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Am. J. Trop. Med. Hyg., 86(2), 2012, pp. 349–358

doi:10.4269/ajtmh.2012.11-0432

Copyright#2012 by The American Society of Tropical Medicine and Hygiene

Assessing the Risk of International Spread of Yellow Fever Virus: A Mathematical Analysis of

an Urban Outbreak in Asuncio ´n, 2008

Michael A. Johansson,* Neysarı ´ Arana-Vizcarrondo, Brad J. Biggerstaff, Nancy Gallagher, Nina Marano, and J. Erin Staples

Division of Vector-Borne Diseases, Centers for Disease Control and Prevention, San Juan, Puerto Rico; Division of Vector-Borne Diseases,

Centers for Disease Control and Prevention, Fort Collins, Colorado; Division of Global Migration and Quarantine,

Centers for Disease Control and Prevention, Atlanta, Georgia

Abstract.

ble of causing large urban outbreaks of human disease. With the ease of international travel, urban outbreaks could lead

to the rapid spread and subsequent transmission of YFV in distant locations. We designed a stochastic metapopulation

model with spatiotemporally explicit transmissibility scenarios to simulate the global spread of YFV from a single urban

outbreak by infected airline travelers. In simulations of a 2008 outbreak in Asuncio ´n, Paraguay, local outbreaks occurred

in 12.8% of simulations and international spread in 2.0%. Using simple probabilistic models, we found that local inci-

dence, travel rates, and basic transmission parameters are sufficient to assess the probability of introduction and autoch-

thonous transmission events. These models could be used to assess the risk of YFV spread during an urban outbreak and

identifylocationsatriskforYFVintroductionandsubsequentautochthonoustransmission.

Yellow fever virus (YFV), a mosquito-borne virus endemic to tropical Africa and South America, is capa-

INTRODUCTION

Yellow fever virus (YFV) is endemic to sub-Saharan Africa

and tropical South America, where it is maintained in nature

by transmission between nonhuman primates and sylvatic

mosquito species.1Humans become infected when they enter

jungle areas and are fed on by infectious mosquitoes. As

infected humans move, they can transport the virus from one

region to another, serving as a source of infection for naı ¨ve

mosquitoes in distant locations. Although the vast majority

of yellow fever occurs in remote, rural areas, urban outbreaks

can occur in areas infested by the anthropophilic mosquito

Aedes aegypti, a highly efficient vector of YFV. In 2008, an

outbreak of urban yellow fever was identified in metropolitan

Asuncio ´n, Paraguay.2This was the first urban yellow fever out-

break documented in South America since 1942 and raised

concerns of the potential spread of the virus to non-endemic

areas with vectors capable of transmitting the virus, such as the

Caribbean, Central America, and North America.

In the Americas, the scale of yellow fever outbreaks over

the last one-half century has been limited by large-scale Ae.

aegypti control efforts3and the use of YFV vaccine.4However,

problems with vector control program sustainability,5,6vaccine

supply,7–9and adverse events associated with vaccination10–12

threaten primary prevention efforts. Recognition of the out-

break in Asuncio ´n was quickly followed by intensive vector

control efforts in over 25,000 households and administration of

more than 1 million doses of YFV vaccine.2Because of either

interventions or natural abatement, the Asuncio ´n outbreak

was limited to only nine confirmed cases. With a more hospi-

table environment and less control effort, this small outbreak

could have led to a larger, possibly international epidemic.

Previous work has quantified the continuing risk of introduc-

tion of YFV into urban environments13but has not addressed

the risk of further spread. With the convenience and speed of

modern airline travel, travelers infected with YFV may quickly

arrive in nearby or distant international locations. Given the

high densities of competent vector mosquitoes in many tropi-

cal and sub-tropical areas of the world and the low vaccine

coverage rates outside of endemic regions, YFV-infected trav-

elers could present a major risk to many populations where

suitable conditions for transmission are present. The challenge

that we confront is to estimate the magnitude of that risk. To

simulate the global spread of YFV from a single urban out-

break by infected airline travelers, we developed a metapo-

pulation model to quantify critical measures of global spread

and estimated the risk of spread associated with the Asuncio ´n

outbreak. We then used probabilistic models to estimate the

probabilities of spread based solely on simplified estimates of

the most critical components.

MATERIALS AND METHODS

Stochastic metapopulation model. A full description

of the model and parameterization can be found in the

Supplemental Information. Briefly, we included 141 cities

(Figure 1) based on their importance to international travel,

proximity to yellow fever endemic areas, or involvement in the

recent spread of chikungunya virus (another arthropod-borne

virus transmitted by Aedes mosquitoes). Each city was given

a local human population consisting of susceptible, incubating,

infectious, and immune individuals, any of whom can engage

in temporary travel to other cities.14Climate data for all cities

were extracted from long-term climate models created by

the Climate Research Unit of East Anglia University, United

Kingdom.15Cities where at least 6 months of a typical year

have an average temperature of less than 10?C or no rainfall

were considered unsuitable for Ae. aegypti habitation.16Each

suitable city was given an Ae. aegypti mosquito population that

varies depending on local, daily, climate-dependent mortality

rates determined using a spline-smoothed version of the

climate data. The mosquito populations included susceptible,

incubating, and infectious mosquitoes. Mosquitoes may be

infected by feeding on viremic humans, at which point they

undergo an incubation period before becoming infectious.

