Page 1

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

Page 2

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

Page 3

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

Page 4

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

Page 5

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