Agent-based model of Dengue Disease Transmission by
Aedes aegypti Populations
Carlos Isidoro and Nuno Fachada and Fábio Barata and Agostinho Rosa Evolutionary System and Biomedical Engineering Lab Systems and Robotics Institute Instituto Superior Técnico Av. Rovisco Pais, 1049-001 Lisboa, Portugal
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This paper presents an agent based model of the Aedes aemosquito showing not only population dynamics but also the Dengue disease propagation in both the vector and host populations (mosquitoes and humans, respectively); this study will focus on the latter aspect. 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. Model veri cation was performed through examination of simulation parameters variation and qualitative assessment with existing models and simulations. The agent based modeling and simulation platform used was the LAIS simulator. Abstract.
gypti
Keywords
RIDL, SIT
1
Arti cial Life, Agent Based Modelling, Aedes aegypti, Dengue,
Introduction
The dengue is a dangerous disease which still lacks a cure, and it is spread through a speci c type of vector, the Aedes aegypti mosquito. Currently, the most aected areas are the ones with tropical climates since factors like high temperature and frequent precipitation are favorable to Aedes aegypti growth. However, if current predictions about climate change happen, many new areas might start facing the dengue threat [1]. Since an eective 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. Various strategies have been developed and used for this purpose, ranging from releasing large amounts of sterile mosquitoes into the environment to clearing areas with still water that might be used as mosquito breeding sites. This paper is a continuation of [2], which studied the mosquito population dynamics and the eects of a particular population control strategy, RIDL. The study presented here will focus on the disease itself, more speci cally on the
propagation of the disease in both the mosquito (vector) and human (host) populations. These studies were performed using an agent based model, developed for the LAIS simulator. ABM is well suited for describing complex systems in general and disease transmission in particular, providing a way to represent the true diversity of intervening components, such as environmental 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 nonlinear 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 formalism provided by dierential equations (although ABM formalism is already a reality [3]). Nonetheless, for explicitly spatial models, such as the one presented here, the advantages of ABM clearly outweigh its limitations. 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; a brief description of the LAIS simulator is given 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 [4,5,6] and extending to present day models of vectors populations or aspects of vector biology, not directly considering disease [7,8,9,10]. One example of modeling the dengue vector mosquito population dynamics is by Focks and colleagues [11,12], examining the biology of Aedes aegypti. This is an exceptionally detailed model, with numerous types of containers for larval development. Hydrology (water levels and drying), temperature-dependent larval development, food availability and survival are explicitly 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 bene ts; it enables consideration of detailed aspects of the mosquito biology, but also makes true sensitivity analysis of the model di cult or impossible. Thus, to develop a model with this level of detail, it is necessary to have extensive data available for parameter estimates and validation. The use of ABM methodologies to model Aedes aegypti populations has been scarse at best. Some interesting ideas are presented in a work by Deng et. al [13], namely the use of an utility function 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 singular agentbased.
Models can be useful to evaluate dierent strategy of mosquito control. Recently, techniques like releasing genetic modi ed mosquitoes have been considered as an enhanced SIT to control the mosquito population, as the genetic manipulation in insects result in sterility or lethal genes[14,15]. Although there wasn't any genetic modi ed mosquito open eld release conducted yet, a couple of mathematical modeling works have been done to assess the control e cacy [16,17,18]. But none of those could provide a tool to simulate the interaction between 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
The LAIS simulator
The LAIS simulator is a multithreaded agent-based simulation platform, oering a modeling paradigm and a set of tools for the simulation of complex systems [19]. The platform is implemented in Java and makes use of several open source libraries which provide tools for spatial organization and visualization, event scheduling, simulation output (e.g., charts, CSV les, movies) an d simple 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 dierent threads, making LAIS scalable on modern multiprocessor systems. There are two main actors in the LAIS framework: agents and elements. Agents are typical ABM discret e and independent decision-making entities. When prompted to act, each agent analyzes its current situation (e.g. what resources are available, what other agents are in the vicinity), and acts accordingly, 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 rul es, such as physical laws (e.g., diusion).
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 dierent agents are considered: Wild Male Mosquitoes (WM), Female Mosquitoes (WF), Sterile Male Mosquitoes (SM), Humans (H) and Oviposition spots (OS). Various dierent elements are also used, with the most important falling into one of the following categories: mosquito attractors and mosquito density measure. The interactions between the various agents are represented in a simplistic way in g. 1; a brief explanation follows: WM are attracted to the pheromone released by WF. If a WM and a WF are on the same cell, there is a chance for the WF to become fertilized. WM-WF
Death Sting Human If fertile, lay eggs
Female Mosquito
Eggs
Mating
Sterile Male Mosquito
Fig. 1.
