, A. J. Population distribution, settlement patterns and accessibility across
Africa in 2010. PLoS ONE 7, e31743 (2012).
24. Central Statistics Oce. Zambia2010 Census of Population and Housing: Population Summary eport (Central Statistics Oce,
Lusaa, Zambia, 2012).
25. National Bureau of Statistics. Tanzania 2012 Population and Housing Census: Population Distribution by Administrative Areas
(Ministry of Finance, Dar es Salaam, Tanzania, 2013).
Content courtesy of Springer Nature, terms of use apply. Rights reserved
www.nature.com/scientificreports/
12
SCIENTIFIC REPORts | (2018) 8:7713 | DOI:10.1038/s41598-018-26023-1
26. Measure DHS Mali Demographic and Health Survey (Macro International, Calverton, Maryland, 2006).
27. Measure DHS Zambia Demographic and Health Survey (Macro International, Calverton, Maryland, 2007).
28. Measure DHS Burina Faso Demographic and Health Survey (Macro International, Calverton, Maryland, 2010).
29. Measure DHS Tanzania Demographic and Health Survey (Macro International, Calverton, Maryland, 2010).
30. Spiegelhalter, D. J., Best, N. G., Carlin, B. P. & van der Linde, A. Bayesian measures of model complexity and t (with discussion). J.
oy. Stat. Soc. Ser. B 64, 583–639 (2002).
31. De Silva, P. M. & Marshall, J. M. Factors contributing to urban malaria transmission in sub-Saharan Africa: A systematic review. J.
Trop. Med. 2012, 819563 (2012).
32. Saxena, V. . & Devadethan, M. A. Impact of the seasonal migration of labour forces on the spread of malaria. Ann. Trop. Med.
Parasitol. 92, 821–822 (1998).
33. Prothero, . M. Migration and malaria ris. Health is & Society 3, 19–38 (2001).
34. Henry, S., Boyle, P. & Lambin, E. F. Modeling inter-provincial migration in Burina Faso, WestAfrica: e role of socio-demographic
and environmental factors. App. Geo. 23, 115–136 (2002).
Acknowledgements
e authors would also like to thank the survey teams in each of the four countries surveyed – Dr. Nina Madjako
Soumahoro-Toure, Dr. Moctar Kardigue Coulibaly, Dr. Kadiatou Kone, Dr. Mohamed Serge Toure, Siaka Traore
and Gaoussou Sogoba in Mali; Apollinaire Nombre, Malik Lankoande, Kadija Ouedraogo, Lassena Kabore,
Moussa Rabo, Marcel Ouedraogo, Houd Kanazoe and Anassa iombiano in Burkina Faso; Maureen Mwambazi,
Audrey Mulungushi, Joseph Daka, Gabriel Karumia, Samuel Daka and Kanyatta Kanyatta in Zambia; and
Sambo Maganga, Daud Mbwana, Patrick Nshana, John Lyatuu, Happyness Kasomangala and Jane Masamu in
Tanzania. We additionally thank Dr. David Aanensen, Dr. Derek Huntley and Chris Powell for assistance with the
EpiCollect 2.0interface, and Dr. Chris Drakeley and Dr. Teun Bousema for input on survey design. is research
was funded by the UK MRC, the Bill and Melinda Gates Foundation and the NIGMS MIDAS initiative. e
funders had no role in the study design, collection, analysis and interpretation of data, in writing the report, or in
the decision to submit the article for publication.
Author Contributions
A.C.G., N.M.F. and J.M.M. conceived and designed the experiments. J.M.M. performed the experiments. J.M.M.,
S.L.W., H.S.C. and H.J.S. analyzed the data. J.M.M., S.S.K., M.N., A.L.O. and M.B.T. conducted the surveys.
J.M.M. wrote the rst dra of the article. All authors edited and contributed to the article and have approved the
nal article.
Additional Information
Supplementary information accompanies this paper at https://doi.org/10.1038/s41598-018-26023-1.
Competing Interests: e authors declare no competing interests.
Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and
institutional aliations.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International
License, which permits use, sharing, adaptation, distribution and reproduction in any medium or
format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Cre-
ative Commons license, and indicate if changes were made. e images or other third party material in this
article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the
material. If material is not included in the article’s Creative Commons license and your intended use is not per-
mitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the
copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
© e Author(s) 2018
Content courtesy of Springer Nature, terms of use apply. Rights reserved
1.
