Predictability of population displacement after the 2010 Haiti earthquake.

Abstract

Most severe disasters cause large population movements. These movements make it difficult for relief organizations to efficiently reach people in need. Understanding and predicting the locations of affected people during disasters is key to effective humanitarian relief operations and to long-term societal reconstruction. We collaborated with the largest mobile phone operator in Haiti (Digicel) and analyzed the movements of 1.9 million mobile phone users during the period from 42 d before, to 341 d after the devastating Haiti earthquake of January 12, 2010. Nineteen days after the earthquake, population movements had caused the population of the capital Port-au-Prince to decrease by an estimated 23%. Both the travel distances and size of people's movement trajectories grew after the earthquake. These findings, in combination with the disorder that was present after the disaster, suggest that people's movements would have become less predictable. Instead, the predictability of people's trajectories remained high and even increased slightly during the three-month period after the earthquake. Moreover, the destinations of people who left the capital during the first three weeks after the earthquake was highly correlated with their mobility patterns during normal times, and specifically with the locations in which people had significant social bonds. For the people who left Port-au-Prince, the duration of their stay outside the city, as well as the time for their return, all followed a skewed, fat-tailed distribution. The findings suggest that population movements during disasters may be significantly more predictable than previously thought.

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Predictability of population displacement
after the 2010 Haiti earthquake
Xin Lua,b,1,2, Linus Bengtssona,1,2, and Petter Holmea,b,c,d
aDepartment of Public Health Sciences, Karolinska Institutet, 17177 Stockholm, Sweden;
Stockholm, Sweden;
Suwon 440-746, Korea
bDepartment of Sociology, Stockholm University, 10691
dDepartment of Energy Science, Sungkyunkwan University,
cDepartment of Physics, Umeå University, 90187 Umeå, Sweden; and
Edited by* H. Eugene Stanley, Boston University, Boston, MA, and approved May 16, 2012 (received for review March 6, 2012)
Most severe disasters cause large population movements. These
movements make it difficult for relief organizations to efficiently
reach people in need. Understanding and predicting the locations
of affected people during disasters is key to effective humanitarian
relief operations and to long-term societal reconstruction. We col-
laborated with the largest mobile phone operator in Haiti (Digicel)
and analyzed the movements of 1.9 million mobile phone users
during the period from 42 d before, to 341 d after the devastating
Haiti earthquake of January 12, 2010. Nineteen days after the
earthquake, population movements had caused the population
of the capital Port-au-Prince to decrease by an estimated 23%. Both
the travel distances and size of people’s movement trajectories
grew after the earthquake. Thesefindings,in combinationwith the
disorder that was present after the disaster, suggest that people’s
movements would have become less predictable. Instead, the
predictability of people’s trajectories remained high and even in-
creased slightly during the three-month period after the earth-
quake. Moreover, the destinations of people who left the capital
during the first three weeks after the earthquake was highly cor-
related with their mobility patterns during normal times, and spe-
cifically with the locations in which people had significant social
bonds. For the people who left Port-au-Prince, the duration of
their stay outside the city, as well as the time for their return, all
followed a skewed, fat-tailed distribution. The findings suggest
that population movements during disasters may be significantly
more predictable than previously thought.
trajectory ∣ human mobility ∣ disaster informatics ∣ disaster relief
I
120 billion worth of damage (1, 2). The humanitarian response to
natural disasters relies critically on data on the geographic distri-
bution of affected people (3). During the early response phase,
data on population distributions are fundamental to the delivery
of water, food, and shelter, and tothe creation of sampling frames
for needs assessment surveys (4). During later stage reconstruc-
tion efforts, population distribution data is required for the allo-
cation of schooling resources, delivery of seeds, construction of
houses, and the like (5, 6).