Humans, in turn, may be infected by infectious mosquitoes

and then undergo an incubation period followed by a viremic

phase and then recovery, at which point they gain immunity

to YFV. We incorporated two vaccination scenarios in the

*Address correspondence to Michael A. Johansson, Division of

Vector-Borne Diseases, Centers for Disease Control and Prevention,

1324 Calle Can ˜ada, San Juan, Puerto Rico 00920. E-mail: mjohansson@

cdc.gov

349

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model: no vaccination and previous vaccination based on the

latest available country-specific vaccine coverage estimates

from the World Health Organization.17Previously vaccinated

individuals were considered immune.

Travel (including connecting travel) between each city pair

was estimated using city and network characteristics in a regres-

sion model based on US sampled itinerary data (US Depart-

ment of Transportation; www.transtats.bts.gov/Tables.asp?DB_

ID¼125) and global airline data (Official Airline Guide; www.

oagaviation.com/Solutions/AnalysisTools/Traffic/t100inet.html).

Incubation periods were modeled based on historical YFV

data.18Temperature- and humidity-dependent Ae. aegypti mor-

tality was derived from previous work by Focks and others.19

Published data on the human infectious period, vector den-

sity, vector biting rate, efficiency of human to vector transmis-

sion, and efficiency of vector to human transmission are too

limited to adequately characterize these components (Table 1).

Rather than analyzing the sensitivity of the model outcome to

eachof these parametersindividually, we combined their lowest

estimates to create a lower-limit low transmissibility scenario,

their highest estimates to create a worst-case high scenario,

and central estimates to create a moderate scenario. For the

ease of discussion, we classify these scenarios in terms of R0,

the basic reproductive number. In the case of a vector-borne

virus such as YFV, R0can be defined as the average number of

human infections resulting from a single human infection (cal-

culation described in Supplemental Information).

Each simulated epidemic is seeded by introducing infected

humans to a single city at a specified day of the year. The

model is discrete with daily time steps, and all interactions are

stochastic. A number of epidemics are simulated to generate a

range of possible outcomes starting from a given scenario.

Probabilistic models. A full description of these models

can be found in Supplemental Information. The models are

parameterized the same as the stochastic metapopulation

model. With pi,jas the probability of travel from city i to city

j and NIi,tas the number of infected individuals in city i at

time t, the probability of infected individuals traveling from a

particular city, i0, to any other city by time T can be written as:

pSPREADði0,TÞ ¼ 1 ?

Y

T

t¼0

Y

I

i6¼i0

ð1 ? pi0;iÞNI

i0;i,

ð1Þ

where i is the city index for cities i ¼ 1, 2, ... , I and I is the total

number of cities. The probability of introduction from any

other city to city i0by time T can be written as:

pINTROði0,TÞ ¼ 1 ?

Y

T

t¼0

Y

I

i6¼i0

ð1 ? pi;i0ÞNI

i;t:

ð2Þ

If the time series NIi,tis unknown, the equation may be refor-

mulated to assume that all we know is an estimate of the num-

ber of people who have been infected and the rates of travel.

Equation 1, describing the probability of an infected traveler

leaving city i0, can be simplified to be a function of cumulative

infected person-days in city i0, Xi0:

pSPREADi0

ð Þ ¼ 1 ?

Y

I

i6¼i0

ð1 ? pi0;iÞXi0:

ð3Þ

To assess the probability of novel autochthonous transmission

events,weusedbranchingprocessanalysis.20Inthecaseofvector-

borne infections, an infectious human generates a random num-

ber of infectious vectors from a distribution determined by the

vector density, feeding rate, transmission efficiency, and proba-

bility of a vector surviving the extrinsic incubation period. An

infectious vector, likewise, may give rise to any number of

infectious humans dependent on the feeding rate, transmission

efficiency, and vector longevity. To analyze the probability of

extinction in a single step, we analyzed the value g(0) for the

respective probability generating function g(s).20In this case,

we use a composite probability-generating function to analyze

the probability that three processes—infectious individuals trav-

eling from city i to j, infection of vectors in city j, and infection

of humans in city j—result in zero new human cases at time t:

gTIgV gHð0,i,j,tÞðÞðÞ ¼ 1 ?

