Cholera Transmission in Ouest Department of Haiti: Dynamic Modeling and the Future of the Epidemic

Abstract

In the current study, a comprehensive, data driven, mathematical model for cholera transmission in Haiti is presented. Along with the inclusion of short cycle human-to-human transmission and long cycle human-to-environment and environment-to-human transmission, this novel dynamic model incorporates both the reported cholera incidence and remote sensing data from the Ouest Department of Haiti between 2010 to 2014. The model has separate compartments for infectious individuals that include different levels of infectivity to reflect the distribution of symptomatic and asymptomatic cases in the population. The environmental compartment, which serves as a source of exposure to toxigenic V. cholerae, is also modeled separately based on the biology of causative bacterium, the shedding of V. cholerae O1 by humans into the environment, as well as the effects of precipitation and water temperature on the concentration and survival of V. cholerae in aquatic reservoirs. Although the number of reported cholera cases has declined compared to the initial outbreak in 2010, the increase in the number of susceptible population members and the presence of toxigenic V. cholerae in the environment estimated by the model indicate that without further improvements to drinking water and sanitation infrastructures, intermittent cholera outbreaks are likely to continue in Haiti. Based on the model-fitted trend and the observed incidence, there is evidence that after an initial period of intense transmission, the cholera epidemic in Haiti stabilized during the third year of the outbreak and became endemic. The model estimates indicate that the proportion of the population susceptible to infection is increasing and that the presence of toxigenic V. cholerae in the environment remains a potential source of new infections.

Full text

RESEARCH ARTICLE
Cholera Transmission in Ouest Department
of Haiti: Dynamic Modeling and the Future of
the Epidemic
Alexander Kirpich
1,2
, Thomas A. Weppelmann
2,3
, Yang Yang
1,2
, Afsar Ali
2,3
,J.
Glenn Morris Jr.
2,4
, Ira M. Longini
1,2
*
1Department of Biostatistics, College of Public Health and Health Professions and College of Medicine,
University of Florida, Gainesville, Florida, United States of America, 2Emerging Pathogens Institute,
University of Florida, Gainesville, Florida, United States of America, 3Department of Environmental and
Global Health, College of Public Health and Health Professions, University of Florida, Gainesville, Florida,
United States of America, 4Department of Medicine, College of Medicine, University of Florida, Gainesville,
Florida, United States of America
*ilongini@ufl.edu
Abstract
In the current study, a comprehensive, data driven, mathematical model for cholera trans-
mission in Haiti is presented. Along with the inclusion of short cycle human-to-human trans-
mission and long cycle human-to-environment and environment-to-human transmission,
this novel dynamic model incorporates both the reported cholera incidence and remote
sensing data from the Ouest Department of Haiti between 2010 to 2014. The model has
separate compartments for infectious individuals that include different levels of infectivity to
reflect the distribution of symptomatic and asymptomatic cases in the population. The envi-
ronmental compartment, which serves as a source of exposure to toxigenic V. cholerae,is
also modeled separately based on the biology of causative bacterium, the shedding of V.
cholerae O1 by humans into the environment, as well as the effects of precipitation and
water temperature on the concentration and survival of V. cholerae in aquatic reservoirs.
Although the number of reported cholera cases has declined compared to the initial out-
break in 2010, the increase in the number of susceptible population members and the pres-
ence of toxigenic V. cholerae in the environment estimated by the model indicate that
without further improvements to drinking water and sanitation infrastructures, intermittent
cholera outbreaks are likely to continue in Haiti.
Author Summary
Based on the model-fitted trend and the observed incidence, there is evidence that after an
initial period of intense transmission, the cholera epidemic in Haiti stabilized during the
third year of the outbreak and became endemic. The model estimates indicate that the pro-
portion of the population susceptible to infection is increasing and that the presence of
toxigenic V. cholerae in the environment remains a potential source of new infections.
PLOS Neglected Tropical Diseases | DOI:10.1371/journal.pntd.0004153 October 21, 2015 1 / 12
OPEN ACCESS
Citation: Kirpich A, Weppelmann TA, Yang Y, Ali A,
Morris JG, Jr., Longini IM (2015) Cholera
Transmission in Ouest Department of Haiti: Dynamic
Modeling and the Future of the Epidemic. PLoS Negl
Trop Dis 9(10): e0004153. doi:10.1371/journal.
pntd.0004153
Editor: Claudia Munoz-Zanzi, University of
Minnesota, UNITED STATES
Received: March 24, 2015
Accepted: September 19, 2015
Published: October 21, 2015
Copyright: © 2015 Kirpich et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any
medium, provided the original author and source are
credited.
Data Availability Statement: All relevant data are
within the paper and its Supporting Information files.
Funding: This work was funded by NIH grants R01
AI097405 and U54 314 GM111274. The funders had
no role in study design, data collection and analysis,
decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared
that no competing interests exist.

