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A multi-agent simulation to assess the risk of malaria re-emergence in southern France

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Page 1: A multi-agent simulation to assess the risk of malaria re-emergence in southern France

e c o l o g i c a l m o d e l l i n g 2 2 0 ( 2 0 0 9 ) 160–174

avai lab le at www.sc iencedi rec t .com

journa l homepage: www.e lsev ier .com/ locate /eco lmodel

A multi-agent simulation to assess the risk of malariare-emergence in southern France

Catherine Linarda,∗, Nicolas Ponconb, Didier Fontenilleb, Eric F. Lambina

a Department of Geography, Université Catholique de Louvain, Place Pasteur 3, B-1348 Louvain-la-Neuve, Belgiumb Institut de Recherche pour le Développement (IRD), UR016, Caractérisation et contrôle des populations de vecteurs,911 avenue Agropolis, BP 64501, 34394 Montpellier Cedex 5, France

a r t i c l e i n f o

Article history:

Received 1 April 2008

Received in revised form

5 August 2008

Accepted 3 September 2008

Published on line 14 October 2008

Keywords:

Multi-agent simulation

Human biting rate

Malaria

Camargue

Anopheles hyrcanus

Land use

a b s t r a c t

A multi-agent simulation (MAS) was developed to assess the risk of malaria re-emergence

in the Camargue in southern France, a non-endemic area where mosquitoes of the genus

Anopheles (Culicidae) live. The contact rate between people and potential malaria vectors,

or the human biting rate, is one of the key factor to predict the risk of re-emergence of

malaria, would the parasite be introduced in the region. Our model (called MALCAM) rep-

resents the different agents that could influence malaria transmission in the Camargue –

people, mosquitoes, animal hosts and the landscape – in a spatially explicit environment.

The model simulates spatial and temporal variations in human biting rate at the landscape

scale. These variations depend on the distribution of people and potential vectors, their

behaviour and their interactions. A land use/cover map was used as a cellular-spatial sup-

port for the movements of and interactions between mobile agents. The model was tested

for its sensitivity to variations in parameter values, and for the agreement between field

observations and model predictions. The MALCAM model provides a tool to better under-

stand the interactions between the multiple agents of the disease transmission system, and

the land use and land cover factors that control the spatial heterogeneity in these interac-

tions. It allows testing hypotheses and scenarios related to disease dynamics by varying the

value of exogenous biological, geographical, or human factors. This application of agent-

based modelling to a human vector-borne disease can be adapted to different diseases and

regions.

transmission were suspected in southern France in 2006

1. Introduction

The southern region of France is part of the malaria-freeareas where mosquitoes of the genus Anopheles (Culicidae) live(Poncon et al., 2007a). Historically, these Anopheles were vec-

tors of Plasmodium, the pathogen responsible for malaria, butthe disease had been eradicated in Europe thanks to improve-ments in living standards, targeted controls and habitat mod-

∗ Corresponding author. Tel.: +32 10 472867; fax: +32 10 472877.E-mail addresses: [email protected] (C. Linard), nicola

[email protected] (D. Fontenille), [email protected] (E.F. L0304-3800/$ – see front matter © 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.ecolmodel.2008.09.001

© 2008 Elsevier B.V. All rights reserved.

ifications (Alten et al., 2007; Kuhn et al., 2003). Anopheles stilllive in southern France and their ability to transmit Plasmod-ium imported from other continents should not be neglected(Alten et al., 2007). For example, two cases of autochthonous

[email protected] (N. Poncon),ambin).

(Doudier et al., 2007). The Camargue region in southern Franceis considered as a potential site for the re-emergence ofmalaria in Europe, even if the risk is low (Poncon et al., 2007a).

Page 2: A multi-agent simulation to assess the risk of malaria re-emergence in southern France

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Land use and climate changes could create more support-ve conditions for this re-emergence. Climate warming is notsufficient factor for the reinstallation of malaria endemicity

Kuhn et al., 2003; Reiter, 2000, 2001). Land use and land coverhanges are likely to have a more direct impact on the risk ofe-emergence of the disease, by affecting mosquito breedingrounds (e.g., the surface of marsh wetlands) and the con-act rate between people and mosquitoes (Kuhn et al., 2003;eiter, 2000, 2001). In the Camargue, anthropogenic ecosystemhanges – particularly those associated with rice cultivation –ave significantly affected vector species in the past (Poncont al., 2007b).

To assess the risk of establishment of a vector-borne dis-ase such as malaria, the Basic Reproductive Rate (R0) – whichuantifies the average number of new cases of the infectionhat will arise from the introduction of an infective host intosusceptible population (Mcdonald, 1957) – has been exten-

ively used (Rogers, 1988; Anderson and May, 1991; Snow andilles, 2002). In this calculation, the degree of contact betweeneople and vectors, or the human biting rate, is an essentialactor for disease dynamics. Factors influencing the humaniting rate include the relative population densities and spa-ial distributions of both vectors and people (Ostfeld et al.,005), and their movements and behaviours. Previous stud-es based on the R0 have typically assumed a constant valuecross space of the human biting rate, given the difficulty inbtaining spatially explicit and quantitative estimates of thisariable.

The literature on the modelling of the spread of vector-orne diseases – and particularly malaria – is abundant.esides mathematical models such as the R0 mentionedbove, the Entomological Inoculation Rate (Rogers, 1988;nderson and May, 1991; Snow and Gilles, 2002), or otherathematical models that include environmental factorsostly related to meteorological conditions (Focks et al.,

993, 1995; Wyse et al., 2007), many statistical models pre-ict the spatial distribution of vectors based on environmentalariables (Sweeney et al., 2007; Vanwambeke et al., 2007a;ran et al., 2008) or temporal fluctuations in human casesChattopadhyay et al., 2004; Hu et al., 2006). Only a fewtudies have so far combined spatial and temporal aspectsf the spread of vector-borne diseases (Torres-Sorando andodríguez, 1997; Muller et al., 2004).

The aim of this study was to develop an innovative,patially explicit modelling approach that integrates theovements and behaviours of people and vectors to model

patial variations in human biting rate at the landscape scale.ur hypothesis was that Multi-Agent Simulations (MASs) orgent-Based Models (ABMs) have the ability to represent the

actors influencing transmission risk of a disease and theirnteractions, in a spatially explicit environment. An agent isn autonomous computer entity capable of interacting withther agents and adapting its behaviour to a changing environ-ent (Bousquet et al., 1999; Hare and Deadman, 2004; Parker

t al., 2003). Each agent pursues its own objectives and followspecific decision rules. Agents can represent heterogeneous

ntities, e.g. people, animals, institutions, or land parcels. Thegent-based approach allows simulation and understandingf complex systems though the modelling of discrete events,

n a bottom-up approach (Bousquet and Le Page, 2004).

0 ( 2 0 0 9 ) 160–174 161

MASs are increasingly used in environmental science(Bousquet et al., 1999; Bousquet and Le Page, 2004; Hare andDeadman, 2004; Parker et al., 2003). MASs allow combiningenvironmental and social processes and are thus particularlyadapted to multidisciplinary approaches of systems. So far,very few studies applied MAS to the spatial epidemiology ofvector-borne diseases (Muller et al., 2004).