Despite a number of studies on human mobility patterns dur-
ing small-scale, short-term emergencies such as crowd panics
(7, 8) and fires (9, 10), research on the dynamics of population
mobility during large-scale disasters such as earthquakes, tsuna-
mis, floods, and hurricanes has been limited (11). Existing re-
search on population movements after large-scale disasters has
been hampered by difficulties in collecting representative longi-
tudinal data in places where infrastructure and social order have
collapsed (12, 13), and where study populations are moving
across vast geographical areas (14). Existing research has found
that people displaced by natural disasters typically stay within
their country of residence, that sudden-onset disasters often lead
to more short-term displacement than do slow-onset disasters
(15), and that postdisaster reconstruction programs in the long
n 2010, natural disasters displaced 42 million people, directly
affected an estimated 217 million people, and resulted in USD
run can cause populations to move into disaster-affected areas
rather than moving away from them (11).
The increased use of mobile phones, even in low- and middle-
income countries (16), offers a new way to circumvent methodolo-
gical problems of earlier research. Data from mobile phones have
the advantage of high resolution in time and space, being instan-
taneously available with no interview bias, and they provide long-
itudinal data for very large numbers of persons (12, 17–23). Even
more importantly,cellphone dataallows forstatisticsbasedon tra-
jectoriesofindividuals.Thismeansonecan,aswewillinthispaper,
studyhow thedisasteraffects people’s daily behaviorand routines.
Pioneering work using mobile phone data to describe human
mobility patterns has been carried out during stable social con-
ditions (17–19). One major conclusion from these studies is that,
despite a broad distribution of average travel distances among
people, the movements of individuals are surprisingly predictable
(17). In this paper, we study mobile phone data from Haiti col-
lected before and after the tragic Haiti earthquake on Tuesday,
January 12, 2010, which left an estimated 1.8 million people
homeless and killed between 65,000 and 300,000 persons (24, 25).
We collaborated with the largest mobile phone operator in
Haiti, Digicel, to analyze the positions of 2.9 million anonymous
subscribers during the period from 42 d before the earthquake to
341 d after (December 1, 2009, to December 19, 2010). Specifi-
cally, we obtained the locations of all anonymous Digicel mobile
phone users at the time of their first call each day. To exclude
relief workers entering Haiti after the earthquake and people
who died or whose SIM cards stopped functioning, we excluded
people who did not call at least once before the earthquake and
at least once during the last month of the study period. After
this filtering, we obtained 1.9 million individuals across Haiti
[10 million inhabitants (26)] out of which 0.8 million were located
within Port-au-Prince [2.6 million inhabitants (26)] on the day
of the earthquake. We assume in this paper that the mobile
phone movements were representative of the general population
movements. Although this issue requires additional research, we
showed in a separate paper (13), using the same data source, that
mobile phone movements after the Haiti earthquake corre-
sponded well with comparable movement data from a large retro-
spective household survey of 12,250 persons, performed by
UNFPA eight months after the earthquake. The spatial resolu-
tion of people’s locations is that of the coverage areas of the mo-
bile phone towers in the network (ranging from less than 100 m in
urban areas to a few tens of kilometers in the hinterland).
Author contributions: X.L., L.B., and P.H. designed research; X.L. and L.B. performed
research; X.L. and L.B. analyzed data; and X.L., L.B., and P.H. wrote the paper.
The authors declare no conflict of interest.
*This Direct Submission article had a prearranged editor.
See Commentary on page 11472.
1X.L. and L.B. contributed equally to this work.
2To
linus.bengtsson@ki.se.
whomcorrespondencemaybeaddressed. E-mail:lu.xin@sociology.su.seor
This article contains supporting information online at www.pnas.org/lookup/suppl/
doi:10.1073/pnas.1203882109/-/DCSupplemental.
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In order to understand fundamental changes in mobility pat-
terns after a large-scale disaster, we analyze how the earthquake
changed the aggregate mobility of individuals in the severely hit
capital Port-au-Prince (PaP), to what extent the chaotic condi-
tions after the earthquake influenced the disorder and predict-
ability of the population’s movements, and the dynamics of the
population flows out of and back into PaP. We address both the
larger-scale prediction of population displacements and the pre-
dictability of the trajectories of individuals. Surprisingly, we find
that despite large changes in the population distribution across
the country, the mobility of the PaP population contained several
highly regular features, and most individuals’ movements re-
mained highly predictable.
