A Malaria Control Model using Mobility Data: An Early Explanation of

Kedougou Case in Senegal

Lynda Bouzid Khiri

, Ibrahima Gueye

, Hubert Naacke

, Idrissa Sarr

and Stéphane Gancarski

Sorbonne Université, Laboratoire d’Informatique de Paris 6, LIP6, F-75005, France

Cheikh Anta Diop University, Department of Mathematics and Computer Science, Fann BP, 5005, Dakar, Senegal

Ecole Polytechnique de Thiès, LTISI, Senegal

Keywords:

Malaria Control, Mobility Model, Discrete Simulation, Data Analysis.

Abstract:

Studies in malaria control cover many areas such as medicine, sociology, biology, mathematics, physics,

computer science and so forth. Researches in the realm of mathematics are conducted to predict the occurrence

of the disease and to support the eradication process. Basically, the modeling methodology is predominantly

deterministic and based on differential equations which take into account important clinical and biological

features. Yet, if the individual characteristics matter when modeling the disease, the overall estimation of the

epidemic evolution relies on a non-speciﬁed percentage of the global population : it is not based on the state

of health of each individual. The goal of this paper is to propose a model that relies on a daily evolution of

the individual’s state, which depends on their mobility and the characteristics of the area they visit. Thus,

the mobility data of a single person moving from one area to another, gathered thanks to mobile networks,

is the essential building block to predict the disease outcome. We implement our solution and demonstrate

its effectiveness through empirical experiments. The results show how promising the model is in providing

possible insights into the failure of the disease control in the Kedougou region.

1 INTRODUCTION

Human malaria is caused by infection by the Plas-

modium falciparum and four other species of par-

asites, leading to almost 600,000 deaths and 100–

250M febrile episodes annually WHO Inc. (2016).

Even though the disease has been investigated for

hundreds of years, it still remains a major pub-

lic health problem in Sub-Saharan Africa (SSA)

where about 90% of malaria cases were reported in

2017 WHO Inc. (2016).

Many SSA countries have set the goal of eliminat-

ing malaria for the upcoming decades outbreaks Ruk-

tanonchai et al. (2016). Among these countries, Sene-

gal has initiated its National Program Against Malaria

(PNLP) du Sénégal (2017). Besides a weekly follow-

up of the disease evolution, the PNLP has allowed

to intensify the coverage of key malaria interventions

over the country in terms of impregnated mosquito

nets, insecticide (ITN), indoor residual spraying, pre-

ventive treatment by intermittent administration to

women intestines (TPI), rapid diagnostic tests (RDTs)

and therapeutic combinations based on Artemisinin

(CTA) Thiam et al. (2011). Those strategies have

lowered the malaria incidence (relative number of in-

fected people for 1000 inhabitants) to a relative small

number estimated to 25 in 2017. However, the south-

eastern part of the country (Kedougou region along-

side Kolda and Tambacounda) accounts for 75% of

malaria cases and 45% of malaria-related deaths. Spe-

cially, the malaria incidence was estimated to 429 in

2017 for Kedougou while the other regions of Sene-

gal had an average incidence below 10. Such sit-

uation on Kedougou reveals the weaknesses of the

overall strategies taken to face the disease, and why

malaria pre-elimination remains a crucial problem in

the country. In this work, we investigate Kedougou

case to show forgotten aspects in antimalarial policies

and to demonstrate that more efﬁcient actions should

be considered.

Actually, Kedougou is the largest city in south-

eastern Senegal 700 km away from Dakar which is

the capital. Kedougou has a dry tropical climate, with

an average annual rainfall over 1000 mm, spread over

a rainy season that lasts from May to November. It is

a mainly agricultural region with the cultivation of ce-

reals (rice, corn, sorghum, millet, fonio ...) and many

forest fruit species including mango, shea, palm, etc.

Khiri, L., Gueye, I., Naacke, H., Sarr, I. and Gancarski, S.

A Malaria Control Model using Mobility Data: An Early Explanation of Kedougou Case in Senegal.

DOI: 10.5220/0009591800350046

In Proceedings of the 10th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2020), pages 35-46

ISBN: 978-989-758-444-2

Figure 1: Kedougou region with its 3 departments.

