Congruity of genomic and epidemiological data in modeling of local cholera outbreaks Mateusz Wilinski1 Lauren Castro2 Jerey Keithley23 Carrie Manore1 Josena Campos4 Ethan Romero-Severson1 Daryl Domman5 Andrey Y. Lokhov1

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Congruity of genomic and epidemiological data in modeling of local cholera outbreaks

Mateusz Wilinski1, Lauren Castro2, Jeﬀrey Keithley2,3, Carrie Manore1, Joseﬁna

Campos4, Ethan Romero-Severson1, Daryl Domman5∗, Andrey Y. Lokhov1∗

1Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM USA

2Analytics, Intelligence and Technology Division,

Los Alamos National Laboratory, Los Alamos, NM USA

3Department of Computer Science, University of Iowa, Iowa City, IA, USA

4UO Centro Nacional de Genomica y Bioinform´atica,

ANLIS “Dr. Carlos G. Malbr´an”, Buenos Aires, Argentina and

5Center for Global Health, Department of Internal Medicine,

University of New Mexico Heath Sciences Center, Albuquerque, NM USA

Cholera continues to be a global health threat. Understanding how cholera spreads between lo-

cations is fundamental to the rational, evidence-based design of intervention and control eﬀorts.

Traditionally, cholera transmission models have utilized cholera case count data. More recently,

whole genome sequence data has qualitatively described cholera transmission. Integrating these

data streams may provide much more accurate models of cholera spread, however no systematic

analyses have been performed so far to compare traditional case-count models to the phylody-

namic models from genomic data for cholera transmission. Here, we use high-ﬁdelity case count

and whole genome sequencing data from the 1991-1998 cholera epidemic in Argentina to directly

compare the epidemiological model parameters estimated from these two data sources. We ﬁnd that

phylodynamic methods applied to cholera genomics data provide comparable estimates that are in

line with established methods. Our methodology represents a critical step in building a framework

for integrating case-count and genomic data sources for cholera epidemiology and other bacterial

pathogens.

INTRODUCTION

Cholera is a major public health threat with an esti-

mated 4 million cases a year and over 150,000 deaths an-

nually [1]. Cholera is an acute diarrheal disease caused by

toxigenic Vibrio cholerae, and is transmitted though the

fecal-oral route from contaminated food or water. Cur-

rently, the burden of disease is primarily in sub-Saharan

Africa and South Asia, in vulnerable populations with a

lack of access to clean drinking water and sanitation [2].

Of note, some of the largest cholera epidemics have oc-

curred since the 1990s. Case counts over 1 million were

documented for the 1991-1998 epidemic in Latin America

[3], over 800,000 cases in Haiti from 2010-2020 [4], and

over 2.5 million cases thus far in the ongoing epidemic in

Yemen that began in 2016 [5].

Understanding how cholera is transmitted within and

across populations is paramount to the rational design

and implementation of control eﬀorts. One of the dif-

ﬁculties in traditional modeling of cholera outbreaks

with case-count data alone is that the inference results

strongly depend on the quality of the reporting proce-

dures, while detailed properties of statistical counting

noise are often unknown and can not be easily estimated.

Furthermore, accurate case counting is hampered by the

large heterogeneity in disease presentation which ranges

from asymptomatic to severe cholera [2]. Genetic se-

quence data oﬀers another data source on transmission

dynamics that could help develop a new generation of

∗ddomman@salud.unm.edu, lokhov@lanl.gov

complex, but well constrained cholera models. This is

possible due to the fact that epidemiological processes

such as transmission and migration of infection leave a

trace in pathogen genetic sequence data by changing the

underlying infection genealogy of a sampled set of se-

quences [6–8]. For example, compared to a stable pop-

ulation, in a population experiencing rapid growth, two

randomly selected people will, on average, share a com-

mon ancestor in the distant past [9], and therefore be sep-

arated by a larger number of mutations. Likewise, in oth-

erwise isolated populations, migration links pathogens

though a network of common descent [10] leading to a

distinctive pattern of interdigitated sequences in a phy-

logeny. Therefore, pathogen genetic sequence data has

generally the potential to inform epidemiological param-

eters such as transmission, migration, and mixing rates.

Previous work have used Vibrio cholerae sequence data

to describe the broad, qualitative ﬂow of cholera at the

global scale that can capture broad trends but not ex-

plicit details of the transmission process [11–15]. How-

ever, the main challenge in the eﬀort to integrate ge-

nomic data into cholera transmission models is the lack

of evidence that genomic data are informative of cholera

transmission processes at the local scale, i.e. that there is

suﬃcient genetic diversity in a single-source, local cholera

outbreak to estimate transmission parameters.