2.
3.
4.
5.
6.
Terms and Conditions
Springer Nature journal content, brought to you courtesy of Springer Nature Customer Service Center GmbH (“Springer Nature”).
Springer Nature supports a reasonable amount of sharing of research papers by authors, subscribers and authorised users (“Users”), for small-
scale personal, non-commercial use provided that all copyright, trade and service marks and other proprietary notices are maintained. By
accessing, sharing, receiving or otherwise using the Springer Nature journal content you agree to these terms of use (“Terms”). For these
purposes, Springer Nature considers academic use (by researchers and students) to be non-commercial.
These Terms are supplementary and will apply in addition to any applicable website terms and conditions, a relevant site licence or a personal
subscription. These Terms will prevail over any conflict or ambiguity with regards to the relevant terms, a site licence or a personal subscription
(to the extent of the conflict or ambiguity only). For Creative Commons-licensed articles, the terms of the Creative Commons license used will
apply.
We collect and use personal data to provide access to the Springer Nature journal content. We may also use these personal data internally within
ResearchGate and Springer Nature and as agreed share it, in an anonymised way, for purposes of tracking, analysis and reporting. We will not
otherwise disclose your personal data outside the ResearchGate or the Springer Nature group of companies unless we have your permission as
detailed in the Privacy Policy.
While Users may use the Springer Nature journal content for small scale, personal non-commercial use, it is important to note that Users may
not:
use such content for the purpose of providing other users with access on a regular or large scale basis or as a means to circumvent access
control;
use such content where to do so would be considered a criminal or statutory offence in any jurisdiction, or gives rise to civil liability, or is
otherwise unlawful;
falsely or misleadingly imply or suggest endorsement, approval , sponsorship, or association unless explicitly agreed to by Springer Nature in
writing;
use bots or other automated methods to access the content or redirect messages
override any security feature or exclusionary protocol; or
share the content in order to create substitute for Springer Nature products or services or a systematic database of Springer Nature journal
content.
In line with the restriction against commercial use, Springer Nature does not permit the creation of a product or service that creates revenue,
royalties, rent or income from our content or its inclusion as part of a paid for service or for other commercial gain. Springer Nature journal
content cannot be used for inter-library loans and librarians may not upload Springer Nature journal content on a large scale into their, or any
other, institutional repository.
These terms of use are reviewed regularly and may be amended at any time. Springer Nature is not obligated to publish any information or
content on this website and may remove it or features or functionality at our sole discretion, at any time with or without notice. Springer Nature
may revoke this licence to you at any time and remove access to any copies of the Springer Nature journal content which have been saved.
To the fullest extent permitted by law, Springer Nature makes no warranties, representations or guarantees to Users, either express or implied
with respect to the Springer nature journal content and all parties disclaim and waive any implied warranties or warranties imposed by law,
including merchantability or fitness for any particular purpose.
Please note that these rights do not automatically extend to content, data or other material published by Springer Nature that may be licensed
from third parties.
If you would like to use or distribute our Springer Nature journal content to a wider audience or on a regular basis or in any other manner not
expressly permitted by these Terms, please contact Springer Nature at
onlineservice@springernature.com
... ; Out of 54 countries, we found only 17 with subnational mobility data. These were informed by census (n = 14 countries), mobile phone records (CDR, n = 5, Côte d'Ivoire, Kenya, Namibia, Sierra Leone, and Senegal), social media records (n = 1) [49] or dedicated surveys (n = 5) [50,51]. Censuses include surveys designed to measure changes in socio-demographic trends (such as internal migration) in a country, e.g. ...
... geolocated tweets) were derived at a high spatial resolution (ADM3 in South Africa) [49]. Dedicated surveys collected mobility data relevant to the spread of a specific disease in a specific location [50,51]. ...
... Typically, mobility proxies quantified movement information as absolute flows over a specified time window (i.e. the number of people moving between a source and destination) [4, 64-66, 68, 69, 72], or relative flows (i.e. probability of moving from a source to a given destination, conditional on moving out of the source) [51,57,60,63]. Some studies focusing on disease spread also characterised directly the probability of transmission of a pathogen between locations in a given time unit [71, 8 . ...