Moreover, it offers a variety of natural attractions in-

cluding those of the Niokolo Koba national park, the

hills where trekking activities are practiced and the

Dindefelo waterfall. The discovery of deposits of ura-

nium, granites, marble and other ornamental rocks,

but also industrial minerals such as phosphate and

kaolin ranks Kedougou as a cornerstone mining re-

gion. All these characteristics, along with its proxim-

ity to Mali and Guinea make Kedougou a true cross-

roads all over the year, which leads to a strong hu-

man mobility rate. As shown in the Figure 1, the re-

gion of Kedougou is divided into three departments,

namely, Salemata with 14.6 % of the population, Ke-

dougou department that shelters 51.9% and Saraya,

33.5% ANSD (2013). As depicted on the map, Ke-

dougou department is on the center of the region and

hosts the main infrastructures such as markets, health

centers, and so on. This geo-administrative division

raises an intra-mobility rate of individuals within Ke-

dougou region.

As a conclusion, Kedougou region is character-

ized by two types of mobility : an intra-mobility for

daily or weekly needs of permanent residents, and an

extra mobility at the country and the west African

community level. Our goal is to provide tools high-

lighting the negative incidence of these mobility pat-

terns on the malaria disease.

Some statistical data from the PNLP and related to

Kedougou region du Sénégal (2017) are used to plot

the Figure 2, that shows the variation of new malaria

cases over 24 months, i,e,. from January 2016 to De-

cember 2017. The ﬁrst observation is that the number

of cases raises drastically just after the beginning of

the rainfall season (each year on June, months 6 and

18) and decreases with the end of the rainy annual pe-

riod (on September, months 9 and 21). This situation

is explained by the fact that mosquitoes population is

growing faster during rainy seasons. Therefore, since

weather conditions are similar over two successive

years, we almost observe the same seasonal trend.

However, when looking deeper at the three curves,

we ﬁnd out that the epidemic of the three departments

are not similar. First of all, the different peaks of

Figure 2: The Variation of malaria between Jan. 2016 and

Dec. 2017.

the malaria cases in each departments do not occur

at the same time and are actually staggered by a few

weeks. Moreover, we note that the epidemic in Saraya

lasts longer than the ones in Kedougou or Salemata

even though the three departments have similar cli-

matic conditions. Thus, rainfalls do not fully explain

the spread of the epidemic over 6 months. Still, we

know that there is a lot of movement towards the

zone (trade and mining with other border countries).

Also, it has been demonstrated that human mobil-

ity has an impact on malaria control and elimination

Gharbi et al. (2013); Ruktanonchai et al. (2016) and

even in malaria-free countries Dharmawardena et al.

(2017). Bearing this in mind, it makes sense to relate

the epidemic outbreak of a given area to the arrival of

outsiders who have been exposed in other areas dur-

ing different periods. Surprisingly, despite the strong

sustained mobility around the Kedougou region, the

PNLP does not include human movements in its con-

trol strategies yet.

We make the assumption that the arrival of in-

fected people in a given area makes the epidemic to

last longer. The impact on the epidemic extension de-

pends on the arrival date of new people and the epi-

demic state of the area they come from. Our goal is to

demonstrate that this assumption is plausible through

a mathematical model. In fact, mathematical mod-

els have been frequently used in related works about

malaria control Chitnis et al. (2006); Dimitrov and

Meyers (2010); Mandal et al. (2011); Chitnis et al.

(2008); Arthur (2017); Ruktanonchai et al. (2016);

Greenwood et al. (1991); Gu et al. (2003a); Koella

(1991); Filipe et al. (2007); Lechthaler et al. (2019).

Existing models consider different parameters and as-

pects that inﬂuence the disease dispersal, such as het-

erogeneity, immunity, recovery time and more re-

cently, human mobility. However, the models with

human mobility only deal with the movement of peo-

ple through a coarse grain approach, which assumes

a global migration ratio from an area to another one.

Rather, a ﬁner grain approach can be used thanks to

personalized geo-position information (GPS coordi-

nates) from mobile phones. Such a ﬁner approach al-

SIMULTECH 2020 - 10th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

lows a better understanding of the disease evolution at

each time, on each area. Therefore, it helps to deter-

mine the antimalarial actions in a more dynamic and

efﬁcient fashion.

The main contributions of this paper can be sum-

marized as follow:

• We deﬁne a mathematical model that takes into

account individual mobility and immunity. To this

end, we assume that we have real-time data from

mobile devices allowing to establish the mobility

pattern of everyone, and his(her) state wrt. the

malaria (ill or not). Hence, we build a discrete

model that mainly differs from existing works by

the fact that the global status of a given space is

obtained by aggregating the health status of each

individual.

