ARTIFICIAL LIFE MODEL OF DENGUE HOST-VECTOR DISEASE

PROPAGATION

Carlos Isidoro, Nuno Fachada, F

abio Barata and Agostinho Rosa

LaSEEB, ISR, Instituto Superior T

ecnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Keywords:

Artiﬁcial life, Agent based modelling, Aedes aegypti, Dengue, RIDL.

Abstract:

The paper presents an agent based model of the Aedes aegypti mosquito, which considers mosquito population

dynamics and a speciﬁc population control strategy, as well the dengue propagation in mosquito (vector) and

human (host) populations. More speciﬁcally, this study concerns the impact that the RIDL strategy (Release

of Insects carrying a Dominant Lethal gene) has on the infection period among humans. The agents model the

main aspects of the mosquito’s ecology and behavior, while the environmental components are implemented

as a layer of dynamic elements obeying to physical laws. The main objective of this approach is to provide

realistic simulations of insect biologic control strategies, namely RIDL. Model veriﬁcation was performed

through examination of simulation parameters variation and qualitative assessment with existing models and

simulations. The LAIS simulator was a valuable tool in this investigation, allowing efﬁcient agent based

modeling (ABM) and simulation deployment and analysis.

1 INTRODUCTION

The dengue is a dangerous disease which still lacks a

cure, and it is spread through a speciﬁc type of vector,

the Aedes aegypti mosquito. Currently, the most af-

fected areas are the ones with tropical climates since

factors like high temperature and frequent precipita-

tion are favorable to Aedes aegypti growth. However,

if current predictions about climate change happen,

many new areas might start facing the dengue threat

(Senior, 2008).

Since an effective treatment is yet to be found,

it is particularly important to focus on prevention,

keeping the mosquito population under transmission

threshold, or better still, eradicate the disease. Vari-

ous strategies have been developed and used for this

purpose, ranging from releasing large amounts of ster-

ile mosquitoes into the environment to clearing areas

with still water that might be used as mosquito breed-

ing sites.

This paper focuses on determining the inﬂuence

the RIDL mosquito population control strategy has

on the dengue infection period in human populations.

The work presented here is a continuation of (Isidoro

et al., 2009b), which is concerned with mosquito

population dynamics, as well as the effects caused

by RIDL on such populations, and (Isidoro et al.,

2009a), which presents a study of dengue propagation

in mosquito (vector) and human (host) populations.

The state of the art in the modeling and simulation of

the Aedes aegypti mosquito, dengue transmission and

other relevant related subjects is presented in section

2; the modeling approach and the used software plat-

form are discussed in section 3, while the model itself

is described in section 4. Sections 5 and 6 present the

performed simulations, and the associated discussion,

respectively.

2 STATE OF THE ART

There have been numerous models of mosquitoes and

mosquito-borne disease, beginning with the classic

Ross-Macdonald malaria models (Ross, 1911; Mac-

donald, 1952; Macdonald, 1957) and extending to

present day models of vectors populations or aspects

of vector biology, not directly considering disease

(Eisenberg et al., 1995a; Eisenberg et al., 1995b; Alto

and Juliano, 2001; Ahumada et al., 2004).

One example of modeling the dengue vector

mosquito population dynamics is by Focks and col-

leagues (Focks et al., 1993a; Focks et al., 1993b),

examining the biology of Aedes aegypti. This is an

exceptionally detailed model, with numerous types of

containers for larval development. Hydrology (water

243

Isidoro C., Fachada N., Barata F. and Rosa A. (2009).

ARTIFICIAL LIFE MODEL OF DENGUE HOST-VECTOR DISEASE PROPAGATION.

In Proceedings of the International Joint Conference on Computational Intelligence, pages 243-247

DOI: 10.5220/0002324102430247

 SciTePress

levels and drying), temperature-dependent larval de-

velopment, food availability and survival are explic-

itly tracked in each container type. Detailed weather

data are used to drive the hydrological and biological

functions. This level of detail has both costs and ben-

eﬁts; it enables consideration of detailed aspects of

the mosquito biology, but also makes true sensitivity

analysis of the model difﬁcult or impossible. Thus,

to develop a model with this level of detail, it is nec-

essary to have extensive data available for parameter

estimates and validation.

The use of ABM methodologies to model Aedes

aegypti populations has been scarce at best. Some in-

teresting ideas are presented in a work by Deng et. al

(Deng et al., 2008), namely the use of an utility func-

tion to determine mosquito movement, taking into

account factors such as population, wind direction,

land use type and landscape roughness. However, the

practical implementation of the model is very limited,

with coarse spatial discretization (30x30) and not sin-

gular agent-based.