1 ? pi;jþ pi;jeRHV

0j;tðe

?RVH

0j;t?1Þ

??NI

i;t

:

ð4Þ

This equation requires RHV

infectious vectors produced per infectious human and the

0

and RVH

0

, the average number of

FIGURE 1.

cated by the largest dot.

The 141 cities included in the analysis. Asuncio ´n is indi-

TABLE 1

Parameters for the low, moderate, and high transmissibility scenarios

ParameterLowModerate HighSource

Female mosquitoes per person*

Vector longevity (days)*

Human blood meals per mosquito per day

Efficiency of human to vector transmission

Efficiency of vector to human transmission

Extrinsic incubation period (days)*

Human infectious period (days)

12452

19

29, 35, 36, 53, 54

29, 31–36

32

18

55

10.6{

0.5

0.2

0.5

6.9{

3

10.6{

0.7

0.5

0.5

6.9{

3

10.6{

1

0.5

1

6.9{

4

Peak R0(at 36?C and 100% relative humidity)0.424.190

*These factors are dependent on local climate and thus, exhibit significant spatiotemporal variation. Their values here correspond to 36?C and 100% relative humidity.

{These factors are considered well-estimated and thus, do not vary between models.

350

JOHANSSON AND OTHERS

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average number of infectious humans produced per infectious

vector, respectively, both of which exhibit spatiotemporal vari-

ation and thus, are subscripted (i,t). As above, introduction

may occur from different cities and at different time points,

and therefore, the probability of novel autochthonous trans-

mission in city i0by time T is:

pAUTOði0,TÞ ¼ 1 ?

Y

T

t¼0

Y

I

i6¼i0

1 ? pi;i0 þ pi;i0eRHV

0i0;tðe

?RVH

0i0;t?1Þ

!NI

i;t

:

ð5Þ

This probability can also be estimated in the absence of com-

plete information by modifying Equation 5 to use infected

person-days, X, for each potential source city rather than a

daily number of infected individuals:

pAUTOði0Þ ¼ 1 ?

Y

I

i6¼i0

1 ? pi;i0 þ pi;i0eRHV

0i0;tðe

?RVH

0i0;t?1Þ

!Xi

:

ð6Þ

The probability of spread from a given city, i0, resulting in

autochthonous transmission in any other city is:

?

pSPREAD!AUTOði0Þ ¼ 1 ?

Y

I

i6¼i0

1 ? pi0;iþ pi0;ieRHV

0i;tðe

?RVH

0i;t?1Þ

?Xi0

:

ð7Þ

In the presence of vaccination, RVH

reproductive number, RVH

tially vaccinated population:

0

is replaced by the effective

E, indicating transmissibility in a par-

RVH

E

¼ RVH

0

ð1 ? pVAXÞ,

ð8Þ

where pVAXis the proportion of the population that has been

effectively vaccinated.

RESULTS

R0. We first established three different model parameter

sets and characterized them in terms of R0, which indicates

the average number of infected humans produced by a single

infected human in a completely naı ¨ve population. Using low,

moderate, and high literature estimates of the parameters for

the human infectious period, vector density, vector biting rate,

efficiency of human to vector transmission, and efficiency

of vector to human transmission, we estimated R0values to

be 0.42, 4.1, and 90 under the respective scenarios at peak

transmissibility conditions (Table 1). Although these R0

estimates classify transmissibility at 36?C and 100% relative

humidity, transmissibility in the model is adapted to reflect

temporal and geographic variation of local climate. Figure 2

shows global climate-adjusted estimates of R0based on the

moderate transmissibility scenario for January and July.

Spread without vaccination. Before the outbreak-associated

vaccination campaign in 2008, reported vaccine coverage

in Paraguay was 34%,17but vaccination efforts had been

concentrated on children throughout the country and people

in rural border areas rather than in Asuncio ´n.2We, therefore,

assumed that the population of Asuncio ´n was 100% susceptible.

Furthermore, to simulate a worst-case scenario, we assumed

that all other populations were also 100% susceptible. The

first cases in Paraguay were reported in January of 2008, and

therefore, we ran 1,000 simulations with the introduction of a

single incubating individual to Asuncio ´n on January 1. Given

the local climate at that time of year, the initial R0values in

Asuncion were 0.047, 0.46, and 10 for the low, moderate, and

high scenarios, respectively.

In the low transmissibility scenario, only 2.3% of the sim-

ulations resulted in local transmission, with a maximum of

seven additional cases occurring (Table 2). Because transmis-

sion under this scenario was so limited and spread to other

cities did not occur, it was not considered in later experiments.

Under the moderate transmission scenario, a single introduc-

tion led to additional human transmission in 128 (12.8%) of

the simulations. In 108 (84.4%) of these outbreaks, the out-

break involved only local transmission, affecting a median

of 2 persons with a range of 1–981 persons. In two out-

breaks, infectious individuals arrived in other cities but did not

initiate any additional transmission. In the other 20 (15.6%)

simulations, however, large epidemics occurred, affecting

450,000–550,000 people in Asuncio ´n, and international spread

occurred, resulting in YFV pandemics. Figure 3 shows epidemic

curves for a selection of cities under the moderate R0model.