• We implement a simulation software with respect

to climatic conditions and human movements over

time. The software is designed so that the relevant

parameters of the disease can be adjusted accord-

ing to the real life situation of a given area.

• We conduct a set of experiments to validate our

approach while we point out many beneﬁts of our

solution in terms of explaining the disease evolu-

tion in areas like Kedougou. To this end, we rely

on synthetic data according to realistic scenarios

since real-time data are not available yet. We

show the impact of different factors (characteris-

tics of areas, mobility and state of individuals) on

the malaria propagation. This allows for measur-

ing the impact of malaria control actions (eradica-

tion, prevention) in an accurate way, which helps

deciding which actions should be prioritized.

2 BACKGROUND

Mathematical models have been used to predict the

occurrence of a disease and to control its dispersal.

Basically, the modeling methodology is mainly de-

terministic and based on differential equations while

selecting clinical and biological features that seem

to be important Greenwood et al. (1991); Chitnis

et al. (2006, 2008); Arthur (2017); Ruktanonchai et al.

(2016). The ﬁrst models that were developed examine

the interaction of human, vectors and parasites with

a coarse granularity, for instance, at the city/country

level Mandal et al. (2011). More recent models have

attempted to handle heterogeneity such as the individ-

ual immunity Gu et al. (2003a); Filipe et al. (2007),

the space and contact network Parham and Ferguson

(2006), the recovery rate Gu et al. (2003b), etc. A re-

cent work integrates human mobility data Ruktanon-

chai et al. (2016) for explaining and eliminating the

disease in a particular area.

One of the ﬁrst model, known as the classical

"Ross model", was developed by Sir Ronald Ross

who explained the relationship between the number of

mosquitoes and incidence of malaria in humans Ross

(1911). In such a model, the population is divided

into several compartments which represent health sta-

tuses regarding the pathogen. These statuses or com-

partments are represented by the standard notation S-

E-I-R, based on the work presented in Kermack and

McKendrick (1927). The S class stands for the frac-

tion of host population that is susceptible to infection,

while the E category indicates the fraction of popu-

lation whose individuals have been infected but are

not infectious yet due to a latency period. The I class

represents infectious individuals who may infect other

individuals through interactions with mosquitoes. Fi-

nally, the R class portrays individuals who have re-

covered from the infection. Notice that sometimes,

R may include individuals who have recovered with

temporary or permanent immunity. With these dif-

ferent classes, one may observe eight possible mod-

els: SIS, SEI, SEIS, SIR, SIRS, SEIR and SEIRS. Note

that both mosquito and host population may be related

with these compartments in a malaria disease case.

That is, the malaria transmission model is described

along two aspects, one representing humans and the

other representing mosquitoes. However, a mosquito

can not recover from being infected, so its infective

period ends with its death.

3 DISCRETE MALARIA MODEL

As we pointed out earlier, we aim at integrating

user mobility information into a malaria transmission

model. The reason behind this is that knowing the

mobility and state of each individuals allows for as-

sessing the speciﬁc persons that diffuse the disease

instead of ﬁnding a proportion of population as done

by existing models. In this sense, our approach differs

to others by the fact that we estimate the probability

of each individual to be part of one class (SEIR), and

therefore, we deduce the global population that be-

long to each class at each time unit.

3.1 Global Model Overview

We assume a multi-patches area where each patch has

a speciﬁc conﬁguration to impact the malaria disease

propagation. Individuals can move from one patch

to another while mosquitoes are set to stay in only

one patch. To model the transmission, we extend the

A Malaria Control Model using Mobility Data: An Early Explanation of Kedougou Case in Senegal

SEIRS-SEI model proposed in Chitnis et al. (2008)

by introducing patches and individuals data mobil-

ity. Fig. 3 shows the proposed malaria transmission

model. Solid arrows denote intra-species progression

into classes while dotted arrows denote inter-species

transmission. With this model, for each patch i the

Figure 3: Malaria model in patch i Chitnis et al. (2008).

human population is divided into four classes: sus-

ceptible S

, exposed E

, infectious I

, and recovered

(partially and/or temporary immune) R

. Moreover,

mosquitoes population is divided into three classes :

susceptible S

, exposed E

, infectious I

. We assume

a constant population (i.e., birth rate equals death

rate). Initially, all individuals are in the susceptible

class except a low percentage that live with the par-

asites. This situation is realistic in a context where

the malaria parasite is still present. Basically, a pro-

portion of the susceptible individuals that move from

the S to the E class due to mosquito bites is charac-

terized by the force of infection (FoI) λ

. Among ex-

posed individuals, there is a proportion ν

that enter

to the infectious class. ν

depends on a time period,

called an intrinsic incubation period, which depends

on the parasite species (i.e., Plasmodium falciparum).