Case counts and the genetic sequence data can be

thought of as being two independent observers of the

transmission dynamics of cholera. In this paper, we uti-

lize a rich data-set of both case count data as well as

a large collection of genomic sequencing data from Ar-

gentina [16] to model the spread of cholera and specif-

arXiv:2210.01956v2 [q-bio.QM] 30 Mar 2023

ically address the role of local migration as a driving

factor in cholera transmission. Our goal is to build a

meta-population model with a minimal number of as-

sumptions which accounts for migration, and understand

if the two observers agree in their predictions. The bridg-

ing and common constraints on both sources of data will

be achieved using yet another source of independent data

such as high-ﬁdelity estimation of migration ﬂows.

Our modeling choices are aimed at simplicity and

driven by the overall goal of checking the consistency be-

tween these data sources. For instance, we deliberately

take an agnostic stance on the open questions related to

the role of the environment or details of bacterial dynam-

ics: while several previous studies explicitly included the

environmental compartment [17–21] leading to a larger

number of model parameters, we choose to model cholera

dynamics as an eﬀective transmission process which in-

cludes a periodic functional dependence on the season-

ality, similarly to the approach of [22]. To account for

discreteness in observed cases, we propose a novel sam-

pling model which relates the continuous model with the

discrete observed case counts.

Most of key model parameters will be directly inferred

from case counts and migration data. Further, a sub-

set of most important parameters such as transmission

amplitudes and fraction of asymptomatic infections are

independently inferred from the genomic sequence data,

and compared to models inferred from other data sources

within their uncertainties. In particular, we don’t make

any a priori quantitative assumptions on the fraction

of asymptomatic infections, in previous studies ranging

from 1% to more than 90% of the population [23–25].

Instead, we keep this important model parameter free,

infer its values from data under diﬀerent settings, and

discuss the sensitivity of this parameter to various mod-

eling assumptions. We also provide a series of careful

sensitivity studies that study the stability of the inferred

parameters related to all of our modeling assumptions.

In this paper, we present initial evidence that phylody-

namic methods can be used to study cholera outbreaks

at a regional level and that they produce parameter esti-

mates that are consistent with established methods. Our

approach provides a common methodology for an early

analysis of the model viability in the context of joint in-

ference from diﬀerent data sources. Given the comple-

mentary view oﬀered by independent data sources, we

anticipate that the analysis presented in this paper will

ﬁnd a widespread use in building joint hybrid epidemi-

ological and genetic models which could help verify the

main modeling assumptions.

RESULTS

Integrated data from case counts, genomics,

and transportation data. Cholera was ﬁrst reported

in Argentina in 1992, and subsequent cholera cases were

reported until 1998 [26–30]. Out of the total 4,281 cases

reported, over 3,500 Vibrio cholerae isolates were stored

at INEI-ANLIS “Dr. Carlos G. Malbr´an”, the national

reference laboratory for Argentina, and a representa-

tive sub-sample of 532 of these isolates were previously

whole-genome sequenced [16], see Supplementary Mate-

rials, section A for more details. We sought to deter-

mine if there was agreement between epidemiological and

genomic data. First, we pre-processed the data set by

removing cities with insuﬃcient genomic samples (less

than 40 sequences). This left us with three target cities:

Tartagal, San Ram´on de la Nueva Or´an (both in Salta

province) and San Salvador de Jujuy (in Jujuy province)

located within in the Northwest of Argentina (see Fig.

1). Initial reports in 1992 indicated that cholera was

ﬁrst introduced into Argentina via this region from Bo-

livia, leading to a large outbreak from 1992-1993 [31].

In addition to the epidemiological and sequence data,

we used publicly available data on domestic travel to es-

timate the movement of population between these three

cities during the study period. Focusing on the two pri-

mary means of transportation, ﬂights and buses, we were

able to estimate the typical number of people travelling

daily between the selected cities (for details see Materials

and Methods and Supplementary Materials, section B).

Modeling assumptions. We modeled the cholera

transmission dynamics using a system of ordinary dif-

ferential equations (ODEs) where the population is split

into compartments representing individuals in diﬀerent

states of infection. Typical cholera models are a sys-

tem of ODEs representing a modiﬁcation of the clas-

sical Susceptible-Infected-Recovered (SIR) type model

[32] with varying degrees of complexity (see [17–22, 33]).