Wild Male Mosquito
Growth Stages
Model overview.
SM are also attracted to the pheromone released by WF. If a SM and a WF are on the same cell, there is a chance for the WF to register having mated, although it has not been fertilized (the implications will be given on the WF-OS interaction). SM-WF
WF follow the Humans body heat, and if they are in the same cell as a human they have a chance to either die or successfully acquire human blood. WF-Hu
After having mated and having acquired human blood, a WF will move towards an OS by following the humidity released by them. After reaching an OS, the WF will lay a certain number of eggs if it mated with a WM, or lay none if its mate was a SM. Afterwards it will again start looking for mates and humans. WF-OS
Mosquitoes only interact with other agents after they mature into adults. After hatching from their eggs, they go through a number of development stages before becoming adults. It is important to note that the elements used as mosquito attractors, are intended to model mosquito behavior and might not correspond to the exact process the mosquitoes use to follow their targets. While not present in gure 1 and on the explanations given above, the spread of the Dengue disease can happen during the WF-Hu or the WF-OS interactions. In the rst case (WF-Hu) an infected WF stinging a healthy human has a certain chance to infect the human. A non-infected WF that stings a contagious human will become infected. An infected human will stay contagious for a certain number of days, after which they stop infecting WF that sting them, and can't become contagious again for the duration of the simulation. For the second case (WF-OS), Eggs layed by infected WF have a small chance to be born infected as well. Table 1 shows the parameters relating to the dengue disease.
A more detailed description of each agent and element can be found in [2]. Table 1.
More parameters related to the dengue disease.
Parameter
Value
Chance to be infected when stinging an infected human 1 Chance to infect a human 0.9 Chance to be born infected if mother was infected 0.003
5
Tests and results
To study the propagation of the dengue disease, a number of simulations were performed. The simulations are done in two steps: a) they begin with the initial numbers WM,WF and humans; b) after the system reaches a steady state, a number of infected WF are simultaneously released. The xed simulation parameters are given in table 2, and the contagious period in humans varies between 8 and 19. For each speci c value of the contagious period a total of 40 simulations were run. Table 2.
Parameter
Model default parameters. Value
Model width (blocks) 100 Model height (blocks) 100 Initial number of Male Mosquitoes 1250 Initial number of Female Mosquitoes 750 Initial Number of Humans 700
The results associated with these tests are presented in gures 2 and 3. Figure 2 shows the relation between average infection period in the human population (the amount of the time before no more humans are contagious) and the contagious period. Figure 3 shows the relation between the average number of infected humans and the contagious period.
6
Discussion
Both graphics seem to show an increasing trend in the average infection period and the total number of humans infected with the increase of the contagious period. The correlation of the contagious period with infection period and disease duration follows almost a linear relationship. The uctuations observed in both
55
50
Disease Duration
45
40
35
30
25
20
8
10
12
14
16
18
20
Contagious Period
Fig. 2.
Relation between the infection period and the contagious period.
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Total of Infected Humans
7.5
7
6.5
6
8
10
12
14
16
18
20
Contagious Period
Fig. 3.
period.
Relation between the number of humans infected and the contagious
gures 2 and 3 are due to the limited number of runs (40); a much higher number would be necessary to reduce the natural variation of the curves due the presence of an accentuated limit cycle.
7
Conclusions and future work
The model presented in this paper can be improved by taking into account other important factors which impact mosquito population dynamics, most noticeably environmental factors like temperature, precipitation and wind. The various parameters can also be further ne-tuned; in particular, some parameters are not entirely correct in relation to the amount of time associated with each iteration. As such, current results can only be used for a qualitative validation of the model. A more realistic representation of the disease will also be implemented, taking into account the dierent strains of the dengue virus and immune status of the human population. Simulations studying the impact of population control strategies on the propagation of the dengue disease will also be investigated. Nevertheless, the current agent based model shows potential as a test bench to help study the propagation of the disease and predict the e ciency of possible treatments before deploying them on the eld.
8
Acknowledgements
This work was partially supported by Fundação para a Ciência e a Tecnologia (ISR/IST plurianual funding) through the POS_Conhecimento Program that includes FEDER funds. The authors C. Isidoro and F. Barata acknowledge their grant BII-2009 to Fundação para a Ciência e Tecnologia (FCT). The author N. Fachada acknowledges its grant SFRH/BD / 48310/2008 to Fundação para a Ciência e Tecnologia (FCT).
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