Under the high R0scenario, nine (0.9%) simulations resulted

in only small-scale local transmission (one to three additional

cases), one of which resulted in a single infected traveler going

to New York (Table 2). In 689 (68.9%) other simulations, there

were large local outbreaks leading to pandemics.

Dynamics were monitored locally for both potential intro-

duction (i.e., the presence of infectious individuals) and

autochthonous transmission, which was evidenced by a locally

acquired human infection (Figure 3). In the moderate R0model,

the first international spread of YFV by an infected or infec-

tious traveler from Asuncio ´n occurred at a median of 259 days

(range ¼ 14–561 days) after introduction into Asuncio ´n. At the

time of introduction, a median of 1,013.5 infections (range ¼

3–6,363 infections) had occurred in Asuncio ´n. The first inter-

national autochthonous transmission occurred after 596.5 days

(range ¼ 203–1,310 days) when there had been 10,654 infec-

tions (range ¼ 1,045–61,240 infections) in Asuncio ´n. In the high

R0model, both introduction and autochthonous transmissions

occurred earlier at a median of 53 (range ¼ 3–80 days) and

68 days (range ¼ 27–94 days), respectively. This finding corre-

sponded to a median of 756 infections (range ¼ 5–8,735 infec-

tions) occurring before the earliest foreign introduction event

and 9,468 infections (range ¼ 28–140,681 infections) before

the first foreign autochthonous transmission event.

The first three cities to which YFV was introduced by

infected travelers in both the moderate and high trans-

missibility scenarios were Paris, London, and New York.

Autochthonous transmission occurred earliest, on average, in

New York, Miami, and Singapore in the moderate R0model

and Miami, Sao Paulo, and Singapore in the high R0model.

This order of initiation of autochthonous transmission varied

greatly between simulations. For example, although Miami

was, on average, the first city to experience autochthonous

transmission in the high R0model, in 25.7% of the simulations,

10 or more cities experienced transmission before Miami.

Spread with vaccination. We then repeated simulations for

both the moderate and high transmissibility scenarios under

the assumption that the population of each city had been

vaccinated at the last reported coverage rate for its respective

country. In Asuncio ´n, for example, 67% of the population was

assumed to be immune, because the estimated YFV vaccine

coverage for Paraguay was 67% after the 2008 vaccination

RISK OF GLOBAL YELLOW FEVER VIRUS SPREAD

351

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campaign.

occurred in 69 and 640 of 1,000 simulations in the moderate

and high transmission scenarios, respectively (Table 2). In the

6.9% of moderate scenario simulations in which transmission

occurred,transmissionwas

infections with a single infected traveler but no subsequent

transmission. In the high R0model, 57.4% of the simulations

resulted in pandemics. When pandemics occurred, the total

number of infections globally was reduced by ?26% (307.2–

307.8 million with vaccination versus 416.4–416.8 without

vaccination).

Probabilistic models. For each simulation, the probabilities

of introduction, pINTRO, and introduction leading to autochtho-

nous transmission, pAUTO, were calculated using the theoretical

models. Figure 4A shows the increase in pINTROover the course

of a single simulation for three cities. Introduction is predicted

when pINTRO¼ 0.5. In the moderate R0model, there were 2,802

simulated introductions of a possible 140,000 (1,000 simula-

tions for 140 cities). On average, predicted introduction was

22 days (middle 95% ¼ ?253–277 days) (Figure 4B and C) and

Under these conditions, localtransmission

limitedto 1–12new local

2 days (middle 95% ¼ ?23–23 days) before introduction in the

moderate and high R0scenario simulations, respectively. Of

the 2,802 simulated introduction events, 2,800 were predicted

for a sensitivity of greater than 99% and a negative predic-

tive value (NPV) of greater than 99%. With 20 false positives,

both the specificity and positive predictive value (PPV) were

TABLE 2

Occurrence of local YFV transmission in Asuncio ´n, infected travelers,

and autochthonous transmission in other cities in simulations under

different transmissibility scenarios

R0parameterization

Transmission in

Asuncion (%)*

Infected

travelers (%)*

Transmission in

other cities (%)*

Low

Moderate

High

Moderate with

vaccination

High with vaccination

2.3

12.8

69.8

0.0

2.2

69.0

0.0

2.0

68.9

6.9

64.0

0.1

57.4

0.0

57.4

*Percentage of 1,000 simulations.

FIGURE 2.

does not account for important extant determinants of transmission, such as the prevalence of vaccination or personal protective practices.

Estimated R0in January and July for an average year. R0is a measure of transmission potential under idealized contact conditions and

352

JOHANSSON AND OTHERS

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also greater than 99%. In the high R0model, all but 1 of 96,460

introductions were predicted for a sensitivity and NPV of

greater than 99%. Specificity was greater than 98% with 689

false positives, and the PPV was greater than 99%.