Later on (approximately a couple of weeks), a part

of infectious humans (γ

ratio) recover and join the

R class where they may acquire a certain immunity

to the disease and do not get clinically ill. However,

they still host low amount of parasites and can trans-

mit the infection to mosquitoes with a low rate. Over

the time, the immunity of individuals vanishes and a

some of them (ρ

ratio) return to the S class. Regard-

ing the mosquitoes population, the same ﬂowchart is

observed with only three classes. It is worth noting

that the mosquitoes FoI (λ

) differs from humans’

FoI, so does the incubation period of mosquitoes and

humans. The main parameters of the model are di-

vided into two categories: patch parameters and in-

dividual parameters. In the following, we present a

short overview of these parameters.

3.2 Dealing with Patch and Individual

Characteristics

3.2.1 Patch Characteristics

Since our model is discrete, we deﬁne the transmis-

sion in patches at a given time step t. For each patch

i, we use almost the same parameters as described in

Chitnis et al. (2008) while adapting them to a multi-

patches context (see Table 1 for parameters details).

After identifying the required parameters, we de-

ﬁne the vector-to-human FoI (λ

) and human-to-

vector FoI (λ

) in a patch as follows :

(t + 1) = b

(t)β

(t)

(1)

(t + 1) = b

(t)(β

(t)

) (2)

3.2.2 Individual Mobility Characteristics

We distinguish residential patches (cities or districts)

to ad-hoc meeting patches. Meeting patches (P

) are

sparsely populated and used as headquarter for social

events while residential patches (P

) are densely pop-

ulated but not attractive for social meetings. Having

this in mind, one may deduce that people more of-

ten move from P

to P

than from P

to P

. We as-

sume that each individual is identiﬁed thanks to mo-

bile applications and/or Telecommunication compa-

nies. Users data are anonymised in such a way that

personal details are hidden while geographical posi-

tions of anonymous individuals are known at each

time. We consider a sequence of consecutive time

windows of equal duration. At anytime, the patch

of an individual h

and how long he stays there are

known. For instance, on Figures 4a and 4b, human h

stayed during w

time in p

, w

in p

, and so on.

For individual h

, his probability of being exposed

is a function of his status and FoI, which depends on

his mobility as well as his immunity. Basically, the

FoI of an individual is the sum of the FoI of each vis-

ited patch i weighted by its time presence in i :

h, j

(t) =

∑

i=1

(t) λ

(t) (3)

Finally, the likelihood to get exposed of h

at time t +

1 is : pe

(t + 1) = pe

(t) + λ

h, j

(t)(1 − pe

(t)). Once

an individual is exposed, the incubation, development

and recovery process are a matter of time. Basically,

an exposed human has a likelihood to get infected and

to recover after a certain period. Details of parameters

SIMULTECH 2020 - 10th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

Table 1: Patches Parameters.

Parameter Description

(t) Human population in patch i at time t

(t) Vector population in patch i at time t

(t) Infected mosquitoes in patch i at time t

(t) Infected humans in patch i at time t

(t) Infected individuals in patch i that recover at time t

Probability that an infectious person infects a susceptible mosquito dur-

ing a contact within the patch i

Probability that an infectious mosquito infects a susceptible individual

during a bite in patch i

Probability that a recovered person infects a susceptible mosquito dur-

ing a contact in patch i

(t) Proportion of bites per human per unit time t in patch i

(t) Proportion of bites per mosquito per unit time t in patch i

Force of infection from vector to human in patch i, i.e., measure of how

likely a human get exposed in patch i

Force of infection from human to vector in patch i, i.e., measure of how

likely a mosquito get exposed in patch i

Table 2: Individual Parameters for a given time window.