Results
Daily Travel Distances and Population Flows. To get an overview of
the aggregate travel patterns before and after the earthquake, we
show (Fig. 1B) the observed distribution of travel distances over
the sampling period. One day after the earthquake (January 13,
2010), 6.5% of the observed individuals had traveled more than
20 km as compared to the preceding day, while the corresponding
figure before the earthquake (December 1–2, 2009) was 3.5%.
The increase in average daily travel distances lasted for two to
three weeks after the earthquake. It is worth noting that other
periods also saw sudden increases in average daily travel dis-
tances. These periods coincided with Christmas and New Year
from around December 20 to January 3—just before the earth-
quake—as well as the Easter holidays (early April).
The earthquake did not directly affect large parts of Haiti. In
the rest of our analyses, we therefore focus on the population of
the heavily affected capital region (PaP). As we show in Fig. 1C,
the population movements after the earthquake on January 12,
2010, led to a rapid decrease in the PaP population. Nineteen
days after the earthquake (January 31), the net population de-
crease was an estimated 23% compared to the stable level before
Christmas (December 1–20, 2009), assuming the phone move-
ments to be representative of the population movements. The
net flow into PaPagain became positive 20 d after the earthquake
(February 1), and the PaP population increased approximately
linearly over the following three months (February 1 to April
30). After this time, the population increase gradually leveled
off and stabilized at the end of the year, with two short deviations
around All Saints Day (November 1) and the election day
(November 28).
There was a similar but smaller population decrease in PaP
during the preceding Christmas and New Year (Fig. 1C). As we
saw in Fig. 1B, this was also a period of generally increased travel
in Haiti. A similar but smaller decrease was also seen during
Easter. The population decrease in PaP during holidays is likely
explained by many people leaving the capital to spend time with
family and friends outside PaP. It is interesting to observe that
the PaP population at the time of the earthquake had not yet fully
recovered after the Christmas and New Year holidays. Assuming
that the people who left PaP over the holidays were all going to
return in the absence of the disaster, approximately 70,000 per-
sons (2.5% of the PaP population) managed for this reason to
avoid being in PaP on the day of the earthquake.
There is a strong weekly regularity in the number of mobile
phone users in PaP. Increased numbers of people are present in
PaP during working days, with corresponding smaller numbers
present during weekends (Fig. 1C). This pattern was restored
as early as three weeks after the earthquake.
To get a detailed view of the daily travel distances, d, we plot
for a few different dates the cumulative probability distributions
of d for two groups of people: persons present and not present in
PaP on the day of the earthquake. The distributions are basically
the same for both groups before the earthquake as well as eight
months after the earthquake, when social life had stabilized
considerably. However, right after the disaster there is a striking
deviation in the distribution of travel distances (Fig. 1D), which is
not present for people located outside PaP on the day of the
earthquake (Fig. 1E). We fitted the curves in panels D and E
Port-au-Prince
A
50 km
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Earthquake
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Distance traveled in one day, D (km)
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Out of PaP on EQ
Cumulative distribution, P(d
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Distance traveled in one day, D (km)
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In PaP on EQ
Dec 10, 2009
Jan 20, 2010
Oct 1, 2010
Ouest
Sud-Est
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Percentage traveled further than d
Time
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December
January
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in PaP at quake
others
Fig. 1.
a cross. (B) Gives the proportion of individuals who traveled more than d km between day t − 1 and t. Distances are calculated by comparing the person’s
current location with his or her latest observed location. In (C), we graph the change in the number of individuals in the various provinces in Haiti. (D) Gives a
cumulative probability distribution of the daily travel distances d for people in PaP at the time of the earthquake. (E) Shows the cumulative probability dis-
tribution of d for people outside PaP at the time of the earthquake. Finally, (F) gives the exponent α of the power-law dependence of d—the probability of d is
proportional to d−α. These are obtained by a maximum-likelihood method (33), and differ from the slopes of the lines in (D) and (E) by unity since these are the
cumulative distributions.