Models can be useful to evaluate different strategy

of mosquito control. Recently, techniques like releas-

ing genetic modiﬁed mosquitoes have been consid-

ered as an enhanced SIT to control the mosquito pop-

ulation, as the genetic manipulation in insects result

in sterility or lethal genes (Thomas et al., ; Atkinson

et al., 2007). Although there wasn’t any genetic modi-

ﬁed mosquito open ﬁeld release conducted yet, a cou-

ple of mathematical modeling works have been done

to assess the control efﬁcacy (Esteva and Mo Yang,

2005; Li, 2004; Maiti et al., 2006). But none of those

could provide a tool to simulate the interaction be-

tween mosquito individuals such as mating behavior,

spatial distribution, and immigration etc. All these are

important for the evaluation and guidance of genetic

control approach.

3 MODELING APPROACH

The use of ABM methodologies is well suited for de-

scribing complex systems in general, being a partic-

ularly useful approach for modeling population dy-

namics and disease transmission; in such a case,

ABM provides a natural way to represent the true

diversity of intervening components, such as envi-

ronmental factors, disease vectors and disease hosts.

Other advantages include the possibility to determine

spatial behavior distribution, rapid insertion of new

components and natural consideration of non-linear

interactions between agents. This approach is not

without problems of its own: it requires considerable

computational power to simulate individual agents;

parameter tuning is not trivial; and it lacks the formal-

ism provided by differential equations, although this

issue is being addressed by recent work on ABM for-

malism (Helleboogh et al., 2007). Nonetheless, for

explicitly spatial models, such as the one presented

here, the advantages of ABM clearly outweigh its lim-

itations.

The model presented in the next section was

developed in the LAIS simulator, a multithreaded

agent based simulation platform, offering a model-

ing paradigm and a set of tools for the simulation of

complex systems (Fachada, 2008). The platform is

implemented in Java and makes use of several open

source libraries which provide tools for spatial orga-

nization and visualization, event scheduling, simula-

tion output (e.g., charts, CSV ﬁles, movies) and sim-

ple class development and instantiation using XML.

Simulations are performed in discrete time and two-

dimensional discrete space. As such, space is divided

into blocks, which are independently processed by

different threads, making LAIS scalable on modern

multiprocessor systems.

There are two main actors in the LAIS frame-

work: agents and elements. Agents are typical ABM

discrete and independent decision-making entities.

When prompted to act, each agent analyzes its cur-

rent situation (e.g. what resources are available, what

other agents are in the vicinity), and acts accord-

ingly, based on a set of rules. These rules incorporate

knowledge or theories about the respective low-level

components. On the other hand, elements are real-

valued objects which obey predetermined rules, such

as physical laws (e.g., diffusion).

4 MODEL DESCRIPTION

The Aedes aegypti LAIS model implements a square

topology where each spatial block has 8 neighbors

(N,NE,E,SE,S,SW,W,NW). Five different agents are

considered: Wild Male Mosquitoes (WM), Female

Mosquitoes (WF), Sterile Male Mosquitoes (SM),

Humans (H) and Oviposition spots (OS). Five differ-

ent elements are also used, and they fall into one of the

following categories: mosquito attractors (of which

there are three kinds), mosquito density measure and

observable mosquito properties.

The interactions between the various agents are

represented in a simplistic way in ﬁgure 1.

WM follow WF and, should they meet in the same

cell, the female has a certain chance of becoming fer-

tilized. Meanwhile the females are following Humans

and, should they meet one in the same cell they can

acquire human blood, but they also risk dying. If a

IJCCI 2009 - International Joint Conference on Computational Intelligence

244

Female

Mosquito

Sting

Human

Mating

Sterile Male

Mosquito

Wild Male

Mosquito

If fertile,

lay eggs

Eggs

Growth

Stages

Death

Figure 1: Model overview.

WF is fertilized and has acquired blood, it then moves

toward an OS to lay a certain amount of eggs, and

then goes back to the beginning of this cycle (look-

ing for humans and males). Each egg has a certain

chance of dying, and before they mature into adults

and start looking for mates, each mosquito has to go

through a number of developing stages. Each itera-

tion all mosquitoes have a certain chance to die, which

might change with the growth stage it is currently in

and the amount of mosquitoes in the area.

SM act in a similar way to WM, but a female that

mates with one does not lay eggs when it reaches an

OS.

The spread of the disease is not represented in

ﬁgure 1, but is easy to describe: whenever an in-

fected WF stings a healthy human, the human has

a chance to be infected. A non-infected WF that

stings an infectious human also has a chance to get in-

fected. WF whose progenitor was infected also have

a small chance to be born infected as well. Infected

humans are infectious for a certain number of days,

after which any WF that stings them no longer be-

comes infected. For simulations the infection can be

introduced by the addition of either infected humans

or infected WF at a user speciﬁed iteration. Location

can be random or speciﬁc.

