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MODELLING MALARIA WITH MULTI-AGENT SYSTEMS
Fatima Rateb1, Bernard Pavard2, Narjes Bellamine-BenSaoud3, J.J. Merelo1 and M.G. Arenas1 1E.T.S.I. Informática, University of Granada, Periodista Daniel Saucedo s/n, 18071 Granada, Spain E-mail: {fatima,jmerelo,maribel}@geneura.ugr.es 2GRIC - IRIT, Institut de Recherche en Informatique de Toulouse, 31062 Toulouse, France 3Laboratoire RIADI-GDL, University of Tunis, La Manoube, 2010 Tunis, Tunisia
KEYWORDS
Multi-agent systems, Education, Health care, Malaria, Malaria is a vector-borne disease that greatly affects social and economic development in the world. In ABSTRACT
1990 it was estimated that approximately 2.2 billion people were at risk of contracting the parasite, and a Malaria is a vector-borne disease that greatly affects further 270 million were already infected. Endemic social and economic development. We adopt the areas are characterised by ‘ideal’ mosquito (anopheles complex system paradigm in our analysis of the being the parasite vector) habitats, which are largely problem. Our aim is to assess the impact of education where: water is present; the temperature is at least on malaria healthcare. Multi-agent systems are 18ºC; and there is little pollution (Baudon 2000). Many employed to model the spread of malaria in Haiti, third world rural areas meet these conditions. Efforts where we introduce malaria education as a possible to eradicate this deadly disease have included using way of regulating deaths due to the parasite. We DDT to minimise the vector population, and launch three experiments, each with environment administering antimalarial drugs to susceptible people, modifications: 3 hospitals; 3 hospitals and 20 schools; as a prevention. However, both methods have proved and 5 hospitals and 20 schools. The results of running only temporarily effective. The former was first 10 simulations for each experiment show that there is a adopted in the mid 1950s with a subsequent significant reduction in malaria deaths not only when including global decrease in mosquito population. This was soon schools, but when in combination with increasing the to become a failure when a resurgence of malaria was detected as a result of anopheles developing a resistance to the insecticide (Krogstad 1996, WHO INTRODUCTION
1996). The latter prophylaxis was the use of chloroquine as an antimalarial drug. Resistance of Plasmodium falciparum (the more prevalent and Our goal is to assess the effect of education on deadly of the four existing parasite species) to healthcare. We first introduce the global malaria chloroquine emerged due to the massive usage of the problem, followed by the paradigm adopted for its drug (Payne 1987). As a consequence, a novel way of analysis. This is followed by an insight into the current combating this plague would have to be devised. malaria situation in Haiti, the country we have chosen Complex Systems
The rest of the paper is organised as follows: the State Pavard (2002) describes a complex socio technical of the Art section introduces current efforts in the field; system to be one for which it is difficult, if not the following section discusses the model; then the impossible to restrict its description to a limited three experiments and their results are presents; the number of parameters or characterising variables Discussion part gives some conclusions and a brief without losing its essential global functional properties. analysis; finally, Future Work discusses ideas for Indeed from this definition four characteristics of such a system appear: non-determinism; limited functional decomposability; distributed nature of information and first problem to tackle is educating the population, representation; and emergence and self-organisation. which could be done through national schooling. However, school attendance by children from lower Simulation as a Tool for Understanding Complex
income families is limited by the cost of school fees The properties above show that dealing with a complex STATE OF THE ART
system entails dealing with the impossibility to anticipate precisely its behaviour despite knowing The motivations that drive us to develop our model are completely the function of its constituents. This, various. Recent research has demonstrated approaches combined with non-linear behaviour means that it is to the global problem, using MAS, from two angles. quite problematic if not impossible to use a Janssen and Martens (1997) focus on the adaptiveness mathematical or statistical approach for its analysis of mosquitoes to insecticides and malaria parasites to (Bagni et al. 2002, Pavard and Dugdale 2002). It is for antimalarial drugs. This work aims to find a solution to these reasons that computer simulations, in this study controlling the spread of the disease by understanding multi-agent systems (MAS), are a more viable method the mechanism