Given the lack of adequate improvements to drinking water and sanitation infrastructure,
these conditions could facilitate ongoing, seasonal cholera epidemics in Haiti.
Introduction
After a massive earthquake struck the island nation of Haiti in 2010, the introduction of an
altered El Tor biotype of Vibrio cholerae O1 has led to one of the largest cholera outbreaks in
recent history [1][2][3]. Almost four years after the identification of the first cholera cases, the
transmission appears to have temporarily slowed, however the future of the cholera epidemic
in Haiti remains uncertain [4]. After the initial isolation of toxigenic V. cholerae O1 from sur-
face water monitoring sites in the Ouest Department of Haiti in 2012 and 2013, there is evi-
dence that the frequency of isolation from the environment has actually increased between
2013 and 2014 [5][6]. In the absence of ongoing transmission, the presence of toxigenic V. cho-
lerae O1 in the aquatic environment has left the international scientific community divided on
the possibility that the causative bacterium has established environmental reservoirs in the sur-
face waters of Haiti [7][8][9]. If this were to be the case, the goal of cholera elimination from
the island of Hispaniola by 2022 would be more challenging, with the potential for cholera to
become endemic in Haiti [10].
To assist in the planning and allocation of resources necessary to mitigate the outbreak,
mathematical models have been developed to investigate the underlying dynamics of cholera
transmission in Haiti. [11]. However, despite empirical evidence that V. cholerae O1 is increas-
ingly present in the surface water as reported cases continue to decline, none of the previous
models have considered the role of environmental reservoirs in cholera transmission [6].
Though the environmental compartment has been included in the models, it is assumed that
V. cholerae O1 occupy a transient state where after being shed from the human host they will
eventually become removed from the environment at a constant rate of decay [12]. However,
in endemic countries, this assumption is often likely to be false; where V. cholerae O1 is able to
persist and multiply in the environment in response to an influx of nutrients into surface
waters after rainfall events or increases in water temperature leading to recurrent outbreaks
after interepidemic periods where very few cases were reported [13]. Since both water tempera-
ture and rainfall have been associated with increased isolation frequency of toxigenic V. cho-
lerae O1 in Haiti [6], a dynamic cholera transmission model was created with the additional
mechanism by which the environmental compartment responds to factors such as precipita-
tion and surface water temperature that increase the concentration of the organism in the
aquatic environment. Hopefully, these extra parameters will assist in the understanding of the
underlying processes of cholera transmission in Haiti and allow for more accurate prediction
of the potential for future outbreaks.
Methods
To reflect the basic differences in the modes of transmission, the model incorporates both the
short cycle transmission from human-to-human and long cycle transmission from human-to-
environment and environment-to-human. The short route relies on data suggesting that toxi-
genic V. cholerae assumes a short-lived hyperinfectious state immediately after passage from
the human intestine [14]. This facilitates rapid transmission of V. cholerae from one person to
another, often related to personal hygiene practices within the household. Alternatively, trans-
mission may occur when V. cholerae is acquired from contaminated drinking water or by con-
tact with the aquatic environment. The presence of toxigenic V. cholerae in the aquatic
Modeling Cholera Transmission in Ouest Department of Haiti
PLOS Neglected Tropical Diseases | DOI:10.1371/journal.pntd.0004153 October 21, 2015 2 / 12