Overview of population movements. (A) Shows the geography of Haiti, with distances from PaP marked. The epicenter of the earthquake is marked by
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(or rather the corresponding probability mass functions) to a
power law pðdÞ ∼ d−α. The coefficient α indicates the slope of
the distribution. The smaller α is, the more fat-tailed is the dis-
tribution. In other words, a small α means larger differences be-
tween the average and the largest travel distances. In Fig. 1F, we
show the α-values of the daily travel distances. We see that the α-
values dip around the holidays for both the people present and
not present in PaP on the day of the earthquake. However, while
α goes back to normal in mid-January for the population outside
PaP, it stays low until the early summer for the Port-au-Princians.
Movement patterns were heterogeneous both under normal
conditions (echoing results of refs. 17 and 19), and after this
large-scale disaster. In the latter case, however, the heterogeneity
is even more pronounced than during normal times. Taken to-
gether, the analyses in Fig. 1, consistently shows that the move-
ment patterns changed primarily for the directly affected people
and returned back to normal after 4 ∼ 5 mon.
Regularity and Predictability of People’s Trajectories.The above ana-
lysis reveals that the earthquake triggered large population move-
ments, caused increases in daily travel distances of people in the
affected area, and produced an increase in the heterogeneity of
travel distances. Since a large-scale disaster throws much of
society into disorder, one may assume that the underlying cause
for these changes is an increase in the disorder in people’s move-
ments—that a large-scale disaster causes people to move irregu-
larly while fleeing unrest and searching for material support. In
this section, we will show that this hypothesis is incorrect.
To analyze the changes in people’s trajectories caused by the
earthquake, we divided the sampling period into three equally
long periods: spring—from January 12 (the day of the earth-
quake) to May 5; summer—from May 6 to August 27; and fall—
from August 28 to December 19. To get good statistics on the
trajectories, we restrict ourselves to those who called 70% or
more of the days during all three periods. To characterize the tra-
vel patterns, we follow ref. 17 and focus on two classes of mea-
sures—radius of gyration (a measure of the size of trajectories)
and entropy measures for analyses of disorder and predictability.
The radius of gyration captures the size of the trajectory as if it
was a physical object. (See the Methods section for a definition.)
It is, in theory, rather different from the daily average travel
distance. Someone who moves in a comparatively confined space
will have a small radius of gyration even though he or she covers a
large distance. R is also different from the physical extent of the
trajectory in that it weighs the contribution from a sector by the
time a person has been there. For example, someone that spends
most of the time at one location (A) but makes one trip to an-
other location (B) on the other side of the country will have a
smaller radius of gyration than someone who constantly travels
between A and B. The probability distribution of the radius of
gyration for PaP residents is presented in Fig. 2A. We see that,
just like the daily travel distance, the average radius of gyration
was higher immediately following the earthquake (spring) than
during the summer and fall periods. The distributions of the ra-
dius of gyration during these later periods (summer and fall) are
very similar to each other, indicating the return to normality after
earthquake. For example, during the spring period, right after the
earthquake, 43% of the studied population had a radius of gyra-
tion of more than 10 km, while the corresponding figures for the
summer and fall periods were 32% and 29%, respectively. To sum-
marize, in terms of the shape of the distributions of the trajec-
tories (like the daily travel distances), the disaster enlarged the
travel patterns, an effect that lasted into the summer. Even if this
is not a true for each individual, other quantities, as we will soon
see, support this general picture.
The trajectories of people in stable societal conditions are
often quite regular—people visit the same places (home, work,
their favorite grocery store, etc.) in the same order (17). Since
history repeats itself in this respect, the movements of people are
predictable. To study this, we use entropy (disorder) and an in-
formation theoretic definition of predictability (described in the
Methods section). Note that, the sense in which we use the word
“predictability” here relates to the regularity of people’s move-
ments after the earthquake. Further below we describe how data
from before the earthquake could be used to predict people’s des-
tinations as they left PaP after the earthquake.