The MAS developed in this study, called MALCAM, repre-sents the spatio-temporal dynamics of interactions betweenthe agents that could influence malaria transmission in theCamargue: people, mosquitoes, animal hosts and the land-scape. In some MASs, the landscape is simply considered asa support for movements of and interactions between agentsthat constraints their behaviours. In other MASs, landscapeunits (e.g., cells of a landscape matrix) are considered as a setof agents with their specific attributes and actions (Bousquetand Gautier, 1999). We adopted this second approach, wherespatial entities interact with other agents of the system.

Vanwambeke et al. (2007b) expressed the contact ratebetween people and vectors of disease as the “actual humanbiting rate” (ABR), i.e. the actual number of bites given tohuman agents, which is different from the “potential bitingrate” (PBR), the number of bites that could be potentially givento human agents. The latter depends on the density of host-seeking female mosquitoes while the former is the fractionof these mosquitoes that actually encounter a human host intheir quest for a blood meal. We adopted this terminology inthis paper. The model computed successively the presence ofvectors, the PBR and the ABR.

2. Study zone and data collection

The Camargue is a wetland area in southern France, coveredby pools and marshes. It is characterized by a Mediterraneanclimate, with warm and dry summers and mild and wet win-ters. Our study zone, called “Carbonnière”, is about 25 km2

and includes the typical biotopes of the Camargue, principallydifferent kinds of marshes and rice fields. This area consti-tutes an ideal habitat for Anopheles. Human activities and theirrelated land uses include residence, cultivation, cattle raising,hunting, and tourism. The number of tourists visiting the areavaries from 350 people per day in winter to more than 2000people per day in summer (Langewiesche, 2005).

2.1. Entomological data

The biology of Anopheles was studied in 2005 in two sites: the“Carbonnière” area and the natural reserve of the “Marais duVigueirat” (Poncon et al., 2007a,b). This study identified fourAnopheles species: An. hyrcanus, An. melanoon, An. atroparvus,and An. algeriensis. Given its abundance and anthropophily,only An. hyrcanus could play a significant role in malariatransmission in the Camargue (Poncon et al., 2007a). Adultmosquitoes were captured in both study areas every 2-week,

from March to October 2005, with different trapping methods:light traps + CO2, horse bait traps, human bait catch, and bycollecting females in resting sites (for detailed trapping meth-ods, see Poncon et al., 2007a).
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162 e c o l o g i c a l m o d e l l

In the study zone, larvae principally develop in rice fields(Tran et al., 2008). An. hyrcanus larvae were also reported inother biotopes such as reed beds and marshes with scirpus,but only when they were close to rice plantations (Tran et al.,2008). We estimated the average number of An. hyrcanus lar-vae per volume of water in rice fields. Larvae were collectedin three different rice fields, at 3 or 4 dates in August 2006. Ineach rice field, we selected between 15 and 23 equally spacedpoints of collection to cover the field with a regular grid. Theminimum distance between two points was 9 m. Around eachcollection point, we took 5 dips of water in a radius of 1.5 maround the point and noted the water depth. Larvae at stagesL3 and L4 in these dips were collected and identified. We thenestimated a range for the total number of larvae in these 5dips based on life-table studies. These studies provide dataon mortality rates of larvae but rarely distinguish the differ-ent stages. Okogun (2005) studied mortality rates of Anophelesmalaria vectors An. pseudopunctipennis and An. gambiae at thedifferent aquatic stages in cultures and found that between27 and 37% of larvae at stages 1 and 2 reached the stages3 and 4. We extrapolated the range for the total number oflarvae from the 5 dips to the volume of water contained ina 30 m × 30 m rice-field pixel. This assumes that larvae weredistributed homogeneously in the water and thus that our dip-ping was representative of the water volume. A collection biaswould arise if the larvae distribution would strongly dependon water level, temperature or other conditions, which is notthought to be the case.

2.2. Spatial data

We used a land use/cover map produced by Tran et al. (2008)based on Landsat satellite data from 2001. We aggregated the21 classes of the original map in 5 classes relevant for the MAS:rice fields, vineyards, marshes and reed beds, urban areas, andother land use/cover types. Some spatial data were collectedin the field using a Global Positioning System (GPS): the exactposition of the hotel and campsite located in the study zoneand the spatial distribution of pastures for horses and bulls.We attributed a parcel number to each pasture with animalsand recorded the number of horses and bulls that were presentin June, August, September and October 2006.

2.3. Socio-economic surveys

The first social survey conducted in the study zone in 2005pursued four objectives (Langewiesche, 2005): (i) to describethe main human activities in the study zone, (ii) to describethe temporal and spatial distribution of these activities, (iii) toestimate the number of permanent inhabitants and the num-ber of people temporarily present in the zone for each monthof the year, and (iv) to interview people on their use of protec-tion measures against mosquitoes. The main human activitiesin the study zone are related to agriculture (rice growing, grapegrowing for wine production, reeds cutting, market garden-ing, horticulture, and cattle farming) and leisure and tourism

(pedestrian visits, visits in sport-utility vehicles or barges,camping, stays in a hotel, dining at restaurants, hunting,and fishing) (Table 1). Interviews with stakeholders showedthat rice growers, wine growers and cattle farmers were most

2 2 0 ( 2 0 0 9 ) 160–174

exposed to mosquitoes because of their working hours (beforesunrise and/or during sunset) and/or their places of work (ricefields and marshes). Tourists and hunters were also particu-larly exposed due to their behaviour that is poorly adapted tomosquito biting and to their presence outdoors after sunset(mainly concerning hunters and campers).

A second survey was carried out in September and Octo-ber 2006 and focused on past and possible future land usechanges (Langewiesche, 2006). We interviewed different landusers (a rice grower, a reeds cutter, a hunter, and two cattlefarmers) who provided additional information on their landuse, movements in the study area and preventive behaviourrelated to mosquitoes. In 2007, a third social survey performedby Torres (2007) aimed at providing quantitative data on thelevel of protection against mosquito bites by local people andtourists. A questionnaire on personal details, perception ofthe risks of mosquito bites, protection measures used, andknowledge of mosquito-borne diseases was submitted to 160persons who agreed to be interviewed after being met inthe study area or contacted by phone from July to October2007.

3. The MALCAM model

The model was developed using NetLogo, a free programmableenvironment for the modelling of complex phenomena(Wilensky, 1999). The description of the model below followsthe standard ODD protocol (Overview, Design concepts, andDetails) for individual-based and agent-based models (Grimmet al., 2006). We also used the Unified Modelling Language(UML), which includes a class diagram and a sequence diagram(Booch et al., 2004).

3.1. Overview

3.1.1. PurposeThe purpose of the model is to simulate spatial and temporalvariations of the contact rate – or ABR – between potentialmalaria vectors and people in the Camargue. The broaderobjective is to understand the factors that control these vari-ations and thus the risk of re-emergence of malaria in thisregion.