environment may reflect contamination of water sources by feces from an infected individual,
and/or the existence of an aquatic reservoir in which the microorganism can persist for months
to years [13]. Transmission through this aquatic route, while still having the potential for being
relatively rapid, tends to involve more time than the short cycle transmission between humans.
In the model, separate compartments for infectious symptomatic and infectious asymptom-
atic cases are used, even though it is not possible to estimate the size of the asymptomatic com-
partment. This is done to increase the model flexibility and to provide the option for sensitivity
analysis. Dichotomization between symptomatic and asymptomatic cases also provides the
option to address different infectivity levels for symptomatic and asymptomatic infections. The
model has the following compartments:
•S(t)—number of susceptible people at time t.
•A(t)—number of asymptomatic people at time t.
•I(t)—number of symptomatic people at time t.
•R(t)—number of recovered people at time t.
•W(t)—bacteria concentration in the water at time t(environmental compartment.)
The model diagram and the relationships between the model compartments and the
observed data are summarized visually in the diagram provided in Fig 1.
In the model the movement of people between the compartments S,A,I,Ris considered
along with the growth and death of bacteria within the environmental compartment W. The
system of ordinary differential equations (ODE) that defines our model has the form:
dSðtÞ
dt ¼mRSRðtÞðmW
SA þmW
SI ÞSðtÞfðtÞðmH
SA þmH
SI ÞSðtÞðAðtÞþIðtÞÞ
dAðtÞ
dt ¼mW
SASðtÞfðtÞþmH
SASðtÞðAðtÞþIðtÞÞmAR AðtÞ
dIðtÞ
dt ¼mW
SI SðtÞfðtÞþmH
SI SðtÞðAðtÞþIðtÞÞmIRIðtÞ
dRðtÞ
dt ¼mARAðtÞþmIR IðtÞmRSRðtÞ
dWðtÞ
dt ¼gðtÞðmAW AðtÞþmIW IðtÞÞþhðtÞmðtÞWðtÞgWðtÞWðtÞ
ð1Þ
In the model equations μand γindicate the transition rates with corresponding subscripts and
superscripts that indicate the direction and the nature of the movement. The superscript H
indicates the rates responsible for human-to-human transmission and superscript Windicates
the rates responsible for environment-to-human transmission.
To address the dynamic of the environmental compartment three main process that affect
bacterial growth and survival in the environment were considered.
The first process is the influx of bacteria via shedding by infected human hosts into the envi-
ronment. Once shed into the environment the bacteria provide a source of exposure for suscep-
tible humans. Those processes are modeled by the functions:
fðtÞ¼ WðtÞ
kþWðtÞand gðtÞ¼ rðtÞ
dþrðtÞ:
The notations ρ(t) for the total weekly precipitation in mm and τ(t) for average weekly temper-
ature in degrees Celsius at time tare used. Here κand δare the threshold parameters.
Modeling Cholera Transmission in Ouest Department of Haiti
PLOS Neglected Tropical Diseases | DOI:10.1371/journal.pntd.0004153 October 21, 2015 3 / 12

The second process is the multiplication of the bacteria in the environment, which is
affected by both temperature and precipitation. This process is modeled by functions h(t) and
m(t):
hðtÞ¼aexp ðrðtÞrcÞ2
2s2

þbtðtÞand mðtÞ¼1WðtÞ
w¼wWðtÞ
w:
Here α,ρ
c
,σand βare the parameters of interest and χis the cap designed to constrain the
excessive growth of bacteria in the environment.
The functional form m(t) represents the logistic growth multiplier widely used in popula-
tion dynamic models. This multiplier allows the growth to be proportional to the current bacte-
rial concentration W(t) and limits the excessive growth when concentration approaches the
limiting capacity using the cap parameter χ.
The proposed multiplier h(t) has a novel structure. In the model it is assumed that bacterial
growth is linearly related to the current temperature which is controlled by parameter β. Pre-
cipitation is assumed to have a maximum effect on the bacterial growth at the value ρ
c
.Itis
assumed that for smaller amounts of precipitation than ρ
c
there is not enough water to wash
the bacteria into the environment which causes slower growth. For amounts of precipitation
above ρ
c
bacteria becomes diluted which diminishes the rate of bacterial growth in the
Fig 1. Compartmental model diagram. The unobserved compartmental SIRS model is linked to the
observed data via a set of modeling assumptions. Blue boundary circular objects are the unobserved
compartments of the SIRS model with the environmental compartment W. Black boundary square objects
represent the collected observed data where Ostands for the reported incidence and Tand Pstand for the
environmental measurements of temperature and precipitation respectively. Temperature and precipitation
affect the environmental reservoir W. The orange arrows indicate the movement of individuals between the
human compartments. The grey arrows represent other processes in the model that do not directly involve
the movement of humans between compartments. The actual bacterial movements such as human shedding
and bacteria death are represented by solid grey lines. The other processes in the model such as the
influence of temperature and precipitation on bacterial growth, the influence of aquatic reservoir and infected
humans on transmission, and the relationship between the reported incidence Oand the unobserved
symptomatic incidence are represented by dashed grey lines. Please refer to S1 Text for more details on the
model formulation, parametrization and relevant assumptions.
doi:10.1371/journal.pntd.0004153.g001
Modeling Cholera Transmission in Ouest Department of Haiti
PLOS Neglected Tropical Diseases | DOI:10.1371/journal.pntd.0004153 October 21, 2015 4 / 12