Parameter Description

Identiﬁcation of the individual j

Visiting ratio of time that h

spends in patch k.

h, j

(t) Susceptible state variable of h

at time step t (1 if susceptible 0 other-

wise)

h, j

(t) Exposed state variable of h

at time step t (1 if exposed 0 otherwise)

h, j

(t) Infected state variable of h

at time step t (1 if infected 0 otherwise)

h, j

(t) Recovered state variable of h

at time step t (1 if recovered 0 otherwise)

(t) Probability that individual h

(being in class S) moves to class E

h, j

incubation period (without symptoms). In the case of P. falciparum par-

asite, which predominates in Senegal, it varies from 9 to 10 days Chitnis

et al. (2008); for Disease Control and Prevention (2015).

h, j

is the infectious period (Chitnis and Al. have set it at 9.5 months Chitnis

et al. (2008))

for calculating the transition over the classes SEIR are

described in Table 2.

After deﬁning FoI of individuals, we identify at

each time the new exposed ones, and apply the model

to get the class of the other individuals. With the

above parameters, we aggregate individual informa-

tion to get patch-level information. The human pop-

ulation over the different classes is deﬁned for each

patch and each time period, as follows :

(t) =

∑

j=1

(t) S

h, j

(t) (4)

(t) =

∑

j=1

(t) E

h, j

(t) (5)

(t) =

∑

j=1

(t) I

h, j

(t) (6)

(t) =

∑

j=1

(t) R

h, j

(t) (7)

The variation of mosquitoes population over the

classes is the same as described in Chitnis et al. (2008)

= ψ

− λ

(t)S

− f

(8)

= ν

− f

(9)

= λ

(t)S

− ν

− f

(10)

A Malaria Control Model using Mobility Data: An Early Explanation of Kedougou Case in Senegal

(a) Individuals visiting different

patches

(b) Mobility pattern of an individual

Figure 4: Human mobility and Patches

where f

) = µ

+ µ

is the per capita density-

dependent death rate for mosquitoes in the patch i

Chitnis et al. (2006).

It is worth noting that our model is computed in an

incremental way. After each time step, we update the

information describing patches and individuals (i.e.,

FoI and health status) since they are used as input for

the next time step.

4 IMPLEMENTATION AND

VALIDATION

4.1 Experimental Setup

We implemented our approach using the version

2.7.15 of Python through Spyder IDE 3.2.6 on Linux.

We rely on Jupyter for visualization and share the

source code of our implementation

. All the parame-

ters about individuals and patches we used to imple-

ment the model are detailed in section 3.2. We re-

call that most of these parameters values have been

reported in the literature.

We consider two patches : the residence zone P

and the meeting one P

, with their respective hu-

man population |P

| and |P

|, their respective vector

(mosquito) population NV

and NV

and the propor-

tion p of human traveling from P

to P

. We observe

, the number of infected persons in P

. Table 3 sum-

marizes the parameters used in the experiments.

4.2 Experimental Objectives and

Method

The overall goal of the validation is to investigate the

beneﬁt of individual mobility for malaria control. We

intend to show that taking into account individual mo-

bility allows for a more accurate modeling of the dis-

ease evolution over time and space (i.e., patches). We

aim to simulate disease evolution which cannot be

captured by existing models that are unaware of in-

dividual mobility. Precisely, we evaluate the gain of

our approach in three different aspects:

1. The impact of individual mobility on the estima-

tion of infected individuals.

2. The relevance of the proposed model to approxi-

mately match recently reported real cases.

3. The vector control opportunities based on individ-

uals movements and patches characteristics.

4.2.1 Size of the Vector Population over Seasons

In this section, we only consider the P

patch, thus we

omit the R indice in the notations. To be as close as

possible to what happens in the real world, we vary

the population of (mosquito) vectors according to the

two main seasons occurring in the Kedougou region:

• the rainy season (approximately from start of June

to the end of November)

• the dry season (the remaining 6 months).

The number of mosquitos grows wrt. a daily birth

rate (ψ, see Section 3). This birth rate still grows and

reaches a stationary value when the rainy season set-

tles deﬁnitively. Indeed, the mosquito birth rate is

correlated with the amount of wet place (reproduc-

tion areas). All potential wet places are full of wa-

ter when the rainy season is in full swing. Thus, we

assume that during the rainy season the total size of

www-bd.lip6.fr/wiki/site/recherche/projets/m4e/start

SIMULTECH 2020 - 10th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

Table 3: Experimental parameters.

name description value

the residential patch

| the number of individuals in P

3000

the number of vectors in P

Varying

the meeting patch

| the number of individuals in P

1000

the number of vectors in P

Varying

p the ratio of moving individuals (p > 0) [0.1, 0.4]

the number of infected individuals in P

[0, 3000]

ψ vector birth rate 0.03

µ vector death rate [0.03, 2E-8]

these wet areas remains almost constant therefore the

vector population NV

max

remains almost constant.