3.1.2. State variables and scalesThe model focuses on An. hyrcanus, the only current potentialmalaria vector in the Camargue (Poncon et al., 2007a,b). SinceAn. hyrcanus only bites at night and during evenings, daytimehours were excluded from the model. The model covers onecomplete season of mosquito activity, from May to October.In NetLogo, agents can be static or mobile. We used the landuse/cover map as a cellular-spatial support for the movementsof and interactions between mobile agents – the mosquito vec-tors and their human and animal hosts – and between mobileand static agents – the landscape cells.

Fig. 1 presents the UML class diagram of agents that com-

pose the MAS. Mobile agents are divided in two classes:humans and animals. The latter class includes horses andbulls, which are also potential hosts for An. hyrcanus. Wedivided human agents in different classes according to their
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Table 1 – Number of people present per day in the study zone for the different months of the year 2005 (adapted from Langewiesche, 2005)

January February March April May June July August September October November December

Permanent inhabitants 200 200 200 200 200 200 200 200 200 200 200 200

Regular workersHorticulture 10 10 10 10 10 10 10 10 10 10 10 10Grape growing 8 8 8 8 8 8 8 8 8 8 8 8Market gardening 85 85 85 85 85 85 85 85 85 85 85 85Rice growing 4 4 4 4 4 4 4 4 4 4 4 4

Total 107 107 107 107 107 107 107 107 107 107 107 107

Seasonal workersGrape growing 0 0 0 0 0 0 0 20 20 20 5 5Cattle farming 0 0 0 6 6 6 6 6 6 0 0 0Reeds cutting 1 1 1 0 0 0 10 10 0 0 0 3Market gardening 10 10 20 60 100 100 40 40 10 10 10 10

Total 11 11 21 66 106 106 56 76 36 30 15 18

Tourist activitiesRice-fields visits 0 0 0 0 4 1 17 17 17 0 0 0Visits in 4 × 4 0 0 0 0 5 5 20 20 0 0 0 0Guided visits 0 0 1 1 1 1 2 2 1 1 0 0Visits in barges 0 0 0 0 200 600 800 800 800 200 0 0Camping 0 0 0 100 100 100 600 600 100 0 0 0Hotel 0 0 0 50 50 300 300 300 300 0 0 0

Total 0 0 1 151 360 1007 1739 1739 1218 201 0 0

Leisure activities:Hunting/fishing 13 13 0 0 0 0 0 13 13 13 13 13Scientific studies 8 8 8 8 8 8 8 8 8 8 8 8

Total 337 337 335 530 779 1426 2108 2141 1580 557 341 344

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clas

Fig. 1 – UML

activities: rice growers, wine growers, hunters, local inhab-itants and tourists. We only considered human activitiesthat were relevant for the evening and nighttime periodsbeing modelled. Human attributes such as the protection levelagainst mosquito bites and the location in a landscape unit ata particular moment depend on the activity and land use. Eachhuman agent can be present or absent in a particular locationdepending on the period of the year, the day, and the hourstypical of a specific activity. Animals are present throughoutthe season on their parcel and can only move within theselimits. Each mobile agent is located on a 30 m × 30 m cell, char-acterized by a land use/cover type. Each cell belongs to oneof the five land use/cover classes. Human agents move onthese cells with respect to their activity and related land use.Tourists are linked to their overnight location: the campsite orthe hotel. Each cell has also an attribute related to the pop-ulation of An. hyrcanus it supports. Given the large number

of mosquitoes, we considered the population of mosquitoeslocated on one cell as a single agent instead of consideringeach individual mosquito as an agent. Procedures related tothe development and movement of mosquitoes are thus rep-

s diagram.

resented by meta-population modelling that, in the case ofmosquitoes only, replace a pure agent-based simulation in ourmodel. For a summary of all parameters and variables of themodel, see Table 2.

Time is modelled as discrete time-steps. Three periods rel-evant for An. hyrcanus–human interactions were representedin the model: (i) from the sunset until 1 h after sunset (period1), (ii) from 1 h after sunset until 2 a.m. (period 2), and (iii) from2 a.m. until the sunrise (period 3). The time-step of the modelis one period.

3.1.3. Process overview and schedulingAt each time-step, the same sequence of procedures is acti-vated, in the same order. Fig. 2 presents the procedures in timeorder in an ULM sequence diagram. Each procedure is appliedby a certain type of agent: cells, humans, animals, or at thesystem level (referred to as scheduler level). After the updat-

ing of global variables, such as daily temperature and lengthof the gonotrophic cycle, cells calculate the number of An. hyr-canus larvae and adults they support. People present at thistime appear in the land use/cover class associated with their
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Table 2 – Summary of input parameters and variables

Parameters and variables Abbreviation Value/range of values/equationa Reference

Global variables

Daily average temperature (◦C) T 14–28 Meteo FranceLength of the gonotrophic cycle (days) u Eq. (1) Detinova (1962)Time-step length P 1/3Reproduction rate r 3.25 Calibrated based on field data

(larvae collection)Development rate d Eq. (3) Jetten and Takken (1994)Daily mortality rate m 0.21 Poncon et al. (2008)Maximum dispersal distance (in number of cells) Flight-dist 70 Service (1997)Proportion of mosquitoes that did not find any host during period 1and continue to move during period 2

Move-1 0.2 Estimated from field data (activityof An. hyrcanus during the night)

Proportion of mosquitoes that did not find any host during period 2and continue to move during period 3

Move-2 0.6 Estimated from field data (activityof An. hyrcanus during the night)

Proportion of mosquitoes that did not find any host during period 3and continue to move the following day

Move-3 0.1 Estimated from field data (activityof An. hyrcanus during the night)

Attributes of cells

Land use LU Rice field; vineyard; marshes andreed beds; urban; other

Landsat classification (Tran et al.,2008)

Parcel number Parcel 1–21Presence of water in rice fields Water True; false Field surveysPresence of vegetation in rice fields Vegetation True; false Field surveysNumber of An. hyrcanus female larvae Larvae Eq. (2)Maximum number of An. hyrcanus female larvae supported larvaemax 400,000 Expert judgmentNumber of An. hyrcanus adult females Adults Eq. (4)Number of An. hyrcanus adult females at the beginning of the season Ad-setup Random number between 0 and 40 Calibrated based on field data

(larvae collection)Number of An. hyrcanus adult females looking for a blood meal adultsMove Eq. (5)Potential biting rate PBR Eq. (6)Actual biting rate ABR Eq. (8)

Attributes of humans

Presence in the study zone Presence True; false Social surveysActivity Activity Rice grower; wine grower; hunter;

inhabitant; hotel tourist; camperSocial surveys

Protection level against mosquito bites Protection 0–1Average protection of local people (workers and inhabitants) p-Local 0.7 Estimated based on social surveysAverage protection of hotel tourists p-Hotel 0.5 Estimated based on social surveysAverage protection of campers p-Camping 0.3 Estimated based on social surveysActual biting rate ABR Eq. (7)

a Single values were assigned to parameters, while ranges of values or equations were assigned to variables that vary at each time step.

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166 e c o l o g i c a l m o d e l l i n g 2 2 0 ( 2 0 0 9 ) 160–174

eque

Fig. 2 – UML s

activity, move, and set their protection level against mosquitobites. Then, cells disperse adult females looking for a bloodmeal to neighbouring cells and calculate their PBR. Humanagents calculate their ABR and each cell then also calculatesits own ABR. Adult female mosquitoes looking for a breedingsite to lay eggs go back to rice fields. Finally, people disappear

and animals move.