environment. Graphically, the function h(t) has a bell-shaped curve where αand σ
2
are the cali-
bration parameters of inferential interest.
The last process in the environmental reservoir is the natural decay (death) of bacteria in
the environment which is modeled by the time-varying death rate γ
W−
(t).
Please refer to the supplement S1 Text for more technical details on model formulation and
assumptions. Overall, the model defined by Eq (1) is neither identifiable (i.e., there are too
many unknown parameters) nor estimable without extra assumptions [15]. Only precipitation,
temperature and the symptomatic compartment I(if underreporting is accounted for) can be
treated as observed. To summarize, a Susceptible-Infected-Recovered-Susceptible (SIRS)
model has been implemented, where the V. cholerae concentration in the water is modeled via
the environmental compartment W.
In the model the SIRS piece is linked to the reported incidence via the symptomatic com-
partment Iusing the reporting probability p
r
. The reported incidence was adjusted before esti-
mation by dividing it by the assumed reporting probability p
r
. To avoid identifiability issues,
extra assumptions about the model parameters and the model itself are made. Since the period
of time under consideration was very short, the population size was considered to be constant.
Please refer to the supplement S2 Text for more technical details about the model
parametrization.
To account for the uncertainty in the deterministic model defined by the ordinary differen-
tial Eq (1) stochastic Gaussian terms were introduced into the model equations. The stochastic
model was fitted to the reported incidence by using the least squares estimation (LSE)
approach. Please refer to the supplement S3 Text for details on stochastic model fitting.
Data were collected from multiple sources. The reported cholera incidence for the Ouest
Department of Haiti, including the capital Port-au-Prince, was collected by the Haitian Minis-
try of Health (Ministère de la Santé Publique et de la Population (MSPP) in French) and com-
piled by the Pan American Health Organization (PAHO) [16][4]. The weekly incidence of
cholera cases was available from October 17, 2010 until April 27, 2014. Daily precipitation (in
millimeters) was obtained from the Tropical Rainfall Measuring Mission (TRMM) satellite
data [17], and daily temperatures (in Celsius) were obtained from the Port-au-Prince airport
(IATA: PAP) monitoring station. The temperature readings were missing for 14.6% of the
dates and the missing values were linearly interpolated. Precipitation data did not have any
missingness. The environmental data were aggregated weekly so that it could be aligned with
the incidence data. The average weekly temperature τ(t) and cumulative weekly precipitation ρ
(t) were used as covariates.
In the analysis, it was assumed that there was no time lag for temperature, whereas there
was a 7-week lag for precipitation when we evaluated the environmental effects on the water
compartment in the model. We did not observe any lag for the temperature from the data.
Temperature had only a mild correlation with reported cholera incidence, and the empirical
evidence suggested that the association between water temperature and isolations of toxigenic
V. cholerae from the environment was the strongest with a time lag of 0 to 1 month [6]. At the
same time a seven-week lag maximizes the sample correlation between total weekly precipita-
tion and weekly reported cholera incidence. Moreover, there is empirical evidence that the bac-
teria concentration peaks in the environments three to four weeks after the rainfall, which is
associated with an increase in the incidence approximately four weeks later [6]. Thus, a seven
week time lag for precipitation was considered plausible. A visual presentation of aligned time
series of incidence, temperature and seven-week-lagged precipitation is shown in Fig 2.
The transmissibility of a pathogen in a susceptible population is often measured using the
basic reproductive number. Unfortunately, because of the complexity of the model, time-
dependent covariates, and the multiple types of sources of infection (humans and the aquatic
Modeling Cholera Transmission in Ouest Department of Haiti
PLOS Neglected Tropical Diseases | DOI:10.1371/journal.pntd.0004153 October 21, 2015 5 / 12

environment), there was no straightforward epidemiological interpretation of R0for this
model. Moreover, in this model R0was technically time dependent because of the time depen-
dent environmental covariates and phage dependent bacterial death rate. The details on the
computation of the the basic reproductive number are provided in the supplement S4 Text.
Results
The obtained model fit provided a good understanding of the dynamics of the epidemic over
time. The visual summary of the model fit together with the adjusted reported cholera inci-
dence is shown in Fig 3. First, the reported incidence was adjusted by rescaling to account for
disease underreporting and plotted in orange in Fig 3 for better visual comparison with the
model output. To produce the model realizations a different Gaussian white noise time series
was generated for each set of 1000 parameter estimates obtained from the previous LSE fits.
The corresponding model outputs are displayed in Fig 3. The transparency was tuned to
Fig 2. Data collected from the Ouest Department of Haiti. From the top to the bottom: new cases reported weekly, average weekly temperature, and total
weekly precipitation with a 7 week lag. Polynomial smoothers (loess function in R) are plotted over each time series to provide better visualization of the
mean trends.
doi:10.1371/journal.pntd.0004153.g002
Modeling Cholera Transmission in Ouest Department of Haiti
PLOS Neglected Tropical Diseases | DOI:10.1371/journal.pntd.0004153 October 21, 2015 6 / 12