The onset of autochthonous transmission is predicted at

pAUTO¼ 0.5. In the simulations, autochthonous transmission was

predicted on average 33 days (middle 95% ¼ ?171–242 days)

(Figure 5) and 11 days (middle 95% ¼ ?14–33 days) before

occurrence in the moderate and high R0simulations, respec-

tively. In the moderate R0model, autochthonous transmission

was predicted on 2,580 occasions, of which 2,560 had simulated

transmission events (PPV > 99%). Specificity was also greater

than 99% with no false negatives, and sensitivity and NPV

were 100%. The high R0model also had no false negatives

(sensitivity ¼ 100%, NPV ¼ 100%). There were 689 false posi-

tives, however, with specificity and PPV approximately 99%.

With preexisting vaccination, only the high R0model led

to autochthonous transmission in other areas (Table 2). For

introduction and autochthonous transmission, sensitivity,

specificity, PPV, and NPV were all greater than 99%. Both the

prediction and occurrence of introduction and autochthonous

transmission were delayed when vaccination was incorporated

(Figure 6).

We also assessed the probabilistic models in the case where

complete data on an epidemic is unknown. Figure 7A shows

the probability of spread, pSPREAD, from Asuncio ´n using the

travel parameters presented here under increasing cumulative

infected person-days and the probability of spread resulting

in autochthonous transmission, pSPREAD!AUTO, in at least one

other city based on the number of infected person-days and

RHV

0

and RVH

0

on January 1. The probability of spread leading

to autochthonous transmission is delayed compared with the

probability of spread, and it is further delayed with decreased

R0or the presence of preexisting vaccination in other cities.

With 10,000 infected person-days, for example, the probability

of spread having already occurred is approximately 0.8, and the

probability of autochthonous transmission having occurred in

another city is approximately 0.5 under the high R0model and

0.2 under the moderate R0model. Note that an average human

infection results in 7.6 infected person-days (4.6 days incubating

and 3 days infectious), and therefore, 10,000 infected person-

days is roughly equivalent to a cumulative total of 1,300 peo-

ple infected.

The modified infected person-day equations can also be

used to calculate the probability of introduction to a particu-

lar city. Figure 7B shows how the cumulative probabilities of

introduction and autochthonous transmission in three cities

follow the number of infected person-days in Asuncio ´n. In the

case of Paris, introduction is highly probable, but R0is so low

on January 1 that the probability of autochthonous transmis-

sion is virtually zero. Meanwhile, when R0is high, such as in

Miami and Johannesburg in the high R0model, the probability

FIGURE 3.

gle moderate R0pandemic simulation.YFV transmission is initiated in Asuncio ´n, where transmission follows a seasonal pattern. The first introduc-

tions to other cities (dashed lines) began with Paris on day 254. The first autochthonous transmission outside of Asuncio ´n (dotted lines) occurred

in Miami on day 629 (after introduction on day 622). Repeated introductions and seasonal variation in transmissibility may lead to recurring epi-

demics. In Denver and Paris, the climate does not support YFV transmission, and therefore, all of the infectious individuals in those locations are

returning or visiting travelers from areas where transmission is ongoing.

Pandemic simulation. The lines indicate the number of individuals becoming infectious each day for nine representative cities in a sin-

RISK OF GLOBAL YELLOW FEVER VIRUS SPREAD

353

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of introduction leading to autochthonous transmission is nearly

equivalent to the probability of introduction.

DISCUSSION

The model described here is the first model to mechanisti-

cally address the potential for a vector-borne pathogen, such

as YFV, to spread around the world through infected airline

travelers. It was built using our best understanding of the

dynamics of Ae. aegypti mosquitoes, YFV infection, and global

travel and was designed to assist in assessing the probabilities

of spread of YFV in the event of an urban epidemic. To put

this model into a real life context, we applied it to an actual

outbreak that occurred in Asuncio ´n, Paraguay, in 2008. Below,

we discuss our estimation of YFV transmission dynamics, what

the models suggest about the outbreak in Asuncio ´n, our find-

ings regarding the probability of introduction and autoch-

thonous transmission of YFV, the effect of existing vaccine

coverage, and the limitations of the data and models.

YFV transmission dynamics. We assessed three transmission

scenarios representing drastically different estimations of

YFV virus transmissibility and pandemic potential (Table 1).

Although all three scenarios incorporate plausible estimates

for individual parameters, it is likely that the moderate

parameter set represents the most realistic scenario. The lowest

estimate that we evaluated for R0was 0.42, too low to reliably

cause epidemics even under the most favorable environmental

conditions. The highest estimate for R0was 90, extremely high

compared with related dengue viruses for which estimates

range from 0 to 103 but with median estimates in the range

of 1 to 6.21–27Moreover, given that most YFV epidemics are

small or progress slowly,1it is more likely that R0for YFV is

generally much lower, closer to 1 than 90.