Then, at the end of the rainy season, the vector

population is gradually decreasing up to the dry sea-

son ceiling (i.e., a rather small number that makes the

epidemic to stop itself). The death rate (µ see Table 3)

is based on the average life duration of a vector (30

days).

Figure 5(a) plots the number of vectors over time

during one year for the residential patch, with differ-

ent characteristics in terms of wet areas. For instance,

in the ﬁrst case (N V = 400) the vector population is

20 times higher than during the dry season, whereas

in the last one, (NV = 1000) it is 50 times higher.

This allows for simulating areas with different charac-

teristics in terms of wet areas and therefore in terms

of vectors population growth. Note that these areas

are located in the same region thus have similar rainy

seasons (from June to November).

To ﬁgure out the effect of the rainy season on the

disease, we compute the number of newly infected in-

dividuals in P

patch when everyone remains seden-

tary (i.e., no mobility). Figure 5(b) reports the results

for the 4 patches from Figure 5(a). In the ﬁrst patch

(Nv = 400) there is almost no disease while in the 3

other ones, the peak disease grows for patch having

more vectors. We use these preliminary simulations,

to set the maximal number of vectors (dented Nv

max

)

that a residential and meeting patch have in the subse-

quent experiments. This allows us to deﬁne a low en-

demicity residential patch (Nv

max

= 400) and a higher

endemicity meeting patch (Nv

max

= 1000)

4.3 Impact of Individual Mobility

The goal of this section is to quantify the impact of

individual mobility in modeling malaria. Based on the

Kedougou case (cf. Section 1), we consider a village

of farmers that sell their products at a remote market.

Basically, there are two patches: a residential place P

and a market place P

. There are 3000 people living

(a) NV max varying from 400 to 1000.

(b) # new exposed indiv. vs. NV max.

Figure 5: Impact of the maximum number of vectors

(NV

max

) on the disease.

in P

. Among them, a group of people (which size

ratio is p relative to P

population) moves everyday

from P

to P

and come back home.

A Malaria Control Model using Mobility Data: An Early Explanation of Kedougou Case in Senegal

4.3.1 Varying the Mobility Rate

The goal of this experiment is to assess the impact of

the mobility on the disease evolution. First, we deﬁne

the mobility rate r as the ratio of people moving from

to P

. Then we investigate how the number of

exposed individuals, E(r), evolves over time for var-

ious mobility rates. To this end we vary the mobility

rate, r, from 0% to 40%. On Figure 6, we report the

number of newly infected individuals per week.

The dashed black line indicates the threshold limit

of exposed people. Above this threshold, the disease

is qualiﬁed as an epidemic situation. The threshold

value is set to 6 new cases per week according to real

observations reported in Kedougou during years 2016

and 2017 du Sénégal (2017).

Figure 6: Varying the mobility rate r from 0 to 40%.

We observe on Figure 6 that the higher the mov-

ing rate, the higher the epidemic and longer is the

epidemic duration too. For example, when nobody is

moving (r=0), the epidemic lasts 8 weeks with 7 new

cases per week; whereas for a moving rate of 10%,

it lasts 16 weeks and reaches a peak of 25 cases per

week.

4.3.2 Early/Late Rainy Season in the Meeting

Patch P

In case the mobility patch and the residential patch

have slightly different raining seasons, this could have

an impact on the epidemic duration.

In this section, we study the impact of having a

rainy season in P

that does not start exactly at the

same time as in P

. The rainy season in P

lasts

from week 22 to week 38 (i.e., 16 weeks from June

to September). The P

rainy season lasts as long as

the P

one but it starts before or after week 22. The

mobility pattern is set to 20 % mobile individuals that

go to P

every day for half of their time. We report on

Figure 7 the number of exposed individuals for sev-

eral starting dates of the P

rainy season.

(a) Starting in P

earlier than in P

(b) Starting in P

later than in P

Figure 7: Varying the starting date of the rainy season in

The results show that the epidemic lasts longer on

Figure 7(b) than on Figure 7(a). That is, it lasts longer

when the rainy season starts in P

later than in P

The extra time duration (between 2 and 6 weeks as

reported in Figure 7(b)) of the epidemic corresponds

to the rainy season starting time gap between the two

patches.