Some procedures are only activated under particular con-ditions. For example, there must be water and vegetation inrice-field cells to activate the setLarvae procedure.

nce diagram.

3.2. Design concepts

3.2.1. ObservationThe user interface of the MALCAM model in NetLogo displaysspatial and temporal variations of the abundance of An. hyr-canus, PBR and ABR. Areas with a high human biting rate at

certain times of the year and groups of human agents mostaffected by mosquito bites can be identified. Global level out-puts, such as the total number of human-vector contacts (totalABR) over the season, are also computed.
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.2.2. Sensingosquitoes react to external environmental factors such as

emperature (via the length of the gonotrophic cycle and theevelopment rate), the presence of human or animal hostsn their cell, and the location of breeding sites (rice fields).uman agents are assumed to know when (i.e., which month,ay and period) and where (i.e., on cells allocated to which

and use/cover class) to exercise their activity.

.2.3. Interactionshe dynamics of the system is driven by interactions betweeneople, mosquitoes, animal hosts, and land. Mosquitoes seeko bite a host on their cell, and people use protective measureso avoid being bitten. Land cover change caused by humanctivity is only represented in rice fields: vegetation cover andater level vary during the season in response to agriculturalractices. Rice fields are flooded and drained artificially usingrivate pumping. These agricultural practices influence theevelopment of larvae as they develop in rice fields from mid-

une to late August.

.2.4. Stochasticityome processes in the model are stochastic. The protection

evels of human agents are represented by Gaussian probabil-ty distributions to reflect the heterogeneity between agents.he movements of people and animals are stochastic within

heir specific land use or parcel. In addition, some initial con-itions are defined stochastically, as described below.

.3. Details

.3.1. Initialisationhe initial conditions of the model are mainly based on fieldata. The land use/cover map was extracted from Landsat

mages. The number of people present in the study zone wasetermined by social surveys. A random number (between 0nd 40) of adult female mosquitoes are present in each rice-eld pixel at the start of summer (we assume that mosquitoesre already in rice fields, even if they stay in marshes andeed beds during the diapause). We determined a maximumumber of animals that can be present on each parcel. At theeginning of each simulation, the presence or absence of eachnimal is randomly chosen. The location of people and ani-als among the cells of a given land use/cover unit or parcel

s defined randomly.

.3.2. Inputhe only external environmental condition is the average daily

emperature for the year 2005. It was extracted for the stationf Aigues Mortes that is located 4 km from the study zone, forhe year 2005 (Meteo France, http://www.meteofrance.com).

.3.3. Submodels

.3.3.1. Updating of globals (updateGlobals). In addition to thepdating of time counters (month, day and period) and dailyemperature (T), the length of the gonotrophic cycle (u) is

pdated once a day, at period 1. It is the time between twolood meals (in days) and includes the total duration of theearch for a blood meal, digestion and oviposition (Jetten andakken, 1994). This length depends on the daily average tem-

0 ( 2 0 0 9 ) 160–174 167

perature (T). For mosquitoes from temperate regions, it iscalculated via the following equation, considering that therelative humidity is between 70 and 80% (Detinova, 1962):

u =(

36.5T − 9.9

)+ 1 (1)

The parenthesis represents the time needed for blood diges-tion, to which 1 day was added to account for the search for ablood meal and the oviposition.

3.3.3.2. Larvae development (setLarvae). The development oflarvae of An. hyrcanus requires both water (flooded fields) andvegetation in rice fields. These conditions have been addedas constrains for the setLarvae procedure. Larvae can appearfrom the middle of June (when vegetation grows) to the end ofAugust (when rice fields are drained). The setLarvae procedureis also activated once a day, at period 1. Under these condi-tions, the abundance of larvae at all stages, in each rice-fieldpixel is calculated as

larvaetx = larvaet−1

x +((

adultst−1x

(3P

u

)r

)− (larvaet−1

x 3Pd))

×(

1 − larvaet−1x

larvaemax

)(2)

where larvaetx is the number of An. hyrcanus female larvae at

time-step t in a rice-field pixel x and larvaet−1x is the number

of An. hyrcanus female larvae at time-step t − 1 in the pixel x.The next part of the equation represents the growth in lar-vae population. The component (adultst−1

x (3P/u)r) is the newlarvae laid, with adultst−1

x being the number of adult An. hyr-canus; P is the time-step length in days (P is multiplied by 3here as larvaet

x is updated only once a day, at period 1), and ris the reproduction rate. The division by u allows to only con-sider adult females that lay eggs at that time. Assuming thatthe sex ratio is 0.5, r is half of the reproduction rate, i.e. thenumber of female larvae laid that will reach the adult stage,thus including mortality rates at larvae stages. The compo-nent (larvaet−1

x 3Pd) is the number of larvae that become adultbetween t − 1 and t (with d being the development rate of lar-vae). According to Jetten and Takken (1994), the developmentrate of Anopheles larvae depends mainly on the temperatureof water, according to the following empirical relationship:

d = 0.021(e0.162(T−10) − e0.162(35−10)−((35−T)/5.007)) (3)

The reproduction rate (or fecundity) depends on the age of thefemale and varies between 100 and 350 eggs per batch (Jettenand Takken, 1994). Given the high mortality rates for theaquatic stages of Anopheles (Jetten and Takken, 1994; Okogun,2005), we expect a very low mean value for the reproductionrate.

Empirical data on larvae densities were used to calibratethe reproduction rate. At the end of August, when larvaedensities are the highest, we roughly estimated the average

density of female larvae to be between 118,000 and 162,000per rice-field pixel (i.e., 900 m2). We tested the model with dif-ferent values for the reproduction rate and retained the valuethat provided late-August larvae densities that were the clos-
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168 e c o l o g i c a l m o d e l l i n g 2 2 0 ( 2 0 0 9 ) 160–174

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Fig. 3 – Number of people present in the study zone

est to empirical data. The average reproduction rate was setat 3.25.

In Eq. (2), we added the component (1 − (larvaet−1x /

larvaemax), where larvaemax is the maximum number of larvaethat a rice-field pixel can support, i.e. the carrying capacity ofthe pixel. It was set at 500,000, which is more than the max-imum observed density of female larvae. This gives a logisticcurve to the larvae population (Mulligan and Wainwright,2004).

3.3.3.3. Update the number of adults (setAdults). Based on thelarvae abundance larvaet

x, the number of adults adultstx at time

t on pixel x is calculated once a day, at period 1, as (adaptedfrom Vanwambeke et al., 2007b):

adultstx = adultst−1

x + (larvaet−1x 3Pd) − (adultst−1

x 3Pm) (4)

where the first parenthesis represents the newly developedlarvae and the second parenthesis represents the number ofadults that died between t − 1 and t (with m being the dailymortality rate). Poncon et al. (2008) estimated the mean sur-vival rate – i.e. the probability of a mosquito surviving througha whole day – of An. hyrcanus in the study zone to be 0.79,based on parity rates observed in June, July and September2005. Given that m = 1 − s, we fixed m to 0.21.