Between the low and high R0estimates, there is much

parameter flexibility. Although our moderate model likely

overestimates some parameters, it likely underestimates oth-

ers, leading to a middle ground. Although this likelihood can-

not be explicitly tested, each parameter that we used falls

within a reasonable range (more details in Supplemental

Information), and the estimated geographic areas where

transmission is favored (Figure 2) correspond to the known,

historical, and estimated spatial distributions of YFV and den-

gue virus transmission.28The YFV R0estimates from the mod-

erate model are also similar to those estimates in previous

studies.25,29,30Note that R0is not an absolute determinant of

potential transmission; many other factors such as vaccination

rates, vector control programs, and personal protective mea-

sures may also determine whether transmission occurs.

Further refining estimates of R0would be difficult because

of the complexity of the underlying components. For example,

various studies estimate that the average human to vector effi-

ciency of YFV transmission is much less than 0.5, the estimate

under the moderate scenario.31–34At lower efficiency esti-

mates, however, R0quickly drops below one, even under ideal

environmental conditions. For YFV to cause even occasional

epidemics, as it does, either this efficiency has been routinely

FIGURE 5.

R0). A shows the probability of autochthonous transmission (solid

line) for threecitiesasafunctionoftimeinasinglesimulation(thesame

simulation as Figure 4). For each city, the threshold, pAUTO¼ 0.5, is

indicated by the horizontal dashed line, and the time of the first locally

acquired human infection in the simulation is indicated by the vertical

dotted line (no transmission was predicted in Paris, and none occurred

in the simulation). B shows the timing of simulated versus predicted

autochthonous transmission events for all cities where simulated

autochthonous transmission occurred (N ¼ 2,560). C is a histogram of

the difference between the simulations and predictions in B (mean

difference¼ 33 days,middle 95%¼ ?171–242 days).

Probability of autochthonous transmission (moderate

FIGURE 4.

the probability of introduction (solid line) for three cities as a function of

time in a single simulation. For each city, the threshold, pINTRO¼ 0.5, is

indicated by the horizontal dashed line, and the time of actual first

introduction in the simulation is indicated by the vertical dotted line.

Bshows simulated versus predicted introduction times for all cities where

introduction was predicted and occurred (N ¼ 2,800). C is a histogram

of the time difference between the predicted and simulated introduc-

tions in B (mean difference ¼ 22 days, middle 95% ¼ -253–277 days).

Probability of introduction events (moderate R0). A shows

354

JOHANSSON AND OTHERS

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underestimated or there are other components that have been

underestimated.

Asuncio ´n. In the actual Asuncio ´n outbreak, a total of nine

locally acquired infections were confirmed. Using the moderate

R0 parameter set to simulate the introduction of a single

infected individual into Asuncio ´n, we found that small local

outbreaks occurred in 10.8% of the simulations. An outbreak

like the one that was reported is, thus, a distinct possibility,

although no further transmission was a more common result

in simulations (87.2%).

It is possible that we underestimated the probability of

local outbreaks by underestimating YFV transmissibility in

Asuncio ´n. In our high R0model, the frequency of local out-

breaks was higher, with local transmission occurring in 70.7%

of the simulations. However, in 98% of those outbreaks, a

pandemic occurred, an eventuality that did not occur in the

real outbreak.

We also lack a complete description of the actual outbreak.

An infected individual with a travel history to rural areas with

ongoing transmission was never identified, and the true num-

ber of people infected is likely underestimated, because many

infected individuals may be asymptomatic. However, if more

than one infected person had arrived, the probability of a local

epidemic would have been substantially higher. For example,

given that 10.8% of introductions in the moderate R0model

resulted in local transmission, if six infected people arrived,

the probability of local transmission would be almost 50%

(1 ? [1 ? 0.108]6).

The most probable explanation for the short-lived out-

break in Asuncio ´n is that it was self-limited because of a rela-

tively inhospitable environment (low local R0) and that spread

beyond Asuncio ´n did not occur, because with so few individu-

als infected, spread is unlikely to occur. Using Equation 3, with

a total of nine infected individuals and average duration of

infection of 8 days, the probability of at least one infected indi-

vidual leaving Asuncio ´n is approximately 0.01.

Probability of introduction by travelers. The first event of

interest relative to the potential spread of YFV by travelers

is the appearance of an incubating or infectious individual in

a population where YFV is absent. The simulations presented

here can be used to directly estimate the probability of spread

under the assumptions that we have presented. In the moderate

R0model, international introduction from Asuncio ´n was rare,

occurring in 2.2% of simulations. However, in 90.9% of those

FIGURE 6.

sampled randomly from the complete set) for the high R0model with (grey) and without (black) prior vaccination. B shows the simulated and pre-

dicted times of the onset of autochthonous transmission under both conditions.