Comparing the entropies S of the three periods (Fig. 2B), we
discover that their probability distributions are conspicuously un-
changed over the three periods, and the predictability Π (Fig. 2C)
is also very similar during the three periods. The only difference is
that people are actually slightly more predictable right after the
disaster than during the rest of the year. As already mentioned,
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Fig. 2.
gyration: rg. (B) Displays the distribution of entropy S. (C) Gives the distribution of the maximal predictability Π. (D) Shows the correlation between radius of
gyration rgand Π. In (E), we graph the fraction of time a person spent in the top n visited communes~Π. (F) gives the averaged R∕Rrandversus the radius
of gyration rg, showing a relative stable dependence.
Trajectory analysis of mobile phone users who were present in PaP on the day of the earthquake. (A) Shows the cumulative distribution of the radius of
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people did not become more predictable because they became
immobile—they moved even more after the disaster. The prob-
ability distribution of entropy PðSÞ peaks at around 1.5 (Fig. 2B).
One interpretation is that a typical mobile phone user present in
PaP on the day of the earthquake had an uncertainty of 21.5∼ 2.8
locations for his or her next destination. The predictability PðΠÞ
peaks at around 0.85 (Fig. 2C), meaning that we have an upper-
limit of 85% to predict the typical person’s next destination during
each of the three periods. These findings show that, even in this
extreme disaster, human movements over the three 3-mon periods
remained highly predictable. People moved farther, but not less
regularly, during the tumultuous time after the disaster.
Data from a high-income country during stable social condi-
tions have shown that Π is almost constant for people with rgran-
ging from 10 up to 1,000 km (17). This is, however, not the case in
our data. In Fig. 2D, we see that predictability increases with
increasing rgduringall three periods (i.e., people traveling farther
are more predictable). Furthermore, predictability remains
slightly higher after the earthquake for most of the rgrange.
Predictability, based on the regularity in people’s movements,
gives us a theoretical upper limit of how well we can forecast a
person’s trajectory, but it does not tell us how to forecast it. The
simplest prediction technique is to count the visiting frequency of
a person’s historical trajectory, taking the most frequently visited
location as a predictor of the person’s next destination. Because
towers are not uniformly distributed across the country, we use a
more relevant division of the country, the Haitian “commune” (in
total, 140 communes). On average, a mobile phone user spent
75% of the time in his or her most frequently visited commune
(see Fig. 2E). In agreement with the results above, this pattern is
even stronger after the earthquake than during later periods. The
top three most visited communes constituted, on average, 95% of
the visited locations during spring and 90% during summer and
fall. The frequency curves are almost identical for summer and
fall, providing additional evidence that the mobility patterns
returned to normal by this time.
Information about an individual’s top visited locations pro-
vides the simplest way to make predictions about a person’s
future location. As with Fig. 2D, we checked whether the accu-
racy of such a predictive procedure is dependent on the people’
travel distances. However, the more locations someone visits, the
lower is the expected frequency of the most visited locations. We
compensate for this effect by measuring the ratio between the
probability of finding a person in his or her most visited location
and the probability of finding an individual at a randomly chosen,
previously visited, location—the relative regularity R∕Rrand. The
results are presented in Fig. 2F, where we can see that the differ-
ence between the time periods is negligible. On the other hand,
the travel distances have, as expected, little effect—the relative
regularity is around 6 for people in PaP with rgranging from
1 to 50 km and 4 to 6 for people with rg> 50 km. This means
that mobile phone users in PaP were, on average, at least four
times more likely to spend their time in the most frequent loca-
tion during the three periods than in a random location he or she
visited during that period.
In sum, we have found that despite the social disorder, the in-
creases in radius of gyration and the increases in average daily
travel distance that we observed after the earthquake, the move-
ments of the population remained highly regular and predictable.
We have also made the same analysis by taking all the days after
the earthquake as a single period and verified that the results are
similar (see the SI Appendix).