4.3.3 Varying the Mobility Starting Date

In this experiment, we vary the starting date (before

this date, nobody moves) from t=0 (beginning of the

year) to t=40 (late October). We want to investigate

the impact of seasonal migration on the development

of the disease. Intuitively, we expect a greater im-

pact when the migration occurs during the rain season

which has the highest vector population. Such migra-

tions are usual in the Kedougou region, where there

SIMULTECH 2020 - 10th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

are few fair places and people from small cities or vil-

lages have to move to sell or buy goods.

(a) Mobility starting before/after the rain season.

(b) Mobility starting during the rain season.

Figure 8: Impact of the mobility starting date on the disease.

With 20% moving people and other parameters set

similar to the ones used in previous experiment (sec-

tion 4.3.2), we plot on Figure 8 the impact of the start-

ing mobility on the disease evolution.

The results (for "Week 40" curve) suggest that the

disease development is quite slow before the migra-

tion start. When the migration starts at the beginning

of the rain season (see "Week 0" curve), the disease

grows slowly because most of the vectors are still in a

susceptible state implying a low vector-to-human FoI.

On the other hand, when a migration starts at the mid-

dle of the rain season (see "Week 32" and "Week 36"

curves), the disease grows very fast because most of

the vectors are already infected, thus, causing a high

FOI.

Figure 9 aggregates 2 different cases of migration

patterns occurring on 2 sub-areas: a migration starting

at week 0 and another one starting at week 40. We re-

port (in red curve) the total number of newly exposed

people on the area.

The results suggest that the disease lasts 35 weeks,

which is longer than any of the two sub-areas. More

interestingly, the disease lasts 8 weeks longer than the

longest epidemic plotted on Figure 6. Notice that the

two sub-areas do have the same rain season because

they are located in the same region. We can conclude

that successive migrations from various speciﬁc ar-

eas (close villages) tend to generate rather long epi-

demic at a higher scale (region level). The results are

consistent with the real Kedougou observations : they

provide a possible explanation of what happened at

Kedougou.

Figure 9: Aggregating on 2 zones.

4.4 Relevance of the Model to Match

the Kedougou Real Case

The objective is to evaluate the relevance of our model

to match real malaria observations recently reported

in PNLP (2017). An observation is reported as a se-

ries of newly infected people, one value per week.

Given a observation occurring in an area of P inhabi-

tants for a period of n weeks, we deﬁne a normalized

report R = {R

, · ·· , R

} such that R

is the number

of newly infected people for week i divided by the

population P. Let M be a model for the observation

reported by R. Running M generates {M

, · ·· , M

}

such that M

is the expected ratio of newly infected

people on week i.

We plot the obtained values in Figure 10 and the

relative accuracy is E

M,R

= 0.016, what gives a mean

absolute error MAE = 0.001. These results show that

the values measured (reports) and those calculated

with the model differ by approximately 1 case per

1000. Therefore we can say that our model produces

A Malaria Control Model using Mobility Data: An Early Explanation of Kedougou Case in Senegal

values that are close to what is reported from real ob-

servations.

Figure 10: Normalized values from real observations vs.

simulation.

Therefore, using our model can help for more efﬁ-

cient malaria control actions. For example, using the

model one can decide on which location to conduct

preventive actions in priority.

4.5 Vector Control Efﬁciency

In this experiment, we measure the beneﬁt of our ap-

proach on controlling the malaria vectors. There are

two types of malaria control actions: 1) a preventive

action, which consists of convincing people to use re-

pellent and mosquito nets in order to avoid mosquito

bites, and 2) an eradication action (i.e., mosquito re-

moval) that consists in suppressing most of the vec-

tors in an area using chemical products. Notice that

this second action type may have dramatic ecological

consequences. Therefore, the ﬁrst action type, pre-

ventive, would be a better choice. However, it comes

at a cost that must be optimized.

We aim to show that preventive action helps re-

ducing the vector-to-human FoI and then reduce the

epidemic intensity and duration.

We already show in previous sections, that the

moving part of the population is the major factor

that impact the epidemic duration and intensity. We

now protect those people who move from residen-

tial patch to meeting patch. Actually, this protection

could be done through repellent and mosquito nets.