3.3.3.4. Human movement (appear and move). Based on theworking hours of each group of agents and on data fromTable 1, we determined the number of people present in thestudy zone for each period of each month (Fig. 3). At each time-step, the human agents present in the zone appear randomlyon the land use associated with their activity. Associationsbetween agents and land uses are detailed in Fig. 1. Peoplemove randomly within the land use classes associated withtheir main activity. During period 1, we consider that a randompercentage of tourists (between 0 and 50%) move to urbanizedcells (e.g., for a late dinner or party). However, all tourists comeback to their campsite or hotel for the rest of the night, during

periods 2 and 3.

3.3.3.5. Update the protection level of humans against mosquitobites (setProtection). The efficacy of protection measures

g the year and during the three periods considered.

against mosquitoes is extremely variable. It depends princi-pally on the method used: mosquito nets, window screens,repellents, clothes with adequate coverage, etc. Touristsmostly use repellents. Results from studies on their efficacyvary considerably between mosquito species and geographicalregions, and are therefore difficult to extrapolate (Coosemansand Guillet, 1999). Moreover, the efficacy of repellents alsodepends on the density of mosquitoes, the biochemical attrac-tiveness of the host to biting species, and the temperature,humidity and wind intensity in the immediate environment(Fradin and Day, 2002).

In the model, the protection level (between 0 and 1) rep-resents the proportion of total bites that are avoided thanksto protection measures. Qualitative and quantitative dataon the protection level of different agents, collected duringsocial surveys, reveal a large difference between local inhab-itants and tourists. Inhabitants of the study area generallyuse air-conditioning systems and mosquito nets. They alsorather stay indoor during peaks of mosquito aggressivity. Bycontrast, the behaviour of tourists is often inadequate—e.g.,they visit marshes wearing shorts and short-sleeved t-shirts.They are poorly informed about mosquitoes, even thoughtourist operators generally warn about mosquito nuisance.We therefore fixed a higher level of protection for localworkers and inhabitants than for tourists. Moreover, as An.hyrcanus is only active at night, campers are more exposedto mosquito bites than tourists staying at the hotel. In themodel, levels of protection follow normal distributions, withthe mean and standard deviation depending on the cate-gory of people: mean of 0.7 for workers and inhabitants, 0.5for tourists staying in the hotel, and 0.3 for campers, witha standard deviation of 0.1 in all three cases. We considerthat inhabitants and tourists staying at the hotel are com-pletely protected during period 2, with a protection level of1.

3.3.3.6. Dispersal of adult females looking for a blood meal(moveToHost). Once they reach the adult stage, mosquitoes

move within or outside rice fields for feeding, shelteringor laying eggs (Service, 1997). This short distance dispersalis represented by neighbourhood rules (cellular automata)in MALCAM and is divided in two phases: the search for
Page 10: A multi-agent simulation to assess the risk of malaria re-emergence in southern France

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lood (moveToHost) and the search for a breeding site (move-oRice).

During the first phase, the number of adult mosquitoes thatove to look for a blood meal (adultsMove) is estimated as

dultsMove = adults3P

u(5)

hese goal-oriented movements are generally over short dis-ances, but can reach more than 1 km if hosts are far from thereeding site (Service, 1997). We considered that mosquitoesove randomly until they find a cell with a human or animal

ost to bite. The CO2 emitted by hosts attracts mosquitoes atmaximum distance of 20 m (Kettle, 1995). Beyond this dis-

ance, a mosquito can detect the CO2 but cannot direct itselfowards the host. We thus considered that mosquitoes cannly detect hosts that are located in the same cell. In theodel, the population of mosquitoes of one rice-field pixel

iffuses homogeneously to the eight neighbouring cells. Thisperation is repeated a maximum of 70 times per time-step,ntil mosquitoes reach a cell with a host. Mosquitoes movehus with a maximum distance of 2100 m, which correspondso 70 pixels, per period. The model computes the number ofhese mosquitoes that find a human or an animal host. Twentyercent of mosquitoes that did not find a host during periodcontinue to move during period 2. This proportion is 60%

etween periods 2 and 3, and 10% between period 3 and theollowing day. The mosquitoes that did not find a human orn animal host and that did not keep moving in the followingeriod are assumed to have biten a small mammal on theirell. These percentages are based on the nighttime activity ofn. hyrcanus observed in the field.

.3.3.7. Calculate the potential biting rate (calculatePBR). Theotential biting rate of the pixel x, PBRx, depends on the abun-ance of vectors looking for a blood meal:

BRx = adultsMovex (6)

ll the mosquitoes that moved during the previous procedurere thus prone to bite if they find a host.

.3.3.8. Calculate the actual biting rate (calculateABR). TheBR depends on the presence and abundance of humannd animal hosts, on adult mosquitoes looking for a bloodeal; and on the level of protection of human agents againstosquitoes. The anthropophily (the preference of mosquitoes

or biting humans rather than other hosts) depends on theresence of humans and on biological characteristics ofosquitoes (Pages et al., 2007). We consider that mosquitoes

ite the first host that they find, whether it is a human or ani-al. If there is more than one host within a pixel, mosquitoes

elect randomly one host to bite. Human and animal hostsave the same probability of being bitten (i.e., the anthro-ophily is 0.5). The model computes the ABR for each humangent, according to its location, and for each cell. The ABR at

ime t of a human y situated on pixel x is calculated as

BRty = PBRt

x

Htx

(1 − protectiony) (7)

0 ( 2 0 0 9 ) 160–174 169

where Hx is the number of hosts (human or animal) present onpixel x; and protectiony is the protection level of the human y.The ABR of each cell is computed by summing human-vectorcontacts occurring on the cell:

ABRtx =

∑ABRt

y (8)

3.3.3.9. Movements of mosquitoes looking for a breeding site(moveToRice). The second phase of movements of mosquitoes(i.e., search for a breeding site) is activated at the end of period3. At this time, mosquitoes that are looking for a breeding siteto lay eggs go back to rice fields. We consider that the propor-tion 3P/u of adult mosquitoes located outside of rice-fields isredistributed homogeneously in all rice-field pixels.

3.3.3.10. Humans disappearance (disappear). At the end of thesequence of procedures that are run over one time step, all thehumans present in the study zone disappear. They may re-appear at the next time-step if their land use activities requireit.

3.3.3.11. Movement of animals (move). Animals move ran-domly between cells that belong to their parcel.

4. Simulation experiments

Simulation experiments performed on MALCAM were aimedat building confidence in the model and identifying possiblefuture improvements. The sensitivity analysis – performed bymeasuring variations in model output in response to vari-ations in input parameters – was aimed at checking therobustness of the model and identifying the parameter val-ues that need to be most accurately estimated. We also testedthe agreement between observations and model predictions ofthe spatial and temporal distribution of mosquitoes based onmosquito collection data for multiple traps over a full season.

4.1. Sensitivity analysis

We tested the model sensitivity to all the parameters for whicha value was defined based on the literature, field data or expertknowledge. The value of 11 parameters was varied one by one,within a range of ±20%, in steps of 5%, while holding all otherparameters constant. We limited the variation of each param-eter to ±20% as this range reflects the level of uncertainty onparameter values. Given the stochastic elements in the model,we performed 10 simulations for each parameter configura-tion and thus ran the model 80 times for each parameter plusone set of 10 simulations with baseline parameter values, giv-ing a total of 890 model runs. We observed the impact of thesevariations on the total number of bites on humans over thefull season (total ABR), which indicates the total human pop-ulation at risk over an entire season.