Preprint
Full-text available
Reliable estimates of human mobility are important for understanding the spatial spread of infectious diseases and the effective targeting of control measures. However, when modelling infectious disease dynamics, data on human mobility at an appropriate temporal or spatial resolution are not always available, leading to the common use of model-derived mobility proxies. In this study we reviewed the different data sources and mobility models that have been used to characterise human movement in Africa. We then conducted a simulation study to better understand the implications of using human mobility proxies when predicting the spatial spread and dynamics of infectious diseases. We found major gaps in the availability of empirical measures of human mobility in Africa, leading to mobility proxies being used in place of data. Empirical data on subnational mobility were only available for 17/54 countries, and, in most instances, these data characterised long-term movement patterns, which were unsuitable for modelling the spread of pathogens with short generation times (time between infection of a case and their infector). Results from our simulation study demonstrated that using mobility proxies can have a substantial impact on the predicted epidemic dynamics, with complex and non-intuitive biases. In particular, the predicted times and order of epidemic invasion, and the time of epidemic peak in different locations can be underestimated or overestimated, depending on the types of proxies used and the country of interest. Our work underscores the need for regularly updated empirical measures of population movement within and between countries to aid the prevention and control of infectious disease outbreaks. At the same time, there is a need to establish an evidence base to help understand which types of mobility data are most appropriate for describing the spread of emerging infectious diseases in different settings.
... The model was parametrized to fit the annual mean Malaria Atlas Project PfPR 2-10 projections for Burkina Faso in 2017 on a 5km-by-5km cell (or pixel) basis with a total of 10,936 pixels modeled (approximately 273,400 sq.km) [11]. Individual movement was fit to available travel survey data for both the destination and frequency of travel ( Fig 1D) [16][17][18]. In the individual-based model, individuals have attributes relevant to the spread and individual response to a P. falciparum infection, such as age, attractiveness to mosquitos, number of parasite infections, genotypes of infecting parasites, level of parasitemia, level of immunity, and current drug concentrations during and after treatment. ...
... The predicted population-weighted annual mean PfPR 2-10 values for each cell were then aggregated to the province level for comparison to the Malaria Atlas Project values ( Fig 1A). Individual movement was added into the model by using a modified gravity model [18] that was re-fit from data presented in Marshall et al. [16,17]. Pixel-level and province-level PfPR 2-10 values were evaluated to ensure that movement did not have too large of an overall effect on PfPR 2-10 trends. ...
Article
Full-text available
Artemisinin combination therapies (ACTs) are the WHO-recommended first-line therapies for uncomplicated Plasmodium falciparum malaria. The emergence and spread of artemisi-nin-resistant genotypes is a major global public health concern due to the increased rate of treatment failures that result. This is particularly germane for WHO designated 'high burden to high impact' (HBHI) countries, such as Burkina Faso, where there is increased emphasis on improving guidance, strategy, and coordination of local malaria response in an effort to reduce the prevalence of P. falciparum malaria. To explore how the increased adoption of ACTs may affect the HBHI malaria setting of Burkina Faso, we added spatial structure to a validated individual-based stochastic model of P. falciparum transmission and evaluated the long-term effects of increased ACT use. We explored how de novo emergence of artemisi-nin-resistant genotypes, such as pfkelch13 580Y, may occur under scenarios in which private market drugs are eliminated or multiple first-line therapies (MFT) are deployed. We found that elimination of private market drugs would result in lower treatment failures rates (between 11.98% and 12.90%) when compared to the status quo (13.11%). However, scenarios incorporating MFT with equal deployment of artemether-lumefantrine (AL) and dihy-droartemisinin-piperaquine (DHA-PPQ) may accelerate near-term drug resistance (580Y frequency ranging between 0.62 to 0.84 in model year 2038) and treatment failure rates (26.69% to 34.00% in 2038), due to early failure and substantially reduced treatment efficacy resulting from piperaquine-resistant genotypes. A rebalanced MFT approach (90% AL, 10% DHA-PPQ) results in approximately equal long-term outcomes to using AL alone but may be difficult to implement in practice.