Evacuation and Return Behavior.We now turn to research questions
that explain and contextualize the high predictability shown in the
previous section. The issues analyzed here are also of direct re-
levance to relief agencies responding to disasters. We investigate
how soon after the earthquake people moved out, how far from
PaP they moved, what proportion of people returned, and how
long time people stayed outside the capital after leaving. We also
look into a strong predictor of the specific geographical area to
which people decided to move after the earthquake, namely their
location during the preceding Christmas and New Year.
To investigate how soon people started to move out of PaP, we
select mobile phone users in PaP on the day of the earthquake
who subsequently left PaP at some point between the earthquake
and the end of June 2010 (170 d after the earthquake). We in-
clude all mobile phone users irrespective of their calling fre-
quency. We plot the proportion, PðtÞ, of people who left PaP for
the first time t days after the earthquake and compare this dis-
tribution to distributions later during the year when considerable
stabilization had taken place. These five reference periods start
on the same weekdays on June 1, 8, 15, 22, and 29 and all end
170 d later (Fig. 3A).
Interestingly, we see that the largest proportion of people left
not immediately, but three days after the disaster. Although this
finding is highly noteworthy, the delay may be partly due to re-
duced network capacity during the first few days after the earth-
quake. For t > 3, the distribution of the fraction of evacuated
individuals is close to a power-law distribution PðtÞ ∼ t−α, and re-
veals that the earthquake caused PaP residents to leave the city
much earlier than on normal days. Another interesting finding is,
again, the existence of weekly cycles in the reference data. These
cycles were absent after the earthquake and then reappeared
more than a month afterwards, indicating a return to normality.
So, how far did people move? Using the same inclusion criteria
and reference periods, we plot the proportional distribution of
the maximum distances the mobile phone users traveled after
the earthquake, measured from the center of PaP (Fig. 3B). A
majority (about 70%) of the individuals traveled quite short dis-
tances, maximally within 50 km of PaP center (note, however, the
small size of Haiti, Fig. 1A). The distribution of maximum dis-
tances traveled by affected individuals is almost identical with
those traveled during normal times, suggesting that the extremes
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Fig. 3.
bution of PaP residents moving out of PaP for the first time by t days after the
day of the earthquake. In (B), we plot the maximum distance to the center of
PaP traveled by PaP residents. Reference curves represent sample periods
from June 1, 8, 15, 22, and 29 to 170 d after these dates. (C) Gives the cumu-
lative distribution of people’s relative distances on January 3 and 31 to their
locations on the day of the earthquake for four different categories of peo-
ple. (D) Gives the distribution of distance to the center of PaP for individuals
present in PaP on the sampled day and outside PaP 19 d later. Results for the
period after February 9 are averaged for clarity.
Analysis of population movements out of PaP. (A) Shows the distri-
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of the trajectories are the same between the PaP population dur-
ing this first period after the earthquake and during normal times.
This is thus another aspect (apart from predictability) that was
conserved in the disaster.
The maximal travel distances do not, however, tell us where
people travelled. Studies from the 1985 Mexico City earthquake,
for example, have shown that people left the city to stay with re-
latives or friends elsewhere (27, 28). Recent analyses have also
shown a high correlation between the locations of people’s social
contacts and their mobility patterns (29). In our data, we can test
thishypothesis by comparing where people were at the timeofthe
earthquake and during the preceding Christmas and New Year
holidays (assuming most people spent this time with their family
and friends). In Fig. 3C, we select the people who were in PaP on
the day of the earthquake and group them into four categories,
depending on where they were on January 3 and 31: in-in for
those in PaP on both these dates; out-out for those not in PaP
on January 3 and 31; in-out for those in PaP on January 3 and not
in PaPon January 31; and out-in for those not in PaPon January 3
and in PaP on January 31. For these groups, we show the cumu-
lative probability distributions of distances between people’s
locations on January 3 and their locations in PaP on the day
of the earthquake (ΔdXmas) as well as the distribution of distances
between their PaP locations on the day of the earthquake and on
January31(ΔdEq).ResultsfromthisanalysisareshowninFig.3C.