Here, we present a new, simple ODE cholera model that

signiﬁcantly advances estimation of key epidemiological

parameters in two ways: (i) we focus on a minimalist

representation which allows us to reliably infer model pa-

rameters from a limited amount of data while introducing

the least amount of assumptions; and (ii) we use a meta-

population structure to leverage the spatial knowledge

on reported cases and travel patterns that can represent

the major spreading mechanism. We also do not con-

sider re-infection in our models of localized outbreaks, as

protective immunity against cholera has been estimated

to last at least 3 years [2]. Prior to formally introduc-

ing our dynamic model, we discuss the main modeling

assumptions behind our approach.

Many cholera models in the literature include an envi-

ronmental compartment [17–21]. Such an environmental

compartment is typically introduced to explicitly model

the transmission of infection through a water source, and

additionally describes the evolution of bacteria in a water

source with a temperature-dependent dynamics. From

the ﬁtting perspective, an environmental component may

have a beneﬁt to help the multi-year epidemic outbreak

(see the span of observed cases in the Supplementary Ma-

terials, Fig. S1) survive the period of cool temperatures

when number of cases drop signiﬁcantly, and re-occur

when the temperature rises. During our initial model

Argentina







Bolivia

β⋅(1−p)

β⋅p

β⋅(1−p)

β⋅p

β⋅(1−p)

β⋅p

f13

f23

f12

FIG. 1: Meta-population model of the cholera transmission dynamics interlayed with a map of the northern

Argentina. Left: Three cities considered in our focused study are marked as follows: Tartagal – green circle, San

Ram´on de la Nueva Or´an (in what follows, referred to as Oran) – blue circle – and San Salvador de Jujuy (in what

follows, referred to as Jujuy) – orange circle. Right: The dynamics inside each city population is modelled using the

Susceptible-Infected-Asymptomatic-Recovered (SIAR) model with seasonality modulated infection rate β(t),

recovery rate γ, and the parameter prepresenting the fraction of asymptomatic cases under the infection process.

The amplitude of the infection rate is βsfor cities with smaller population (Tartagal and Oran), and βlfor a larger

city (Jujuy). Black arrows represent the migration ﬂows of susceptible and asymptomatic individuals between cities,

proportional to the ﬂow rates fij for migration between locations iand j. A more detailed description of the model

is provided in the Materials and Methods, as well as in the Supplementary Materials, section C.

exploration, we tested an extension of our model that in-

cluded an environmental compartment, ﬁnding that its

inclusion did not improve the quality of the ﬁt, while at

the same time it introduced additional parameters that

needed to be inferred from data. For this reason and in

order to keep the number of model parameters small, we

do not explicitly include the environmental compartment

in our model. Instead, the seasonal component of cholera

transmission, well documented in [34–36], is included in a

direct transmission parameter of our model. This direct

contact parameter is an eﬀective parameter describing

the spread of cholera which includes all potential trans-

mission channels, similarly to an approach used in [22].

Previously, seasonally-modulated transmission parame-

ters was suggested in a fully theoretical framework in

[37], but it was not applied to empirical data.

Our second key assumption is related to the presence

of an asymptomatic population, which does not display

any strong symptoms, but nevertheless contributes to the

infection spread via migration. This population is not di-

rectly observed, but contributes to the cholera dynamics

via a dedicated compartment A. The associated param-

eter pdescribes the fraction of infected population which

falls into the Acompartment upon infection, while the

rest of the population falls into the Icompartment which

describes the symptomatic population. In spite of the

general agreement that a signiﬁcant number of individ-

uals infected by cholera display no apparent symptoms

and play a crucial role in spreading the disease between

diﬀerent locations, the literature is not conclusive about

the proportion of asymptomatic carriers. For instance,

[23] suggests that between 1% and 25% of infected cases

are asymptomatic; [24] estimates pcloser to 50%; and

according to [25], the asymptomatic population repre-

sents the majority of cases. Therefore, we treat pas one

of the key free parameters in our model which will need

to be inferred from data. We further assume that the

transmission dynamics between cities through migration

is mediated by the asymptomatic carriers only. This as-

sumption is incorporated into the meta-population model

through a migration term which is proportional to the

number of asymptomatic individuals in the population,

and is appropriately normalized so that the city popula-

tions do not change. Additionally, these migration terms

are informed by independently estimated travel rates, as

we discuss below. These migration terms link epidemic

trajectories in diﬀerent cities and thus facilitate the iden-

tiﬁcation of the parameter prelated to the fraction of

asymptomatic cases upon infection.