The effect of vaccination on simulated and predicted events (high R0). A shows simulated and predicted introduction times (N ¼ 2,000,

FIGURE 7.

at least one other city. The solid line is the probability of an infected traveler departing Asuncio ´n, pSPREAD, and the dashed and dotted lines are the

probabilities of the spread of autochthonous transmission to any other city, pSPREAD!AUTO, occurring under the high and moderate R0models, respec-

tively. The influence of vaccination is shown as indicated, with hardly any difference in the high R0model. pSPREAD!AUTOis calculated based on R0on

January 1. B shows the probability of introduction (solid) and autochthonous transmission (dashed, high R0; dotted, moderate R0) to three cities

from Asuncio ´n. In Paris, pAUTOis almost zero under both the moderate and high R0scenarios. In Miami and Johannesburg, pAUTOunder the high R0

scenario is approximately equivalent to pINTRO.

Probability of spread. A shows the relationship between accumulating infected person-days in Asuncio ´n and the risk of spread to

RISK OF GLOBAL YELLOW FEVER VIRUS SPREAD

355

Page 8

simulations, YFV-infected travelers eventually reached every

city in the model, leading to a pandemic. Thus, although the

probability of spread is low, the consequences may be drastic.

In the high R0model, both of these events were more common,

with 69.0% of simulations resulting in international spread

and 99.9% of spread resulting in pandemics.

Focusing on the simulations in which pandemics did occur

in the moderate R0model, the median time to spread was 259

days, but spread occurred as soon as 14 days after the initial

case was introduced to Asuncio ´n. At the time of the earliest

spreading events, the median outbreak size in Asuncio ´n was

just over 1,000 people and spread occurred with as little as

3 people infected. This timing, in terms of both actual time and

the number of people infected, shows that outbreaks could

quickly spread to other locations before being recognized.

The probabilistic models were highly sensitive and specific

for the prediction of introduction in the simulations and tended

to predict introduction before actual introduction (Figure 4).

As Equation 3 makes clear, the cities with the highest rates of

travel are the ones where the first introductions are expected.

In our model, Asuncio ´n had the highest rates of travel to Paris,

London, and New York, the cities where introduction occurred

earliest in the simulations. After the initial spread, the situa-

tion becomes more complicated, because there are multiple

sources of infected individuals.

In the midst of an ongoing outbreak, precise data on the

number of people infected and the timing of their infectious

periods is generally not available. Therefore, it may be of more

use to estimate the risk of spread using an estimate of cumu-

lative infected person-days. As presented in Equation 3, this

estimate and an estimate of travel rates are sufficient to esti-

mate both the probability of infected travelers leaving a

given city and the probability of infected travelers arriving in

a given city.

Probability of introduced autochthonous transmission.

Assessing the risk of introduction is only the first step.

Often more critical is assessing whether introduction will

lead to autochthonous transmission. The only additional

information needed to estimate the probability of autoch-

thonous transmission after introduction is the transmission

components RHV

0

and RVH

0

for the time and location of

interest (Equation 5). As discussed above, we have estimated

R0 and its subcomponents mechanistically, with reassuring

concordance with historical observations and environmental

suitability models.

Using probability generating functions to estimate the prob-

ability of one or more autochthonous infections, we reliably

predicted our simulations of these events (Figure 5). We also

estimated the probability of autochthonous transmission occur-

ring in other cities based solely on the cumulative number of

infectious person-days in a source city, showing that the prob-

ability of autochthonous transmission depends on both the

probability of introduction and the efficiency of local transmis-

sion (Figure 7B). The stochasticity of these processes contrib-

utes to the high degree of variability in the city where the

earliest autochthonous infections occurred in the simulations.

Prior vaccination. Prior vaccination in Asuncio ´n reduced

the probability of outbreaks (Table 1). This finding is because

of both reduced individual susceptibility (direct effect) and

reduced rate of vector to human transmission, because some

infectious vectors feed on immune humans (indirect effect).

Because the number of local infections is a key determinant

of the probability of international spread, vaccination in

Asuncio ´n reduces the frequency of spread (Table 1), and the

slower growth of those epidemics that do occur leads to a

delay in spread (Figure 6).

Despite the decreased probability of a seed epidemic and

slower spread when these epidemics did occur, pandem-

ics still occurred. Overall, the probability of autochthonous

transmission in other cities is slightly decreased, reflecting the

decreased transmissibility in the cities with high vaccine cov-

erage (Figure 7A). Previous vaccination also contributed to a

global reduction in the number of persons affected by approx-

imately 26% or 100 million persons. Thus, although prior

vaccination decreases the probability of spread occurring

and slows its pace, the potential for a major global health

problem persists.