... Several epidemic models have proposed the introduction of regional mobility patterns [3,7,6,16,59,31] for human-to-human infectious diseases [34,5,27] or vector-borne diseases [29,14,2,32]. These can incorporate mobility with an emphasis on a regional scale, which is critical in the increasing number of cases at the beginning of the outbreak [33]. ...
Preprint
Full-text available
Abstract It is often necessary to introduce the main characteristics of population mobility dynamics to model critical social phenomena such as the economy, violence, transmission of information, or infectious diseases. In this work, we focus on modeling and inferring urban population mobility using the geospatial data of its inhabitants. The objective is to estimate mobility and times inhabitants spend in the areas of interest, such as zip codes and census geographical areas. The proposed method uses the Brownian bridge model for animal movement in ecology. We illustrate its possible applications using mobile phone GPS data in 2020 from the city of Hermosillo, Sonora, in Mexico. We incorporate the estimated residence-mobility matrix into a multi-patch compartmental SEIR model to assess the effect of mobility changes due to governmental interventions.
... Previous research has been conducted in Africa on the implications of mobility patterns for transmission of infections other than COVID-19 [21,22] and during the COVID-19 epidemic, analysis of movement patterns in Ghana has been conducted to inform policy makers about the volume of reductions coinciding with lockdown interventions in Accra and Kumasi [23]. These indicators may be used as a proxy for social contact [13] and therefore, for potential COVID-19 transmission, although the "link" between movement and disease transmission may decrease due to greater adherence to social distancing or personal protective equipment guidelines [24]. ...
Article
Full-text available
Governments around the world have implemented non-pharmaceutical interventions to limit the transmission of COVID-19. Here we assess if increasing NPI stringency was associated with a reduction in COVID-19 cases in Ghana. While lockdowns and physical distancing have proven effective for reducing COVID-19 transmission, there is still limited understanding of how NPI measures are reflected in indicators of human mobility. Further, there is a lack of understanding about how findings from high-income settings correspond to low and middle-income contexts. In this study, we assess the relationship between indicators of human mobility, NPIs, and estimates of R t , a real-time measure of the intensity of COVID-19 transmission. We construct a multilevel generalised linear mixed model, combining local disease surveillance data from subnational districts of Ghana with the timing of NPIs and indicators of human mobility from Google and Vodafone Ghana. We observe a relationship between reductions in human mobility and decreases in R t during the early stages of the COVID-19 epidemic in Ghana. We find that the strength of this relationship varies through time, decreasing after the most stringent period of interventions in the early epidemic. Our findings demonstrate how the association of NPI and mobility indicators with COVID-19 transmission may vary through time. Further, we demonstrate the utility of combining local disease surveillance data with large scale human mobility data to augment existing surveillance capacity to monitor the impact of NPI policies.
... Developing rural regions, which are shaped by human activities, also have a great potential to increase the abundance of mosquitoes (Chaves et al. 2021). The reason behind it is sometimes the increased frequency of human movement in the region (Marshall 2018), and it has additionally been reported that socioeconomic changes, lack of proper housing and sanitation, and limited access to health facilities may also intensify the transmission of malaria (Austin et al. 2017). With cases of the Covid pandemic, which is still mutating and very much active throughout the world (Doug et al. 2020), co-infections with mosquito borne diseases such as Dengue are also expected to strain the healthcare systems to near the breaking point in countries such as Brazil (Lorenz et al. 2020). ...
Preprint
Full-text available
Combating vector-borne diseases requires a multidisciplinary approach for best results. Here we undertook field surveys in the potential mosquito breeding habitats in a rapidly urbanizing rural region in West Bengal, India. Secondly, we measured the knowledge about the mosquito vectors from students of a local college and we introduced a multilingual mobile software application “Mosa Nirmul” (EradicationOfMosquitoes) with an AI and game element and measured their perception and future scopes. The seasonal survey about the possible breeding grounds of mosquitoes revealed the presence of the larva of all three common genera of disease carrying mosquitoes Aedes , Culex and Anopheles . The presence was noted in a various types water and garbage sources. Their prevalence was found to be the highest in the post-monsoon season. In the second study, the college students demonstrated reasonably competent knowledge about the basics of protection against mosquitoes, but the score was lower when the questions were about the breeding grounds of mosquitoes. In the third study, the software application was received on the positive side, with a mean score of 3.98/5.. The AI module was also understood by many with about half of them were confident to collect data by themselves for related projects, with a score of mean score of 3.56. The surveys showed that mosquito vectors are still a threat in rural areas. However, with the positive results from the usage of the app, existing baseline knowledge, and willingness to adopt modern technologies, many factors looked promising for the future.