Meta-population model. Here, we formally sum-

marize our dynamic meta-population model. The cholera

dynamics in each of the three cities is described using a

homogeneous SIR-like SIAR model, linked by a ﬂow of

asymptomatic infected individuals between cities. More

precisely, we divide the population of each city into four

compartments: susceptible (S), infected symptomatic (I),

infected asymptomatic (A) and recovered (R). The mi-

gration mechanism allows for a mixing of diﬀerent city

populations with two conditions: (i) symptomatic in-

fected individuals do not move between locations; (ii)

traveling on average does not change the population of

each city. A schematic representation of the structure of

the meta-population model and the details of the single-

city model are shown in Fig. 1. The exact system of

ordinary diﬀerential equations used to build the model is

described in detail in the Supplementary Materials, sec-

tion C.

The model contains a total of 10 epidemiological,

travel, and demographic parameters. The epidemiologi-

cal parameters are the recovery rate γ, which represents

the inverse of expected days to recovery, the parameter

p, which represents the fraction of asymptomatic cases

emerging upon infection, and the infection rate β(t) mod-

ulated by a time-dependent function reﬂecting the sea-

sonal changes. Importantly, while the seasonality itself

is assumed to be the same for all three geographically

close cities, the amplitudes βsand βl, respectively rep-

resenting the smaller population cities Tartagal and San

Ram´on de la Nueva Or´an, and the larger population San

Salvador de Jujuy, may be diﬀerent. The transmission

amplitudes βsand βlcan a priori take diﬀerent values,

for instance due to an expectation of a better infrastruc-

ture in larger cities, potentially leading to access of higher

quality health care and resulting in lower infection rates.

Additionally, the model parameters include the initial

demographic structure of all four compartments in each

location. Finally, the model contains a set of migration

parameters fij describing the ﬂow of people between the

cities. The procedure for estimating the migration pa-

rameters is given in the Supplementary Materials, sec-

tion B. A more detailed description of the ﬁxed and free

parameters is included in the Materials and Methods, as

well as in the Supplementary Materials, section C.

Estimation of model parameters from case

count data. Using a least-squares-based estimator min-

imizing the error between the case counts data and model

predictions (see Materials and Methods for more details),

we estimated the transmission rates, seasonality param-

eters, initial conditions, and asymptomatic fraction p.

One of the main challenges faced by the ﬁtting of our con-

tinuous meta-population SIAR model was the fact that

the case counts are not reported continuously in the data

set, but instead appear as discrete peaks at certain sam-

pling days. To address this reporting delay challenge,

we proposed a sampling model which establishes a cor-

respondence between the continuous model and the case

counts sampled at speciﬁc dates by looking at a cumula-

tive number of cases between subsequent sampling dates

(see Materials and Methods and Supplementary Materi-

als, section D).

TABLE I: Key model parameters inferred from the case

count data, together with their single

standard-deviation uncertainty averaged over several

families of statistical counting noise.

parameter lower bound inferred value upper bound

p0.041 0.319 0.597

βs0.144 0.157 0.170

βl0.148 0.155 0.162

The results of the inference procedure are presented

in Table I for the key model parameters p,βs, and βl

(see Supplementary Materials, section E). In the absence

of ground truth, we use the following approach to es-

timate the uncertainty of our inference procedure. We

construct a synthetic model with a planted ground-truth

parameters equal to the parameters inferred from data.