Fig 3. Visual representation of the model fit. A) 1000 Realizations of symptomatic infections producedby the model. B) 1000 Realizations of symptomatic
and total infections produced by the model.
doi:10.1371/journal.pntd.0004153.g003
Modeling Cholera Transmission in Ouest Department of Haiti
PLOS Neglected Tropical Diseases | DOI:10.1371/journal.pntd.0004153 October 21, 2015 7 / 12

display the density of the curves in each part of the graph and to improve visualization. The
symptomatic cases produced by the model are displayed in dark green in panel Aof Fig 3. The
realizations of both the symptomatic (dark green) and total (light green) cases produced by the
model are displayed for comparison in panel Bof Fig 3 on a different scale. The total underly-
ing realizations of the model that include both symptomatic and asymptomatic infections are
much larger than the symptomatic realizations alone.
The peak precipitation effect was estimated at ^
rc¼45:1mm with 95% CI (43.0; 47.3) and
the threshold parameter for the effect of shedding at ^
d¼27:0mm with 95% CI (6.7; 101.3),
which was estimated to be more variable than ^
rc. Those estimates did not change much from
the starting points that were used for the iterative LSE minimization procedure, indicating the
potential lack of information in the data about ρ
c
and σ. The estimate for the effect of tempera-
ture had a median value much higher than the mean value, which indicated a heavy left tail.
The median was used over 1000 realizations instead of the mean βto provide a more robust
estimate. The estimate for ^
bwas 0.014 with 95% CI (−0.041; 0.027), which led to the conclusion
that temperature had a mild association with V. cholerae growth. The complete list of parame-
ters is provided in Table A in S3 Text.
If a single estimate for R0that summarizes the epidemic behavior is desired, a reasonable
approach is to use the averaged values of the time dependent covariates and bacterial death
rate to obtain the average estimate ^
R0¼1:6with 95% CI (1.3, 2.1) based on the mean of 1000
stochastic realizations. Alternatively, one may extend the definition of the basic reproductive
number to allow for time-dependent covariates and denote it by R0ðtÞ. Readers please refer to
the supplement S4 Text for details. Another useful measure is the time-dependent effective
reproductive number RðtÞwhich is defined as a product of the basic reproductive number
R0ðtÞand the proportion of susceptibles at a given time t. The change in the value of the esti-
mated basic reproductive number ^
R0ðtÞ(using the extended definition) and the estimated
effective reproductive number ^
RðtÞover time are shown in panel Bof Fig 4.
Additional characteristics of the epidemic are illustrated in Fig 4. In panel Athe reported
incidence adjusted for underreporting and the pointwise prediction bands for symptomatic
infections are displayed. As shown the pointwise prediction bands were able to capture the
majority the dynamics of the cholera epidemic. In panel Cthe concentration of V. cholerae in
the environment and the corresponding prediction bands are shown over time. In panel Dthe
changes in the proportion of the susceptible individual during the course of the epidemic pro-
duced by the model and corresponding prediction bands are shown.
Based on the trend produced by the model and the observed incidence displayed in panel A,
it was concluded that the epidemic of cholera likely stabilized in Ouest Department of Haiti
after three years of transmission and became endemic. In the model output displayed in panel
Dthe proportion of susceptible individuals at the end of the epidemic remains very high and is
gradually increasing, which provides the necessary conditions to facilitate further cholera
transmission. Furthermore, as displayed in panel C, since the concentration of toxigenic V.
cholerae in the environment produced by the model remains sufficiently high at the end of the
observation period, it is also likely that future cholera outbreaks will occur.
Discussion
In this work, a dynamic model that incorporated the available environmental data was used to
describe the transmission of cholera in Ouest Department of Haiti. The model output sug-
gested the existence of a large environmental reservoir of toxigenic V. cholerae that reached a
peak concentration early in 2012, with a subsequent slow decline (Fig 4). The presence of such
Modeling Cholera Transmission in Ouest Department of Haiti
PLOS Neglected Tropical Diseases | DOI:10.1371/journal.pntd.0004153 October 21, 2015 8 / 12