4.2. Observations versus model predictions

To test the ability of the model to reproduce the spatial andtemporal distributions of An. hyrcanus, we compared the num-ber of adults collected in the field with the number predicted

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170 e c o l o g i c a l m o d e l l i n g 2 2 0 ( 2 0 0 9 ) 160–174

Fig. 4 – Total ABR per pixel predicted by the MALCAM model (average calculated from 10 simulations). Discretizationmethod: quantiles. The map also shows the spatial location of trapping sites, tourist residences, rice fields and urban areas

in the study zone (Carbonnière).

by the model. Model predictions were calculated as the aver-age value of 10 simulations. We computed Pearson correlationcoefficients to test for the degree of association betweenobserved and predicted values.

To evaluate the spatial distribution of An. hyrcanus aroundrice fields, we used the total number of mosquitoes over theseason at different locations. As mosquitoes were collectedevery 2-week in the field, we also took model predictions every2-week. Field data were collected at 8 different locations inthe “Carbonnière” zone (Fig. 4). However, during trapping ses-sions (in July 2005), insecticide spraying to control Ochlerotatuscaspius mosquitoes was performed in a rice field of the studyzone. As spraying impacts An. hyrcanus populations as well(Tran et al., 2008), we conducted the analysis with and withoutthe two trapping locations at less than 200 meters from thisrice field (field sites 6 and 7 in Fig. 4). To increase the num-ber of collection points for statistical significance, we addeddata collected in the field at the nearby and ecologically sim-ilar “Marais du Vigueirat”, where no spraying was performed.We thus computed predicted values for the 8 locations in the“Carbonnière” were field trapping took place and for 8 loca-tions in the “Carbonnière” situated at the same distance from

rice fields as trapping sites in the “Marais du Vigueirat”.

To evaluate the temporal distribution of An. hyrcanus overthe season, we compared the total number of mosquitoescollected in the field and predicted by the model at the 6

trapping locations in the “Carbonnière” for 13 different datesequally spread over the season. Trapping sites 6 and 7 werealso removed from the calculation as they were strongly influ-enced by mosquito control measures.

5. Results

5.1. Sensitivity

Results from the sensitivity analysis (Fig. 5) show that twoparameters strongly influence the modelling of human-vectorcontacts: the reproduction and mortality rates of mosquitoes(Fig. 5a). These two parameters are related to the biology ofmosquitoes and control their abundance. They have an expo-nential relationship with the ABR. An increase of 20% of thereproduction rate induces an increase of more than 250% inthe total ABR. The model is also sensitive to two other param-eters, to a lesser extent: the maximum number of adult femaleAn. hyrcanus at the start of summer and the proportion ofmosquitoes that did not find any host during period 2 andcontinue to move during period 3 (move-2). For these two

parameters, an increase of 20% of the input parameter inducesan increase of the output variable that exceeds 20%. For all theother parameters, changes in the output variable never exceed20%. Some parameters such as the percentages of mosquitoes
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e c o l o g i c a l m o d e l l i n g 2 2 0 ( 2 0 0 9 ) 160–174 171

Fig. 5 – Results from the sensitivity analysis for (a) the reproduction and mortality rates of mosquitoes, (b) other biologicalp at cop

tap

5

Fdlfiup0b

lASftboWcF

arameters of mosquitoes, (c) percentages of mosquitoes throtection levels of people.

hat continue to move from one period to the other (move-1nd move-3, Fig. 5c) and the average protection level of localeople do not have a clear relationship with the total ABR.

.2. Observations versus model predictions

ig. 6 shows the decreasing abundance of An. hyrcanus withistance to rice fields. The low number of mosquitoes col-

ected at the two sites close to the insecticide-treated riceelds confirms the impact of this measure on An. hyrcanus pop-lation. The Pearson correlation coefficient between field andredicted data is 0.31 (p = 0.25; N = 16) for all trapping sites and.74 (p = 0.003; N = 14) after removal of the two sites influencedy mosquito-control measures.

For the seasonal variation of An. hyrcanus population, col-ected and predicted data show a marked increase in earlyugust, a peak in late August, followed by a drop in earlyeptember (Fig. 7). Data collected in the field show a peakollowed by a sharp drop in July, which could be attributedo insecticide spraying in one-rice field among other possi-le causes. The Pearson correlation coefficient between field

bservations and model predictions is 0.94 (p < 0.0001; N = 13).e were not expecting that absolute numbers of mosquitoes

ollected in the field and predicted by the model would match.irst, there is an undersampling of mosquitoes by field traps

ntinue to move from one period to the other, and (d)

because not all mosquitoes present in a 15 m radius from thetrap are actually collected. Secondly, the model representsideal conditions—e.g., no wind, square grids, no obstacle inthe field.

6. Discussion

The contact rate between people and vectors – or ABR – isone of the key factor to predict the risk of re-emergenceof malaria, would the parasite be introduced in the region.This factor varies spatially as it depends on the spatial andtemporal distributions of both human agents and vectors. Inparticular, it depends on the contact area between mosquitoesand people. It depends firstly on the habitat and dispersaldistance of mosquitoes around rice fields, and secondly onthe spatial distribution of human activities as a function oftheir land use. The actual biting rate is particularly high inhighly populated areas that are close to rice fields. Simulationswith the MALCAM model showed that people-vectors con-tacts are particularly frequent in the north of the study area,where the density of human agents is high (due to the city

of Saint-Laurent d’Aigouze and the presence of a campsite)(Fig. 4). In addition, mosquito bites require that human activi-ties coincide with the periods of the day when biting is likely.Different agents present in the region are exposed differently
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172 e c o l o g i c a l m o d e l l i n g 2 2 0 ( 2 0 0 9 ) 160–174

Fig. 6 – Comparison of collected and predicted mosquitoes related to the distance to rice fields. Dots and crosses representthe total number of adult An. hyrcanus collected in the field every 2-week from May to October 2005 for each light + CO2 trapin the “Carbonnière” and “Marais du Vigueirat” zones. Crosses represent the two trap locations (trapping sites 6 and 7)influenced by mosquito control measures in the “Carbonnière”. The line is an exponential function describing the total

” zon

number of adult An. hyrcanus predicted in the “Carbonnièrestarting at the rice field.

to mosquito bites. Hunters are the most exposed agents justafter sunset, when An. hyrcanus mosquitoes are very active(period 1). Human risk behaviours and the use of preventivemeasures can accentuate or reduce the risk of mosquito biting.

Results from simulation experiments are consistent withfield observations and therefore increase our confidence in themodel. It suggests that the rules of the model and parametervalues were defined appropriately and that no major processwas omitted. Given field data availability and reliability, com-parisons between observations and model predictions were

limited to the spatial and temporal distribution of An. hyrcanus.However, more reliable data on human biting rate in the studyzone would allow model validation based on actual biting ratesinstead of the abundance of mosquitoes.