... T ij = exp −9.71866096 + 0.63624388 ln ln (V i ) − 0.12195776 − (−0.1101434) ln d ij (10) where T ij is the modeled number of infections in count j due to interaction with county i, V i is the population of county i, and d ij is the distance between county i and j; for the county itself, the distance taken into account was the radius of a circle of equal area to the county area. The coefficient of determination R2 equaled 0.85, meaning that the developed model explains 85% of the variance of the phenomenon and the actual number of cases. ...
Article
Full-text available
This article describes an original methodology for integrating global SIR-like epidemic models with spatial interaction models, which enables the forecasting of COVID-19 dynamics in Poland through time and space. Mobility level, estimated by the regional population density and distances among inhabitants, was the determining variable in the spatial interaction model. The spatiotemporal diffusion model, which allows the temporal prediction of case counts and the possibility of determining their spatial distribution, made it possible to forecast the dynamics of the COVID-19 pandemic at a regional level in Poland. This model was used to predict incidence in 380 counties in Poland, which represents a much more detailed modeling than NUTS 3 according to the widely used geocoding standard Nomenclature of Territorial Units for Statistics. The research covered the entire territory of Poland in seven weeks of early 2021, just before the start of vaccination in Poland. The results were verified using official epidemiological data collected by sanitary and epidemiological stations. As the conducted analyses show, the application of the approach proposed in the article, integrating epidemiological models with spatial interaction models, especially unconstrained gravity models and destination (attraction) constrained models, leads to obtaining almost 90% of the coefficient of determination, which reflects the quality of the model’s fit with the spatiotemporal distribution of the validation data.
... The diffusion model that was used to represent spatial dispersion of parasites assumed that movement is isotropic in space and did not consider landscape features, such as heterogeneity in human population densities and environmental factors that may affect mosquito ecology. A study analysing self-reported movement patterns in Mali, Burkina Faso, Zambia, and Tanzania found that gravity and radiation models of spatial dispersion fit the data well, although the appropriateness of each model depended on the type of traveller, the travel distance, and the population size of the destination considered [36]. Although a variety of spatial kernels could have been used in the analysis, the conclusions reached are expected to be robust to the choice of spatial kernel, because the spatial kernel used in the likelihood matched that used to simulate the data. ...
Article
Full-text available
Background Inference of person-to-person transmission networks using surveillance data is increasingly used to estimate spatiotemporal patterns of pathogen transmission. Several data types can be used to inform transmission network inferences, yet the sensitivity of those inferences to different data types is not routinely evaluated. Methods The influence of different combinations of spatial, temporal, and travel-history data on transmission network inferences for Plasmodium falciparum malaria were evaluated. Results The information content of these data types may be limited for inferring person-to-person transmission networks and may lead to an overestimate of transmission. Only when outbreaks were temporally focal or travel histories were accurate was the algorithm able to accurately estimate the reproduction number under control, R c . Applying this approach to data from Eswatini indicated that inferences of R c and spatiotemporal patterns therein depend upon the choice of data types and assumptions about travel-history data. Conclusions These results suggest that transmission network inferences made with routine malaria surveillance data should be interpreted with caution.
... We compared the metapopulation model parameterized by the mobile phone calling data with a standard diffusion model (gravity model 14 ) that is often used in the absence of mobility data. Since empirical travel data other than the mobile phone calling data were not available for model fitting, we simply assumed that human movements increased with population sizes of both locations and decreased with the geographic distance between them in the gravity model. ...
Article
Full-text available
Identifying sources and sinks of malaria transmission is critical for designing effective intervention strategies particularly as countries approach elimination. The number of malaria cases in Thailand decreased 90% between 2012 and 2020, yet elimination has remained a major public health challenge with persistent transmission foci and ongoing importation. There are three main hotspots of malaria transmission in Thailand: Ubon Ratchathani and Sisaket in the Northeast; Tak in the West; and Yala in the South. However, the degree to which these hotspots are connected via travel and importation has not been well characterized. Here, we develop a metapopulation model parameterized by mobile phone call detail record data to estimate parasite flow among these regions. We show that parasite connectivity among these regions was limited, and that each of these provinces independently drove the malaria transmission in nearby provinces. Overall, our results suggest that due to the low probability of domestic importation between the transmission hotspots, control and elimination strategies can be considered separately for each region.