Fig 4. The behavior of the epidemic over time. A) Pointwise prediction bands for the symptomatic
infections produced by the model. B) The change in the value of the estimated basic reproductive number
^
R0ðtÞ(using extended definition) and in the value of the estimated effective reproductive number ^
RðtÞover
time. C) V. cholerae concentration in the environment over time and the corresponding prediction bands. D)
Change in the proportion of the susceptible individuals during the course of the epidemic produced by the
model and the corresponding prediction bands.
doi:10.1371/journal.pntd.0004153.g004
Modeling Cholera Transmission in Ouest Department of Haiti
PLOS Neglected Tropical Diseases | DOI:10.1371/journal.pntd.0004153 October 21, 2015 9 / 12

an environmental reservoir was consistent with environmental studies conducted in the Leo-
gane flood basin of the Ouest Department, which identified V. cholerae O1 in multiple river
and estuarine ecosystems [5][6]. A similar trend was observed in the human susceptible com-
partment of the model, where the smallest number of susceptible population members was
observed in early 2012, with a slow but steady increase since that time (Fig 4).
The model of the cholera epidemic in Haiti described by this study was novel in the way in
which the environmental compartment was considered. As previously mentioned, most previ-
ous dynamic models of the cholera epidemic in Haiti postulated that toxigenic V. cholerae only
occupy a transient state in the environment, where pathogenic bacteria shed into the surface
water by humans decay at a constant rate and cannot increase without additional cases. This
assumption precludes the ability for toxigenic V. cholerae to become more prevalent in the
environment during periods of decreased cholera incidence and does not explain the resur-
gence of cholera cases after inter-epidemic periods; both of which have recently been observed
in Haiti [4][6].
As with any mathematical model of infectious disease transmission, this approach was not
without limitations. One important theoretical concern was the assumption of homogenous
mixing. The contact transition rates between compartments assume homogenous mixing and
do not account for the local population density, presence of human mobility networks, and
personal hygiene practices within households [18]. Likewise, the contact rates between humans
and the environment are also dependent on the proportion of the population that consume
contaminated surface water, which varies between urban and rural areas and by demographic
factors [19][20]. Besides the reliance of our model on previously published estimates of some
parameters, there are also unobserved processes that occurred during the epidemic, such as
increased consumption of bottled water in urban areas of up to 38% and the fluctuation in the
number of cholera treatment centers (CTC) as the incidence began to decline [21][22]. How-
ever, the demographic data as well as the number of interventions applied from the interna-
tional network of aid organizations are also difficult to quantify, making their inclusion in the
model speculative at best.
Thus far, only a single serological study of cholera in Haiti was conducted in high-risk popu-
lations near the Artibonite River six months after the onset of the epidemic, which reported
that 39% of the participants had antibody titers consistent with a recent cholera infection [23].
Our model, which used incidence data from the neighboring Ouest Department, where the
onset of the epidemic occurred later, showed a projected population proportion of susceptibles
that was somewhat higher at that time. Aside from the one study cited, there have been no fur-
ther serologic studies reported in Haiti, so it is not possible to comment directly on the validity
of the model’s projections. Nonetheless, a rising proportion of susceptibles is plausible, given
the anticipated waning of immunity to El Tor cholera over time, and a birth rate that is over
40% higher than other developing countries in Latin America and the Caribbean [24][25]. The
combination of environmental reservoirs of toxigenic V. cholerae, lack of adequate sanitation
and hygiene infrastructure, and a slowly rising proportion of susceptible population members
suggests that seasonal epidemics are likely to be observed in the future. Furthermore, there
remains the possibility of major cholera epidemics following hurricanes that generate severe
flooding or other environmental disasters that could damage the existing sanitation and drink-
ing water infrastructure. Given the potential for future cholera outbreaks and the demonstrated
efficacy of the oral cholera vaccine in Haiti, it would be useful to have epidemic mitigation
plans in place that include provisions for the use of the WHO mobile stockpile of cholera vac-
cine [26][27].
Modeling Cholera Transmission in Ouest Department of Haiti
PLOS Neglected Tropical Diseases | DOI:10.1371/journal.pntd.0004153 October 21, 2015 10 / 12