In order for the agents to follow each other, cer-

tain elements were used. WF release Pheromone (Ph)

for the males to follow, Humans and OS release body

heat (BH) and humidity (Hu), respectively, for the fe-

males to follow. It should be noted that these elements

are used to model mosquito behavior and might not

correspond to the exact process the mosquitoes use to

follow their targets. For example, females might not

track humans based on their body heat, but through

other means, be it vision, or some other property the

female identiﬁes. The element called body heat is

just a way to implement the ability to follow humans

that female mosquitoes show. Two more elements

are also used in the model: Density (De) and Adult

Pheromone (AP). The former is used to measure the

amount of mosquitoes in a given area, which will have

an impact on the mortality rate, and the latter is placed

by WM on themselves when they mature to inform

WF that they are suitable mates.

Element diffusion and degradation is performed

using a simple method where element concentration

in each local block is determined by eq. 1. In this

equation, C

is the substance concentration at tick n,

is the substance concentration at neighbor i, N is

the number of neighbor blocks (8 in this case) and α

and β are the diffusion and evaporation coefﬁcients,

respectively.

t+1

= β

+ α(

∑

i=1

− C

)

(1)

WF are by far the most complex agents in the

model, but ﬁgure 2 resumes its life cycle in a clear

way. A more detailed description of each agent and

element can be found in (Isidoro et al., 2009b).

Eggs

Growth Stages

Adult: Looking

for Humans

Found a

Human?

Survives?

Successfully

stung the

Human?

Has already

mated?

Moves to

breeding site

Dies

If mate was

fertile, lay

eggs

Adult: Moving

Randomly

Found a

mate?

Yes Yes

Yes

Figure 2: Female Mosquito Model.

5 TESTS AND RESULTS

In order to determine the relation between the appli-

cation of a RIDL strategy and the dengue infection

period in human populations, a number of simulations

consisting of the following steps were performed: a)

start simulation with initial numbers of WM, WF and

humans; b) after the system reaches steady-state, a

number of infected WF are simultaneously released;

c) after a variable interval, the treatment (which con-

sists on the release of a ﬁxed number of SM per day)

starts. The ﬁxed simulation parameters are given in

table 1, while the interval between the release of in-

fected WF and beginning of treatment (no treatment

interval) varies from 0 to 20 days, with a step of 5

days. For each value of the no treatment interval,

40 simulations were performed. In this model, each

block represents around 100 square meters, and each

ARTIFICIAL LIFE MODEL OF DENGUE HOST-VECTOR DISEASE PROPAGATION

245

Table 1: Model parameters.

Parameter Value

Model width (blocks) 100

Model height (blocks) 100

Initial number of WM 1250

Initial number of WF 750

Initial number of Humans 700

Number of infected WF released

Number of SM released per day

300

Contagious period in humans (days) 12

Number of infected WF simultaneously released

after the system as reached steady-state.

Number of SM simultaneously released per day

after the treatment starts.

(Isidoro et al., 2009a)

iteration corresponds to a single day (Isidoro et al.,

2009b).

Fig. 3 shows the relation between the average in-

fection period in the human population and the no

treatment interval and ﬁg. 4 shows the average num-

ber of infected humans as function also of the interval

without treatment.

0 2 4 6 8 10 12 14 16 18 20

No Treatment Interval

Infection Period

Figure 3: Relation between the infection period and

the no treatment interval.

6 DISCUSSION

Both ﬁgure 3 and 4 show an increasing trend of out-

come of the infection period with the delay of the

treatment in average duration and average number of

humans infected. The simulations results suggest the

earliest deployment of this speciﬁc treatment and each

day of delay the infection period is also increased for

half a day.

0 2 4 6 8 10 12 14 16 18 20

5.9

6.1

6.2

6.3

6.4

6.5

6.6

6.7

6.8

6.9

No Treatment Interval

Total of Infected Humans

Figure 4: Relation between the number of humans in-

fected and the no treatment interval.

Current results without validation with ﬁeld sam-

pled real data can only be used for a qualitative eval-

uation of the model.

7 CONCLUSIONS AND FUTURE

WORK

The model presented in this paper can be improved

by taking into account other factors, of which envi-

ronmental aspects like temperature, precipitation and

wind are probably the most important.

In the virus, host and vector relationships, many

aspects could be added in expense of simulation time.

It would be interesting to include immune status of

the human population, the density distribution and

movement of human hosts, the virulence of the virus

strains, the characteristics of mosquito-human inter-

action and also mosquito-virus interaction.

ACKNOWLEDGEMENTS

This work was partially supported by Fundac¸

ao para

a Ci

encia e a Tecnologia (ISR/IST plurianual fund-

ing) through the POS Conhecimento Program that in-

cludes FEDER funds. The authors C. Isidoro and F.

Barata acknowledge their grant BII-2009 to Fundac¸

para a Ci

encia e Tecnologia (FCT). The author N.

Fachada acknowledges its grant SFRH / BD / 48310 /

2008 to Fundac¸

ao para a Ci

encia e Tecnologia (FCT).

IJCCI 2009 - International Joint Conference on Computational Intelligence

246

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