Fig. 7 – Total number of adult An. hyrcanus collected/predicted atdates from May to October.

e from May to October, every 2-week, along a transect

The MALCAM model has some limitations that could beimproved in future versions. First, the model is very sensitiveto the mortality and reproduction rates of mosquitoes. Theestimation of these two parameters should therefore deservemore attention, even though they are difficult to measurein natural conditions. Simulation experiments underlinedalso the important role of insecticide spraying on mosquitopopulations. The treatment of one rice field in the Carbon-nière influenced data collected in the field. The mortalityand reproduction rates of mosquitoes are directly affected by

insecticide spraying. It is thus an essential factor for futuremodel runs. Secondly, we considered the entire populationof mosquitoes on one pixel as one population unit. We thusoverlooked details of within-patch dynamics. The model could

6 light + CO2 traps in the “Carbonnière” for 13 different

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e improved by modelling each mosquito individually, whichould allow for a better representation of movements by indi-idual mosquitoes. However, this would require very highomputing power. Thirdly, some external factors such as theind and relative humidity were not explicitly taken into

ccount in the model. There is a lack of quantitative data onheir impact on mosquito behaviour. MASs have the ability toe improved incrementally with the evolution of knowledgen the system. Yet, striking a balance between a complex butealistic model and a simple but intelligible model must be aonstant preoccupation.

Agent-based modelling is a powerful tool to represent thepatio-temporal dynamics of vector-host contacts, principallyecause of its ability to represent spatial heterogeneity andhe behaviour of multiple, autonomous agents. The MALCAM

odel provides a tool to better understand the interactionsetween agents that could be associated with a potential re-mergence of malaria in the Camargue. Once the best availablenowledge has been properly represented in the MAS, theodel allows testing hypotheses related to disease dynamics.

cenarios of possible futures can be formulated and rep-esented by varying the value of exogenous variables (e.g.,ourist population visiting the area), initial conditions (e.g.,and cover, in response to changes in land use policies or mar-et forces) or parameters (e.g., level of protection of visitorsgainst mosquito bites). The MALCAM model can be used asvirtual laboratory to test hypotheses that would be impos-

ible to test in the field. Some of these hypotheses couldelp local public health authorities in policy formulation.elevant hypotheses can be related to biological processes

e.g., the antropophily of Anopheles), the geographical settinge.g., impact of land use changes or breeding site modifica-ions via insecticide spraying in rice fields) and the socialontext (e.g., changes in tourist activities, better commu-ication between humans about disease transmission risk).his will be the object of a follow up study. Future versionsf the model could also allow for the calculation of a spa-ially explicit R0 in case of parasite introduction in the region.his R0 would be based on a space-dependent human bitingate.

To our knowledge, the MALCAM model is one of the firstttempts to apply agent-based modelling to a human vector-orne disease. It constitutes a useful basis to represent thepatial dynamics of other vector-borne diseases, in differentegions of the world.

. Conclusion

o evaluate the risk of re-emergence of malaria, the contactate between people and vectors was simulated. The actualiting rate of mosquitoes depends on the spatial and temporalistributions of both human agents and vectors. In addition,isk behaviours or the use of preventive measures, which varyetween agents, can accentuate or reduce the biting risk. TheALCAM model was developed to simulate spatio-temporal

ariations in vector-host contacts in the Camargue. MASs arearticularly adapted to represent the dynamics of disease sys-ems. The model can be adapted to different diseases andegions.

0 ( 2 0 0 9 ) 160–174 173

Acknowledgments

This research was partially funded by EU grant GOCE-2003-010284 EDEN and the paper is catalogued by the EDENSteering Committee as EDEN0107 (www.eden-fp6project.net).The French Ministry of Agriculture paid the salary of NicolasPoncon. The contents of this publication are the responsibil-ity of the authors and do not necessarily reflect the viewsof the European Commission. The authors thank AnneliseTran (CIRAD) for providing the Landsat classification and forher comments on the manuscript, Céline Toty (IRD) and JeanBaptiste Ferré (EID-Méditerranée) for the collection and anal-ysis of larvae, Nicole Vernazza, Daniel Bley, Alain Dervieux(CNRS, DESMID), Marc Eric Gruenais (IRD), and Katrin Langewi-esche for their help in the social surveys, Francois Bousquet(CIRAD) for his helpful suggestions on agent-based modellingand UML, and Sophie Vanwambeke and Elise Dion (UCL) fortheir comments on the manuscript.

e f e r e n c e s

Alten, B., Kampen, H., Fontenille, D., 2007. Malaria in SouthernEurope: resurgence from the past? In: Takken, W., Knols, B.G.J.(Eds.), Emerging Pests and Vector-borne Diseases in Europe.Wageningen Academic Publishers, Wageningen, TheNetherlands, pp. 35–58.

Anderson, R.M., May, R.M., 1991. Infectious Diseases of Humans:Dynamics and Control. Oxford University Press, Oxford, 757pp.

Booch, G., Rumbaugh, J., Jacobson, I., 2004. The Unified ModelingLanguage User Guide. Addison-Wesley, Boston, USA, 482 pp.

Bousquet, F., Gautier, D., 1999. Comparing two ways of modellingspatial dynamics through multi-agents simulation: “spatial”and “actor” approaches. CyberGeo 89 (in French).

Bousquet, F., Le Page, C., 2004. Multi-agent simulations andecosystem management: a review. Ecol. Model. 176, 313–332.

Bousquet, F., Barreteau, O., Le Page, C., Mullon, C., Weber, J., 1999.An environmental modelling approach: the use ofmulti-agents simulations. In: Blasco, F. (Ed.), Advances inEnvironmental and Ecological Modelling. Elsevier, Paris,France, pp. 113–122.

Chattopadhyay, J., Sarkar, R.R., Chaki, S., Bhattacharya, S., 2004.Effects of environmental fluctuations on the occurrence ofmalignant malaria—a model based study. Ecol. Model. 177(1–2), 179–192.

Coosemans, M., Guillet, P., 1999. Individual protection againstmosquito bites. Medecine et Maladies Infectieuses 29 (Suppl.3), 390–396 (in French).

Detinova, T.S., 1962. Age-grouping methods in Diptera of medicalimportance with special reference to some vectors of malaria.WHO (World Health Organization) Monogr. Ser. 47, 13–191.

Doudier, B., Bogreau, H., DeVries, A., Poncon, N., Stauffer, W.M.,Fontenille, D., 2007. Possible autochthonous malaria fromMarseille to Minneapolis. Emerg. Infect. Dis. 13, 1236–1238.

Focks, D., Haile, D., Daniels, E., Mount, G., 1993. Dynamic life tablemodel for Aedes aegypti (Diptera: Culicidae): analysis of theliterature and model development. J. Med. Entomol. 30 (6),1003–1017.

Focks, D., Daniels, E., Haile, D., Keesling, J., 1995. A simulationmodel of the epidemiology of urban dengue fever: literatureanalysis, model development, preliminary validation, andsamples of simulation results. Am. J. Trop. Med. Hyg. 53 (5),489–506.

Page 15: A multi-agent simulation to assess the risk of malaria re-emergence in southern France

i n g

174 e c o l o g i c a l m o d e l l

Fradin, M.S., Day, J.F., 2002. Comparative efficacy of insectrepellents against mosquito bites. New Engl. J. Med. 347 (1),13–18.