Supporting Information
S1 Text. Model formulation. This section describes how the proposed model is formulated in
terms of ordinary differential equations (ODE), and how the environmental data are incorpo-
rated into the model.
(PDF)
S2 Text. Model parametrization. Model parameters are defined and explained in this section,
including which parameters are fixed at empirical values based on literature review, and which
are estimated from the data.
(PDF)
S3 Text. Stochastic LSE Approach. How stochastic components are added to the differential
equations and how the model is fitted are described in this section.
(PDF)
S4 Text. Estimation of the basic reproductive number R0.This section gives the definition
and derivation of the basic reproductive number R0for the proposed model. The challenges of
defining R0in the presence of time-varying transition rates are discussed.
(PDF)
Acknowledgments
The authors would like to thank Eben Kenah Ph.D. and Juliet Pulliam Ph.D. for their help and
critical reviews.
Author Contributions
Conceived and designed the experiments: AK TAW YY AA JGM IML. Performed the experi-
ments: AK TAW YY AA JGM IML. Analyzed the data: AK TAW YY AA JGM IML. Contrib-
uted reagents/materials/analysis tools: AK TAW YY AA JGM IML. Wrote the paper: AK TAW
YY AA JGM IML. Worked on the literature review, performed the data analysis and corre-
sponding estimation, outputs and graphs: AK TAW. Participated in discussions and interpre-
tation of the results: AK TAW YY AA JGM IML.
References
1. Barzilay EJ, Schaad N, Magloire R, Mung KS, Boncy J, Dahourou GA, et al. (2013) Cholera surveil-
lance during the Haiti epidemic–the first 2 years. N Engl J Med 368(7):599–609. PMID: 23301694
2. Ali A, Chen Y, Johnson JA, Redden E, Mayette Y, Rashid MH, et al. (2011) Recent clonal origin of chol-
era in Haiti. Emerg Infect Dis 17(4):699–701. doi: 10.3201/eid1704.101973 PMID: 21470464
3. Tappero JW, Tauxe RV. (2011) Lessons Learned during Public Health Response to Cholera Epidemic
in Haiti and the Dominican Republic. Emerging Infectious Diseases 17(11):2087–2093. doi: 10.3201/
eid1711.110827 PMID: 22099111
4. Pan American Health Organization. (2014) Interactive atlas of the cholera outbreak in la Hispaniola,
2010–2014. http://new.paho.org/hq/images/Atlas_IHR/CholeraHispaniola/atlas.html Accessed March
2015.
5. Alam MT, Weppelmann TA, Weber CD, Johnson JA, Rashid MH, Birch CS, et al. (2014) Monitoring
water sources for environmental reservoirs of toxigenic Vibrio cholerae O1, Haiti. Emerg Infect Dis
2014; 20(3):356–63. doi: 10.3201/eid2003.131293 PMID: 24571741
6. Alam MT, Weppelmann TA, Longini I, De Rochars VM, Morris JG Jr, Ali A. (2015) Increased isolation
frequency of toxigenic Vibrio cholerae O1 from environmental monitoring sites in Haiti. PLoS One 2015;
10(4):e0124098. doi: 10.1371/journal.pone.0124098 PMID: 25853552
7. Baron S, Lesne J, Moore S, Rossignol E, Rebaudet S, Gazin P, et al. (2013) No Evidence of Significant
Levels of Toxigenic V. cholerae O1 in the Haitian Aquatic Environment During the 2012 Rainy Season.
Modeling Cholera Transmission in Ouest Department of Haiti
PLOS Neglected Tropical Diseases | DOI:10.1371/journal.pntd.0004153 October 21, 2015 11 / 12