First, we notice that the distances for the out-out group are almost
identical on January 3 and 31, implying that the people who spent
the holidays outside PaP are quite likely to have moved to these
locations after a disaster. Second, people who were in PaP during
Christmas and New Year, but moved out after earthquake (in-
out), tend to have had longer travel distances than the others,
possibly because they had safe social connections farther away
and were thus less likely to travel to them during the holidays.
Finally, the ΔdXmasdistance distribution of the out-in group is
very similar to that of the out-out group, indicating that the rea-
sons these people did not move out of PaP after the earthquake
was not determined by their having a different geographic distri-
bution of social contacts than the out-out group.
If one can generalize these findings, they point to a way of
using the population distributions during the holidays as a way
to estimate the distribution of displacement during a disaster.
We have confirmed our results on the level of the smallest admin-
istrative area in Haiti, the communal section (a total of 570 com-
munal sections). For people in PaP on the day of the earthquake
who were outside PaP on both days (out-out), 68.5% were in the
same communal section on January 31 as they were on January 3.
The percentage rises to 85.5% when we use the larger adminis-
trative area of department (province).
We now relate the travel distributions in Fig. 3C to normal
mobility patterns. We analyze two groups of people—individuals
in PaP on December 1, 2009 and individuals in PaP on the day of
the earthquake (January 12, 2010), and we use as reference the
groups of individuals present in PaP on Tuesday after February 9.
For these groups, we plot (Fig. 3D) the cumulative distribution of
distances from PaP center to the individuals’ locations 19 d after-
wards (on December 19, January 31, etc.). Again, the postearth-
quake distributions are very similar to those of the reference
periods. Differences consist of a slightly higher proportion travel-
ing longer distances, possibly for the same reasons as discussed
for the Christmas and New Year analysis above. There is also a
small variation in the short to intermediate distances (30 to
70 km). The difference when comparing the postearthquake dis-
tributions in Fig. 3B (red curve) and Fig. 3D (red curve) is the
large proportion of very short trips in the former. This is due
to that Fig. 3B also captures a large number of persons who stray
outside the city boundaries for short periods of times, while
Fig. 3D captures predominantly those who left for a longer per-
iod. A further analysis ofthe duration people stayoutside PaP can
be found in the SI Appendix.
In order to investigate the potential bias from differences in
calling frequencies, we have repeated all analyses for subgroups
of users with different calling frequencies. These analyses reveal
that the results overall are robust. For analyses where time or
duration is an outcome (Fig. 3A), the conclusions in the text
remain when analyzing groups with different calling frequencies,
although the exact size of the differences between the earthquake
and reference periods should be interpreted with caution (see SI
Appendix).
Discussion
We have shown that, despite sharp changes in people’s mobility
patterns after the tragic earthquake of January 12, 2010, in Haiti,
the predictability of people’s movements over the three-month
period after the earthquake was very high and remained un-
changed in comparison to later parts of the year after consider-
able stabilization had taken place. We show that the destinations
of people who left the capital early (during the first three weeks
after the earthquake) were highly correlated to their mobility
patterns during normal times, and specifically to the locations at
which people had significant social bonds, as measured by where
they spent Christmas and New Year holidays.
The above findings imply that population movements follow-
ing large-scale disasters may be significantly more predictable
than previously thought. Given the fundamental importance of
knowing the locations of affected populations during disaster
relief operations, these findings suggest that disaster planning
and response may be significantly improved. On a more abstract
level, the results force a change in our conceptualization of dis-
asters as fundamentally chaotic events. People’s movements are
highly influenced by their historic behavior and their social bonds,
and this fact remained even after one of the most severe disasters
in history.
In the quest for a globally applicable model of human mobility,
the present study confirms several findings from high-income
countries, including the power-law distribution of travel distances
and the high predictability of travel trajectories during stable
social conditions (17). A further investigation in the SI Appendix
shows that for people in PaP, the waiting times until leaving PaP,
as well as the time until they returned, was power-law distributed,
both during normal days and after the earthquake, albeit with
different exponents. The results also highlight the very high mo-
bility of people during normal conditions and the importance of
taking these movements into account when investigating postdi-
saster movements.