Although pandemics may occur in the presence of prior vac-

cination, in our simulations, they only occurred in the high R0

model. Under the more realistic assumptions of the moderate

R0model, they did not occur, suggesting that previous vaccina-

tion in the population where the first infections occur may be

sufficient to prevent international spread. We did not assess the

critical threshold for vaccination coverage, but optimal cover-

age rates can be derived based on R0values.29,35,36Preventive

vaccination may seem a logical control measure, but there are

also problems with vaccine supply, cost, and safety.7–12In future

work, we will evaluate the potential impact of both preventive

vaccination and reactive interventions, such as local vaccina-

tion and vector control, vaccination of travelers, and restric-

tion of travel.

Limitations. Two important sources of uncertainty are the

parameterizations of the travel network and YFV transmission

dynamics (Table 1). The former requires more data,14and the

latter is partly captured in the different R0scenarios. However,

even within a given scenario, there is likely more variability

than we could reasonably incorporate. Different vector densi-

ties and contact rates, for instance, may vary greatly between

cities based on housing characteristics and other factors

that cannot be reliably assessed on a global scale. It is also

not necessarily true that Ae. aegypti are present in all of the

areas where YFV transmission may occur in our model.28In

some areas, Ae. aegypti has been replaced by Ae. albopictus,37

another competent vector.32,34,38,39Because the geographical

distributions of the two species are dynamic and imprecisely

known and because the relative importance of each species to

YFV transmission is not well-understood, we did not attempt

to model any differences between them.

Beyond the parameterization assumptions above, one of the

most important assumptions that we make is that local transmis-

sion is a mass action-based process. There is ample evidence to

suggest that virus transmission by Ae. aegypti is highly focal,40–43

thus treating each city as a single pool of individuals all

experiencing equal exposure risk masks significant underlying

heterogeneity. However, our primary interest is the probability

of spread between populations, and the local heterogeneity is

likely of little importance. Perhaps most critical to the subject of

interest here is the simple fact that not all travelers are equiva-

lent. It is well-documented that travelers visiting friends and

family are more likely to stay longer, stay in homes rather

than hotels, and be infected by pathogens while traveling.44–49

Unfortunately, adding more local heterogeneity for human and

vector interaction would require parameterization beyond the

reach of available data, especially when applied globally.

356

JOHANSSON AND OTHERS

Page 9

Lastly, we made significant simplifications regarding the

immune status of the populations. We assumed either com-

plete susceptibility or partial immunity on the population

scale because of vaccination at a level consistent with the

reported country-wide rates, which do not necessarily reflect

immunity in the cities. Furthermore, vaccines are not the only

source of immunity. Some populations have experienced natu-

ral exposure, and others may have acquired some degree of

cross-immunity because of exposure to other flaviviruses. For

example, cross-protection afforded by prior dengue virus expo-

sure is a principal hypothesis for why YFV has not emerged

in Asia, where competent vectors and dengue viruses are

ubiquitous.50,51Because of these complications and a lack of

data to address them on a global scale, more accurate estima-

tion of YFV susceptibility is a formidable challenge.

General conclusions. The models presented here provide

general approaches to assessing the risk of vector-borne

disease spread by infected travelers. Despite their limitations,

these models may serve as useful tools and starting points for

future models of vector-borne disease spread and interventions

designed to reduce the risk of spread. The models also represent

formal hypotheses about the YFV transmission system and travel

network, which is detailed in Materials and Methods and Supple-

mental Information. We found that the most critical predictors

of disease spread are the rates of travel, number of infected

individuals, general transmission parameters (RHV

and vaccination rates when vaccines are concerned. With esti-

mates of these components, calculation of the probability of intro-

duction and autochthonous transmission can easily be estimated

for any ongoing outbreak. Meanwhile, as improved estimates of

transmission components and travel rates become available, they

can be incorporated into complete mechanistic models, enabling

more detailed analyses of a wider variety of potential outcomes.

0

and RVH

0

),

Received July 5, 2011. Accepted for publication October 9, 2011.

Note: Supplemental information appears online at www.ajtmh.org.

Acknowledgments: This work was partly supported by the Centers for

Disease Control and Prevention Preparedness Modeling Initiative.

Authors’ addresses: Michael A. Johansson and Neysarı ´ Arana-

Vizcarrondo, Division of Vector-Borne Diseases, Centers for Disease

Control and Prevention, San Juan, Puerto Rico, E-mails: mjohan

sson@cdc.gov and nnarana@gmail.com. Brad J. Biggerstaff and

J.Erin Staples, Division ofVector-BorneDiseases, Centers for Disease

Control and Prevention, Fort Collins, CO, E-mails: bbiggerstaff@

cdc.gov and estaples@cdc.gov. Nancy Gallagher and Nina Marano,

Division of Global Migration and Quarantine, Centers for Disease

Control and Prevention, Atlanta, GA, E-mails: ngallagher@cdc.gov

and nmarano@cdc.gov.

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