PLoS Curr 2013; 5. doi: 10.1371/currents.outbreaks.7735b392bdcb749baf5812d2096d331e PMID:
24077904
8. Kahler AM, Haley BJ, Chen A, Mull BJ, Tarr CL, Turnsek M, et al. (2015) Environmental surveillance for
toxigenic Vibrio cholerae in surface waters of Haiti. Am J Trop Med Hyg 92(1):118–25. doi: 10.4269/
ajtmh.13-0601 PMID: 25385860
9. Stanislas R, Renaud P. (2015) Monitoring Water Sources for Environmental Reservoirs of Toxigenic
Vibrio cholerae O1, Haiti. Emerging Infectious Disease journal 21(1):169. doi: 10.3201/eid2101.
140627
10. Haitian Ministry of Public Health and Population (MSPP). National plan for the elimination of cholera in
Haiti 2013–2022. 2012.
11. Fung IH (2014) Cholera transmission dynamic models for public health practitioners. Emerging Themes
in Epidemiology 11(1):1–11. doi: 10.1186/1742-7622-11-1 PMID: 24520853
12. Bertuzzo E, Finger F, Mari L, Gatto M, Rinaldo A (2014) On the probability of extinction of the Haiti chol-
era epidemic. Stochastic Environmental Research and Risk Assessment.
13. Vezzulli L, Pruzzo C, Huq A, Colwell RR (2010) Environmental reservoirs of Vibrio cholerae and their
role in cholera. Environmental Microbiology Reports 2010; 2(1):27–33. doi: 10.1111/j.1758-2229.2009.
00128.x PMID: 23765995
14. Hartley DM, Morris JG Jr, Smith DL (2006) Hyperinfectivity: A critical element in the ability of V. cholerae
to cause epidemics? PLoS Med 3:7. doi: 10.1371/journal.pmed.0030007
15. Eisenberg MC, Robertson SL and Tien JH. (2013). Identifiability and estimation of multiple transmission
pathways in cholera and waterborne disease. Journal of theoretical biology, 324, 84.102. doi: 10.1016/
j.jtbi.2012.12.021 PMID: 23333764
16. Haitian Ministry of Public Health and Population (MSPP). Daily reports of cholera cases by commune.
May 2014 [cited March 2015]. http://mspp.gouv.ht/newsite/documentation.php
17. NASA. NASA earth data daily: TRMM and other satellites precipitation product. (3B42 V7 derived)
(TRMM_3B42_daily). 2014 [cited March 2015]. http://mirador.gsfc.nasa.gov/cgi-bin/mirador.
18. Mari L, Bertuzzo E, Righetto L, Casagrandi R, Gatto M, Rodriguez-Iturbe I, et al. Modelling cholera epi-
demics: the role of waterways, human mobility and sanitation. Journal of The Royal Society Interface.
2011; 9(67):376–88. doi: 10.1098/rsif.2011.0304
19. Patrick M, Berendes D, Murphy J, Bertrand F, Husain F, Handzel T. Accessto Safe Water in Rural Arti-
bonite, Haiti 16 Months after the Onset of the Cholera Epidemic. The American Journal of Tropical Med-
icine and Hygiene. 2013; 89(4):647–53. doi: 10.4269/ajtmh.13-0308 PMID: 24106191
20. Lund AJ, Keys HM, Leventhal S, Foster JW, Freeman MC. Prevalence of cholera risk factors between
migrant Haitians and Dominicans in the Dominican Republic. Pan American journal of public health.
2015; 37(3):125–32. PMID: 25988248
21. Archibold RC and Sengupta S. UN Struggles to Stem Haiti Cholera Epidemic. The New York Times.
Published April 19, 2014. Cited August 13 from http://www.nytimes.com/2014/04/20/world/americas/
un-struggles-to-stem-haiti-cholera-epidemic.html.
22. Demographic and Health Surveys. STATcomiler: Haiti from 2005–6 to 2012. ICF International. 2012
[cited February 13, 2015]. Available from: http://www.statcomplier.com
23. Jackson BR, Talkington DF, Pruckler JM, Fouché MDB, Lafosse E, Nygren B, et al. Seroepidemiologic
Survey of Epidemic Cholera in Haiti to Assess Spectrum of Illness and Risk Factors for Severe Dis-
ease. The American Journal of Tropical Medicine and Hygiene. 2013; 89(4):654–64. doi: 10.4269/
ajtmh.13-0208 PMID: 24106192
24. Clemens JD, van Loon F, Sack DA, Rao MR, Ahmed F, Chakrabort YJ, et al. Biotype as determinant of
natural immunising effect of cholera. Lancet (London, England). 1991; 337(8746):883–4. doi: 10.1016/
0140-6736(91)90207-6
25. The World Bank Group. Global birth rate online database. 2013 [cited August 15, 2015]. Available from:
http://data.worldbank.org/indicator/SP.DYN.CBRT.IN/countries
26. Ivers LC, Hilaire IJ, Teng JE, Almazor CP, Jerome JG, Ternier R, et al. Effectiveness of reactive oral
cholera vaccination in rural Haiti: a case-control study and bias-indicator analysis. The Lancet Global
health. 2015; 3(3):e162–8. doi: 10.1016/S2214-109X(14)70368-7 PMID: 25701994
27. Chao DL, Halloran ME, Longini IM (2011) Vaccination strategies for epidemic cholera in Haiti with impli-
cations for the developing world. Proceedings of the National Academy of Sciences 108, 7081–85. doi:
10.1073/pnas.1102149108
Modeling Cholera Transmission in Ouest Department of Haiti
PLOS Neglected Tropical Diseases | DOI:10.1371/journal.pntd.0004153 October 21, 2015 12 / 12