... More recently, the radiation model (RM) for human migration 10 was introduced and predicts the average flow of migrants T ij from locality i to locality j as where T i is the total number of migrants from i, p i and p j are the population in i and j, respectively, and s ij is the total population in the circle centered at i and touching j excluding the source and the destination populations. It has been shown that this model and its variations can replicate the observed changes in population across several cities in developed countries 2,10-13 but less so in developing countries 6,14 . ...
Article
Full-text available
One of the main problems in the study of human migration is predicting how many people will migrate from one place to another. An important model used for this problem is the radiation model for human migration, which models locations as attractors whose attractiveness is moderated by distance as well as attractiveness of neighboring locations. In the model, the measure used for attractiveness is population which is a proxy for economic opportunities and jobs. However, this may not be valid, for example, in developing countries, and fails to take into account people migrating for non-economic reasons such as quality of life. Here, we extend the radiation model to include the number of amenities (offices, schools, leisure places, etc.) as features aside from population. We find that the generalized radiation model outperforms the radiation model by as much as 10.3% relative improvement in mean absolute percentage error based on actual census data five years apart. The best performing model does not even include population information which suggests that amenities already include the information that we get from population. The generalized radiation model provides a measure of feature importance thus presenting another avenue for investigating the effect of amenities on human migration.
... Previous research has been conducted in Africa on the implications of mobility patterns for disease transmission 21,22 and during the COVID-19 epidemic, analysis of movement patterns in Ghana has been conducted to inform policy makers about the volume of reductions coinciding with lockdown interventions in Accra and Kumasi 23 . These indicators may be used as a proxy for social contact 13 and therefore, for potential COVID-19 transmission, although the "link" between movement and disease transmission may decrease due to NPI 4 . ...
Preprint
Full-text available
Background: Governments around the world have implemented non-pharmaceutical interventions to limit the transmission of COVID-19. While lockdowns and physical distancing have proven effective for reducing COVID-19 transmission, there is still limited understanding of how NPI measures are reflected in indicators of human mobility. Further, there is a lack of understanding about how findings from high-income settings correspond to low and middle-income contexts. Methods: In this study, we assess the relationship between indicators of human mobility, NPIs, and estimates of R t , a real-time measure of the intensity of COVID-19 transmission. We construct a multilevel generalised linear mixed model, combining local disease surveillance data from subnational districts of Ghana with the timing of NPIs and indicators of human mobility from Google and Vodafone Ghana. Findings: We observe a relationship between reductions in human mobility and decreases in R t during the early stages of the COVID-19 epidemic in Ghana. We find that the strength of this relationship varies through time, decreasing after the most stringent period of interventions in the early epidemic. Interpretation: Our findings demonstrate how the association of NPI and mobility indicators with COVID-19 transmission may vary through time. Further, we demonstrate the utility of combining local disease surveillance data with large scale human mobility data to augment existing surveillance capacity and monitor the impact of NPI policies.
Article
Full-text available
Background: Reducing the burden of malaria is a global priority, but financial constraints mean that available resources must be allocated rationally to maximise their effect. We aimed to develop a model to estimate the most efficient (ie, minimum cost) ordering of interventions to reduce malaria burden and transmission. We also aimed to estimate the efficiency of different spatial scales of implementation. Methods: We combined a dynamic model capturing heterogeneity in malaria transmission across Africa with financial unit cost data for key malaria interventions. We combined estimates of patterns of malaria endemicity, seasonality in rainfall, and mosquito composition to map optimum packages of these interventions across Africa. Using non-linear optimisation methods, we examined how these optimum packages vary when control measures are deployed and assessed at national, subnational first administrative (provincial), or fine-scale (5 km2 pixel) spatial scales. Findings: The most efficient package in a given setting varies depending on whether disease reduction or elimination is the target. Long-lasting insecticide-treated nets are generally the most cost-effective first intervention to achieve either goal, with seasonal malaria chemoprevention or indoor residual spraying added second depending on seasonality and vector species. These interventions are estimated to reduce malaria transmission to less than one case per 1000 people per year in 43·4% (95% CI 40·0–49·0) of the population at risk in Africa. Adding three rounds of mass drug administration per year is estimated to increase this proportion to 90·9% (95% CI 86·9–94·6). Further optimisation can be achieved by targeting policies at the provincial level, achieving an estimated 32·1% (95% CI 29·6–34·5) cost saving relative to adopting country-wide policies. Nevertheless, we predict that only 26 (95% CI 22–29) of 41 countries could reduce transmission to these levels with these approaches. Interpretation: These results highlight the cost–benefits of carefully tailoring malaria interventions to the ecological landscape of different areas. However, novel interventions are necessary if malaria eradication is to be achieved. Funding: Bill & Melinda Gates Foundation, UK Medical Research Council.