Grimm, V., Berger, U., Bastiansen, F., Eliassen, S., Ginot, V., Giske,J., Goss-Custard, J., Grand, T., Heinz, S.K., Huse, G., Huth, A.,Jepsen, J.U., Jorgensen, C., Mooij, W.M., Muller, B., Pe’er, G.,Piou, C., Railsback, S.F., Robbins, A.M., Robbins, M.M.,Rossmanith, E., Ruger, N., Strand, E., Souissi, S., Stillman, R.A.,Vabo, R., Visser, U., DeAngelis, D.L., 2006. A standard protocolfor describing individual-based and agent-based models. Ecol.Model. 198 (1–2), 115–126.

Hare, M., Deadman, P., 2004. Further towards a taxonomy ofagent-based simulation models in environmentalmanagement. Math. Comput. Simulat. 64, 25–40.

Hu, W., Tong, S., Mengersen, K., Oldenburg, B., 2006. Rainfall,mosquito density and the transmission of Ross River virus: atime-series forecasting model. Ecol. Model. 196 (3–4), 505–514.

Jetten, T., Takken, W., 1994. Anophelism Without Malaria inEurope. A Review of the Ecology and Distribution of the GenusAnopheles in Europe. Landbouwuniversiteit Wageningen,Wageningen, Netherlands, 69 pp.

Kettle, D.S., 1995. Medical and Veterinary Entomology. CABInternational, Wallingford, UK, 725 pp.

Kuhn, K.G., Campbell-Lendrum, D.H., Armstrong, B., Davies, C.R.,2003. Malaria in Britain: past, present, and future. Proc. Natl.Acad. Sci. U.S.A. 100 (17), 9997–10001.

Langewiesche, K., 2005. Risk assessment of malaria emergence,installation and diffusion in France in a global change context(environment and climate): EDEN project, social sciences part.Montpellier, France (in French).

Langewiesche, K., 2006. Risk assessment of malaria emergence,installation and diffusion in France in a global change context(environment and climate): EDEN project, social sciences part.Montpellier, France (in French).

Mcdonald, G., 1957. The Epidemiology and Control of Malaria.Oxford University Press, London, UK, 201 pp.

Muller, G., Grébaut, P., Gouteux, J., 2004. An agent-based model ofsleeping sickness: simulation trials of a forest focus insouthern Cameroon. C. R. Biol. 327, 1–11.

Mulligan, M., Wainwright, J., 2004. Modelling and model building.In: Wainwright, J., Mulligan, M. (Eds.), EnvironmentalModelling: Finding Simplicity in Complexity. John Wiley andSons, Chichester, UK, pp. 7–73.

Okogun, G.R.A., 2005. Life-table analysis of Anopheles malariavectors: generational mortality as tool in mosquito vectorabundance and control studies. J. Vector Borne Dis. 42 (2),45–53.

Ostfeld, R.S., Glass, G.E., Keesing, F., 2005. Spatial epidemiology:an emerging (or re-emerging) discipline. Trends Ecol. Evol. 20(6), 328–336.

Pages, F., Orlandi-Pradines, E., Corbel, V., 2007. Vectors of malaria:biology, diversity, prevention, and individual protection.Medecine et Maladies Infectieuses 37 (3), 153–161 (in French).

Parker, D.C., Manson, S.M., Janssen, M.A., Hoffmann, M.J.,Deadman, P., 2003. Multi-agent systems for the simulation of

2 2 0 ( 2 0 0 9 ) 160–174

land-use and land-cover change: a review. Ann. Assoc. Am.Geogr. 93 (2), 314–337.

Poncon, N., Toty, C., L’Ambert, G., Le Goff, G., Brengues, C.,Schaffner, F., Fontenille, D., 2007a. Biology and dynamics ofpotential malaria vectors in Southern France. Malaria J. 6 (18).

Poncon, N., Balenghien, T., Toty, C., Ferré, J., Thomas, C.,Dervieux, A., L’Ambert, G., Schaffner, F., Bardin, O., Fontenille,D., 2007b. Effects of local anthropogenic changes on potentialmalaria vector Anopheles hyrcanus and West Nile virusvector Culex modestus, Camargue, France. Emerg. Infect. Dis. 13(12).

Poncon, N., Tran, A., Toty, C., Luty, A., Fontenille, D., 2008. Aquantitative risk assessment approach for mosquito-bornediseases: malaria re-emergence in Southern France. Malaria J.7, 147.

Reiter, P., 2000. From Shakespeare to Defoe: malaria in England inthe little ice age. Emerg. Infect. Dis. 6 (1), 1–11.

Reiter, P., 2001. Climate change and mosquito-borne disease.Environ. Health Perspect. 109, 141–161.

Rogers, D.J., 1988. The dynamics of vector-transmitted diseases inhuman communities. Trans. R. Soc. Lond. B: Biol. Sci. 321(1207), 513–539.

Service, M.W., 1997. Mosquito (Diptera: Culicidae) dispersal: thelong and short of it. J. Med. Entomol. 34 (6), 579–588.

Snow, R., Gilles, H., 2002. The epidemiology of malaria. In: Warrel,D., Gilles, H. (Eds.), Essential Malariology. Arnold, London, pp.85–106.

Sweeney, A.W., Beebe, N.W., Cooper, R.D., 2007. Analysis ofenvironmental factors influencing the range of anophelinemosquitoes in northern Australia using a geneticalgorithm and data mining methods. Ecol. Model. 203 (3–4),375–386.

Torres, N., 2007. Perception, knowledge, and attitude towardsmosquitoes in Saint Laurent d’Aigouze and Mas Thibert.Arles, France (in French).

Torres-Sorando, L., Rodríguez, D.J., 1997. Models ofspatio-temporal dynamics in malaria. Ecol. Model. 104 (2–3),231–240.

Tran, A., Poncon, N., Toty, C., Linard, C., Guis, H., Ferré, J., Lo Seen,D., Roger, F., de la Rocque, S., Fontenille, D., Baldet, T., 2008.Use of remote sensing to map larval and adult populations ofanopheles species in Southern France. Int. J. Health Geogr. 7(9).

Vanwambeke, S.O., Somboon, P., Harbach, R.E., Isenstadt, M.,Lambin, E.F., Walton, C., Butlin, R.K., 2007a. Landscape andland cover factors influence the presence of Aedes andAnopheles larvae. J. Med. Entomol. 44 (1), 133–144.

Vanwambeke, S.O., Lambin, E.F., Eichhorn, M.P., Flasse, S.P.,Harbach, R.E., Oskam, L., Somboon, P., van Beers, S., vanBenthem, B.H.B., Walton, C., Butlin, R.K., 2007b. Impact ofland-use change on dengue and malaria in northern

Thailand. EcoHealth 4, 37–51.

Wilensky, U., 1999. NetLogo. http://ccl.northwestern.edu/netlogo/.Wyse, A.P.P., Bevilacqua, L., Rafikov, M., 2007. Simulating malaria

model for different treatment intensities in a variableenvironment. Ecol. Model. 206 (3–4), 322–330.