In this respect, we consider the experiment conﬁgura-

tion where individuals mobility rate is 10% (see ﬁg-

ure 6 when r = 0.1 ) and we use use different values

of protection rate (ptr) for people who regularly move

. The protection rate ptr depicts the ratio of protected

people among the moving ones. The results of these

experiments are shown on Figure 11.

We show that for ptr = 1 when we protect 100%

of the moving population, the epidemic intensity and

duration is as low as if no people is moving (see the

r = 0 case in ﬁgure 6). Therefore, preventive actions

targeting moving people can be rather efﬁcient. In a

residential patch where few people are moving, such

preventive action would be cost-optimized assuming

Figure 11: Malaria evolution according to the mosquito

control strategy.

that the preventive action cost per individual is low.

When p is varying from 1 to 0.8, the total number of

exposed individuals is growing respectively from 118

to 169. This means that the preventive action must be

rather complete to be efﬁcient.

5 DISCUSSION

Among the various outcomes of the model, one

may retain the following ones.

• Risk Customizing. The model helps to compute

the likelihood p

of a given individual to get ex-

posed based on its mobility pattern through the

different patches over the time. We have shown

how important it is to distinguish, within a patch,

moving people from residential ones. In a context

like Kedougou, such an ﬁne-grained model advo-

cates that truckers, traders, and others with a high

mobility rate should be observed more carefully

since their risk to get infected, with the disease

dispersal knock-on effect, is more signiﬁcant.

• Reducing Antimalarial Costs. Since the model

is devised for each individual, it allows to tar-

get speciﬁc persons at higher risk than the over-

all population. Bearing this in mind and the

fact that each antimalarial action costs, then us-

ing the model can contribute to reduce the neces-

sary means for the surveillance, and eventually,

the elimination of the disease. Moreover, with

the tight budgets in developing countries, com-

bined with the rapid growth of the demography

as well as the explosion of other infectious dis-

eases that create new priorities for governments,

the proposed approach seems to come up at the

right time for facing deﬁnitively against malaria.

• Mobility Impact. As shown in the validation sec-

tion, mobility may have either a great or low im-

pact on a visited patches. Therefore, the time-

based follow-up of a patch FoI using individu-

SIMULTECH 2020 - 10th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

als’ mobility should go along with more clinical

testings to reach better predictions. In opposite

of current strategies applied in Kedougou, which

do not include human mobility details and ﬁgure

out the overall disease trends weeks or months

later, our model instantly plots detailed informa-

tion about malaria dispersal. Hence, policy mak-

ers may foresee the right actions to do in each

patch even though the disease has not happened

yet.

• What-if Analysis Boost. Last but not the least,

our solution can be used to calibrate the overall

actions against malaria. In fact, we can model the

disease spread while asking or supposing a spe-

ciﬁc pattern. For instance, we can suppose (or

eventually suggest) that people have to stay home

during their incubation period in order to reduce

the global evolution of the disease. Likewise,

we can suggest them following a speciﬁc mobil-

ity pattern based on the FoI of different patches.

In other words, we offer policy maker a tool that

can be used as dashboard to evaluate different sce-

nario and their effects.

Even if the experimental results we got are in-

teresting and rather intuitive sometime, they could

be more accurate with real mobility data. In ongo-

ing work, we plan to acquire those data and conduct

deeper experimental validation.

6 CONCLUSION

In this article we proposed a malaria model that takes

into account individual information such as mobility

patterns, health statuses, and so on. The model is a

discrete SEIR-SIS approach and differs mainly from

existing models by the fact that global details about

the disease are obtained by gathering the health sta-

tus of each individual among a given population. Our

approach is more accurate in terms of estimating the

disease level, and affords the possibility to setup more

efﬁcient vector control strategies aiming to eliminate

malaria in Africa. Actually, our model is an early ex-

planation of Kedougou case where the malaria inci-

dence is still high despite the strategies of the Senegal

national program. In this respect, it unveils kind of

solutions that decision makers can use with respect to

individuals movement in order to eliminate the dis-

ease. Moreover, the results from our model match

real observations in Kedougou with a mean absolute

error of 0.001 while using synthetic data. Such a re-

sult is promising and let us believe that with real data,

our approach will behave efﬁciently. Thus, ongoing

works are conducted to collect on-line mobility data

obtained, for instance, through mobile networks. We

are aware that the results presented in this paper are

mainly based on synthetic data and thus cannot be in-

terpreted as realistic results. However, as we obtain

expected values we believe that our model behaves

correctly and should give useful information when ap-

plied to real data in the future.

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