Article
Full-text available
Background As malaria prevalence declines in many parts of the world due to widescale control efforts and as drug-resistant parasites begin to emerge, a quantitative understanding of human movement is becoming increasingly relevant to malaria control. However, despite its importance, significant knowledge gaps remain regarding human movement, particularly in sub-Saharan Africa. MethodsA quantitative survey of human movement patterns was conducted in four countries in sub-Saharan Africa: Mali, Burkina Faso, Zambia, and Tanzania, with three to five survey locations chosen in each country. Questions were included on demographic and trip details, malaria risk behaviour, children accompanying travellers, and mobile phone usage to enable phone signal data to be better correlated with movement. A total of 4352 individuals were interviewed and 6411 trips recorded. ResultsA cluster analysis of trips highlighted two distinct traveller groups of relevance to malaria transmission: women travelling with children (in all four countries) and youth workers (in Mali). Women travelling with children were more likely to travel to areas of relatively high malaria prevalence in Mali (OR = 4.46, 95 % CI = 3.42–5.83), Burkina Faso (OR = 1.58, 95 % CI = 1.23–1.58), Zambia (OR = 1.50, 95 % CI = 1.20–1.89), and Tanzania (OR = 2.28, 95 % CI = 1.71–3.05) compared to other travellers. They were also more likely to own bed nets in Burkina Faso (OR = 1.77, 95 % CI = 1.25–2.53) and Zambia (OR = 1.74, 95 % CI = 1.34 2.27), and less likely to own a mobile phone in Mali (OR = 0.50, 95 % CI = 0.39–0.65), Burkina Faso (OR = 0.39, 95 % CI = 0.30–0.52), and Zambia (OR = 0.60, 95 % CI = 0.47–0.76). Malian youth workers were more likely to travel to areas of relatively high malaria prevalence (OR = 23, 95 % CI = 17–31) and for longer durations (mean of 70 days cf 21 days, p < 0.001) compared to other travellers. Conclusions Women travelling with children were a remarkably consistent traveller group across all four countries surveyed. They are expected to contribute greatly towards spatial malaria transmission because the children they travel with tend to have high parasite prevalence. Youth workers were a significant traveller group in Mali and are expected to contribute greatly to spatial malaria transmission because their movements correlate with seasonal rains and hence peak mosquito densities. Interventions aimed at interrupting spatial transmission of parasites should consider these traveller groups.
Article
Full-text available
Humans move frequently and tend to carry parasites among areas with endemic malaria and into areas where local transmission is unsustainable. Human-mediated parasite mobility can thus sustain parasite populations in areas where they would otherwise be absent. Data describing human mobility and malaria epidemiology can help classify landscapes into parasite demographic sources and sinks, ecological concepts that have parallels in malaria control discussions of transmission foci. By linking transmission to parasite flow, it is possible to stratify landscapes for malaria control and elimination, as sources are disproportionately important to the regional persistence of malaria parasites. Here, we identify putative malaria sources and sinks for pre-elimination Namibia using malaria parasite rate (PR) maps and call data records from mobile phones, using a steady-state analysis of a malaria transmission model to infer where infections most likely occurred. We also examined how the landscape of transmission and burden changed from the pre-elimination setting by comparing the location and extent of predicted pre-elimination transmission foci with modeled incidence for 2009. This comparison suggests that while transmission was spatially focal pre-elimination, the spatial distribution of cases changed as burden declined. The changing spatial distribution of burden could be due to importation, with cases focused around importation hotspots, or due to heterogeneous application of elimination effort. While this framework is an important step towards understanding progressive changes in malaria distribution and the role of subnational transmission dynamics in a policy-relevant way, future work should account for international parasite movement, utilize real time surveillance data, and relax the steady state assumption required by the presented model.