Then, by generating counting noise on the same sam-

pling dates as the ones that appear in the real data, we

can construct synthetic data sets which have the same

properties as the original case count data, but with the

advantage that these data sets now come with a planted

ground truth. We run our estimator on many instances of

synthetic data with diﬀerent noise realizations and com-

pare the inference results with the planted parameters

of the synthetic model. This procedure allows us to re-

liably estimate the uncertainty bounds of our inference

procedure. Previously, a similar procedure for estimating

the uncertainty in the absence of ground truth has been

used in other applications involving statistical inference

[38, 39]. To check robustness with respect to the (un-

known) counting noise, we consider the estimation error

for noise generated from several families of probability

distributions, and report the standard deviation results

averaged over these families. The details of this proce-

dure are given in the Supplementary Materials, section

A comparison of the true case count data and the sam-

ples obtained from the model with the inferred parame-

ters is shown in Fig. 2. Despite some discrepancies ob-

served for the highest case count peaks, our simple model

is able to adequately describe the variations present in

the data, including the seasonal character of the cholera

outbreak in Argentina. The obtained seasonality of the

transmission rate highly correlates with seasonal temper-

ature variations in the analysed cities (see Supplementary

Materials, section F), even though such an information

was not explicitly implemented in the model and was not

provided to the inference algorithm. The model suggests

that cholera from this initial outbreak dies out after 1997,

which is consistent with a hypothesis that the nature of

the further peaks may have been signiﬁcantly inﬂuenced

by external factors such as Mitch hurricane in 1998 or El

Ni˜no in 1997-1998 [40] (see Materials and Methods).

Our results are highly robust. We successfully tested

our ﬁtting procedure with synthetic data generated with

1992 1993 1994 1995 1996 1997 1998

Date

number of cases

observed cases

model cases

I(t)

(a) Tartagal

1992 1993 1994 1995 1996 1997 1998

Date

number of cases

observed cases

model cases

I(t)

(b) San Ram´on de la Nueva Or´an (Oran)

1992 1993 1994 1995 1996 1997 1998

Date

number of cases

observed cases

model cases

I(t)

t1−14 t2

cases included in sampling

(d) Sampling procedure example

FIG. 2: Comparison of the case count data (blue bars) and the samples obtained from the model with the inferred

parameters (orange bars) for three cities: (a) Tartagal, (b) Oran, and (c) Jujuy. The red dashed line represents the

number of active infected symptomatic cases according to the predictions of our continuous meta-population SIAR

model. In the real data set, the case counts are not reported every day, but instead appear as discrete peaks at

certain sampling days, which complicates the ﬁtting of the continuous model. For this reason, we propose a

correspondence between the continuous model and the case counts sampled at speciﬁc dates. The panel (d) explains

the sampling model we use in our ﬁtting procedure. We assume that the case counts reported on a given date

correspond to a cumulative number of cases predicted by the continuous model between the minimum of the current

and the previous sampling dates and 14 days before the current sampling date. This cut-oﬀ cumulative horizon

represents the double of expected recovery period (ﬁxed to 7 days, as explained in the Materials and Methods). A

more detailed explanation of the sampling procedure and the study of the impact of the choice of the sampling

horizon is presented in the Supplementary Materials, sections D and I, respectively.

diﬀerent types of noise (see Supplementary Materials,

section E). We have also studied the scenario of a non-

centered counting noise distribution corresponding to a

signiﬁcant under-reporting of the case counts. In the

Supplementary Materials, section G, we show that this

scenario is unrealistic as it leads to an unreasonably large

number of predicted infected individuals, of the order of

the whole city population. Moreover, we tested sensitiv-

ity of our procedure with respect to the misspeciﬁcation

of the inferred migration rates (see Supplementary Ma-

terials, section H) and diﬀerent sampling horizons (see

Supplementary Materials, section I). Finally, we investi-

gated how the much the length of the case count time

series aﬀected the estimated parameters (see Supplemen-

tary Materials, section J. We conclude that despite many

sources of potential discrepancies, estimates are robust to

reasonable levels of model misspeciﬁcation.

Estimation of model parameters from genetic

sequence data. We used phylodynamic analysis meth-

ods to estimate the transmission rates and the asymp-

tomatic fraction parameter pfrom the genetic sequence

data (see Materials and Methods and Supplementary Ma-

terials, section K for a description of the data and the

details on the inference procedure). The inferred time-

scaled phylogenetic tree ﬁxed to its maximum likelihood

topology is shown in Fig. 3. The tree topology suggests

an intermixed outbreak with evidence of multiple trans-

missions occurring between the three cities, which pro-

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CongruityofgenomicandepidemiologicaldatainmodelingoflocalcholeraoutbreaksMateuszWilinski1,LaurenCastro2,JereyKeithley2;3,CarrieManore1,JosenaCampos4,EthanRomero-Severson1,DarylDomman5,AndreyY.Lokhov11TheoreticalDivision,LosAlamosNationalLaboratory,LosAlamos,NMUSA2Analytics,IntelligenceandTechnol...

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Congruity of genomic and epidemiological data in modeling of local cholera outbreaks Mateusz Wilinski1 Lauren Castro2 Jerey Keithley23 Carrie Manore1 Josena Campos4 Ethan Romero-Severson1 Daryl Domman5 Andrey Y. Lokhov1

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