Several limitations and avenues for future work exist (for
additional discussions, see ref. 13). First and foremost, the exact
correlation between disaster-related movements of people with
and without mobile phones needs to be better understood. We
have, however, shown very promising results in this area in earlier
research (13). Additionally, mobility patterns in different types of
disasters and different social contexts may vary considerably. The
present dataset covered 42 d before the disaster. Additional data,
including a longer period before the earthquake, would have
allowed better differentiations of people’s permanent place of
living, social contacts, and predisaster mobility patterns.
Another limitation is that the data set included only one loca-
tion update per day. This means that movements taking place
during the course of 24 h, especially people’s movements inside
their cities and home communes, will not be included in the data.
Granted this limitation, since our interest in this paper is primar-
ily on movements over distances that are sufficiently large to pre-
vent access to relief supplies, a daily resolution should provide the
most important features of mobility relevant to relief coordina-
tors. Yet another issue is how the societal changes during the
disaster affect the sampling. The mobile phone network suffered
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Page 6

reduced capacity immediately after the earthquake, but was func-
tioning again within a few days. This may have contributed to bias
in thefirst week’s data, but does not alter ourconclusions. Lack of
access to electrical charging could perhaps have reduced the
number of calls. However, power was also frequently interrupted
before the earthquake, and existing electric generators seem to
have supplied considerable charging capacity. The effects of fatal-
ities and the loss of phones in the disaster were circumvented by
only studying users present at both the beginning and end of the
dataset. Lack of possibilities to put credit on the phones shortly
after the earthquake could have been another bias. However, the
mobile phone operator, Digicel, supported their customers by
adding five USD in calling credit to all accounts after the disaster.
In summary, the results show that population movements fol-
lowing the Haiti disaster had a high level of predictability and
seemed highly influenced by people’s social support structures.
These findings form an important first step in forecasting the ef-
fects of large-scale disasters. With future research in other disas-
ter contexts, such forecasts are likely to become an important part
of national disaster preparedness planning and in predicting po-
pulation movements during ongoing disaster relief operations.
Methods
Radius of Gyration. Let Ti¼ ft1; t2; ⋯; tLig be the sequence of mobile phone
towers that person i visited during a period. Let rðtÞ be the location of t. Then
the radius of gyration of i’s trajectory in the specific period is
rgðiÞ ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Li∑
k¼1
1
Li
ðrðtkÞ −¯ rÞ2
v
u
u
t
;
[1]
where ¯ r ¼1
Li∑Li
k¼1rðtkÞ is the center of mass of the trajectory.
Predictability. To evaluate the predictability, we (following ref. 17) use a mea-
sure of entropy, or disorder, that accounts for both the relative frequency of
the visited locations and the order of the visits:
Si¼ −∑
Ti0⊂Ti
PðT0
iÞlog2½PðT0
iÞ?;
[2]
where PðT0
measure of entropy, one can estimate the upper bound of the success rate in
predicting the future location of the mobile phone user immediately after Ti.
We get the maximum predictability, Πi, by solving a limiting case of Fano’s
inequality (a relation derived from calculation of the decrease in information
in a noisy information channel):
iÞ is the probability of finding a subsequence T0
iin Ti. Based on this
Si¼ HðΠiÞ þ ð1 − ΠiÞlog2ðN − 1Þ;
[3]
where
HðΠiÞ ¼ −Πilog2ðΠiÞ − ð1 − ΠiÞlog2ð1 − ΠiÞ;
[4]
and N is the number of distinct locations visited by person i (30–32).
ACKNOWLEDGMENTS. This project would not have been possible without
dedicated support from Digicel Haiti. We would especially like to thank
Maarten Boute, David Sharpe, Roy Ojiligwe, Jouvain Petit-Frere, Jean
Williama, Kello Julien, Luigi Roy, and Rabih Youssef at Digicel Haiti. P.H. ac-
knowledges financial support from the Swedish Research Council and the
WCU program through NRF Korea funded by MEST (R31-2008-000-10029-0).
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