Article
Full-text available
We generalized the recently introduced "radiation model", as an analog to the generalization of the classic "gravity model", to consolidate its nature of universality for modeling diverse mobility systems. By imposing the appropriate scaling exponent λ, normalization factor κ and system constraints including searching direction and trip OD constraint, the generalized radiation model accurately captures real human movements in various scenarios and spatial scales, including two different countries and four different cities. Our analytical results also indicated that the generalized radiation model outperformed alternative mobility models in various empirical analyses.
Article
Full-text available
Since the year 2000, a concerted campaign against malaria has led to unprecedented levels of intervention coverage across sub-Saharan Africa. Understanding the effect of this control effort is vital to inform future control planning. However, the effect of malaria interventions across the varied epidemiological settings of Africa remains poorly understood owing to the absence of reliable surveillance data and the simplistic approaches underlying current disease estimates. Here we link a large database of malaria field surveys with detailed reconstructions of changing intervention coverage to directly evaluate trends from 2000 to 2015, and quantify the attributable effect of malaria disease control efforts. We found that Plasmodium falciparum infection prevalence in endemic Africa halved and the incidence of clinical disease fell by 40% between 2000 and 2015. We estimate that interventions have averted 663 (542–753 credible interval) million clinical cases since 2000. Insecticide-treated nets, the most widespread intervention, were by far the largest contributor (68% of cases averted). Although still below target levels, current malaria interventions have substantially reduced malaria disease incidence across the continent. Increasing access to these interventions, and maintaining their effectiveness in the face of insecticide and drug resistance, should form a cornerstone of post-2015 control strategies.
Article
Full-text available
Simple spatial interaction models of human mobility based on physical laws have been used extensively in the social, biological, and physical sciences, and in the study of the human dynamics underlying the spread of disease. Recent analyses of commuting patterns and travel behavior in high-income countries have led to the suggestion that these models are highly generalizable, and as a result, gravity and radiation models have become standard tools for describing population mobility dynamics for infectious disease epidemiology. Communities in Sub-Saharan Africa may not conform to these models, however; physical accessibility, availability of transport, and cost of travel between locations may be variable and severely constrained compared to high-income settings, informal labor movements rather than regular commuting patterns are often the norm, and the rise of mega-cities across the continent has important implications for travel between rural and urban areas. Here, we first review how infectious disease frameworks incorporate human mobility on different spatial scales and use anonymous mobile phone data from nearly 15 million individuals to analyze the spatiotemporal dynamics of the Kenyan population. We find that gravity and radiation models fail in systematic ways to capture human mobility measured by mobile phones; both severely overestimate the spatial spread of travel and perform poorly in rural areas, but each exhibits different characteristic patterns of failure with respect to routes and volumes of travel. Thus, infectious disease frameworks that rely on spatial interaction models are likely to misrepresent population dynamics important for the spread of disease in many African populations.
Article
The failure of the Global Malaria Eradication Program (GMEP) during the 1960s highlighted the relevance of human movement to both re-introducing parasites in elimination settings and spreading drug-resistant parasites widely. Today, given the sophisticated surveillance of human movement patterns and key traveler groups, it is hoped that interventions can be implemented to protect and treat travelers, prevent onward transmission in low transmission settings, and eliminate sources of transmission, including sources of drug-resistant parasites.
Article
The explosive pandemic of Zika virus infection occurring throughout South America, Central America, and the Caribbean (see map) and potentially threatening the United States is the most recent of four unexpected arrivals of important arthropod-borne viral diseases in the Western Hemisphere over the past 20 years. It follows dengue, which entered this hemisphere stealthily over decades and then more aggressively in the 1990s; West Nile virus, which emerged in 1999; and chikungunya, which emerged in 2013. Are the successive migrations of these viruses unrelated, or do they reflect important new patterns of disease emergence? Furthermore, are there secondary health consequences . . .