that renders this prophylaxis useless. Similarly, the same result is sought by Carnahan et al. (1997) but by studying the problem at a different level: Studying complex systems through multi-agent the dispersal of anopheles. Here there is a focus on systems has yielded useful results such as in: the understanding the behaviour of malaria-transmitting evolutionary population dynamics of settlement mosquitoes, their geographical displacement, with the systems in the search of emerging spatial regularities aim to consequently monitor their movements and thus (Aschan-Leygonie 2000); demographic phenomena reduce the number of malaria cases. Presently there is through its roots in individual choice behaviour and little information available showing the impact of social interactions (Janssen and Martens 2001); education on healthcare in general, and even less in simulations of crowd behaviour aiming to understand tackling the problem of malaria. We therefore attempt its dynamic and consequent control (Gomez and Rowe to approach the problem from this standpoint using MAS (StarLogo, http://www.media.mit.edu/starlogo/), THE MODEL
The level of poverty in Haiti is approximately 65% (PAHO 2001), a socio-economic factor affecting Our model aims to encompass the malaria problem in access to public healthcare. Not only is an adequate Haiti. We have programmed the environment to health infrastructure not fully developed, but represent the geographical terrain and the agents to ‘individual’ poverty also hinders access to healthcare. This is aggravated further by not having the financial resources to travel to the place of care, or not judging it The Environment
The environment we create, for our agents to inhabit, is Malaria is considered a public health problem in Haiti made up of a model map of Haiti, with geographical (PAHO 2001), especially in rural areas. Malaria terrain granularity sufficient to represent that which education, or its lack thereof, plays an extremely affects the dynamics of what we intend to model. This important role in the ‘healing’ process. It is primordial granularity is such that the simulation space is divided for effective and efficient treatment that malaria be into micro-environments: sea; hospitals; land; diagnosed at an early stage (Baume and Kachur 1999). mountains; cities; roads; and schools. All of these In order for this to apply, the population must be micro-environments have a direct impact on our agents completely aware of its symptoms and act and hence the simulations we run, as will be described consequently. Symptoms which can be easily mistaken further in the Human Population section. A snapshot for another disease include: high fever; vomiting; of the simulation graphical user interface can be seen in convulsions; and anaemia. Not only must the population attribute specific symptoms to malaria, but they must also seek the correct medical attention. The The Human Population
The initial human population in our model is evenly
distributed in the 5 cities in our map, with 200 agents
in each. Our agents have been assigned one of the
following three states: safe, when they are susceptible
to contracting malaria; contaminated; and immune.
Each agent can go through the malaria cycle of being
safe, becoming contaminated and consequently either
dying of lack of treatment or becoming cured as a
consequence of a hospital visit, see Fig. 2. These states
are dependent on the interaction of agents with their
surrounding environment.
Figure 1 : StarLogo Simulation Interface The Mosquito Population
Our model represents only the parasite carriers of the entire anophele population, unlike in Janssen and Martens (1997). We do not model seasonal mosquito population variations. All of our modelled mosquitoes pose a malaria threat to the human (agent) population We have endowed some of our agents with the ability to be mobile, and if so, a fraction with a car. This We have decided not to model mosquitoes as an agent translates into those mobile exiting their city of origin whose behaviour is affected by its interaction with both with greater ease than those not mobile. Similarly, car the environment and other agents. Their presence in owners can move throughout the country at a greater the model is stochastic, embedded in the environment speed, especially on roads, than those without a we create. The probability of an agent contracting malaria varies according to conditions the seven micro- environments present, the probability of an agent Natural inoculation occurs through continuous contracting malaria differs. We can observe for repetitive contamination, where a person cured from example that ‘land’ (rural areas) is the ideal breeding malaria is immune to the parasite for an average of one ground for mosquitoes. This is contrary to mountains year (Baudon 2000). As there must be malaria-person where despite the adequate water level and lack of contact, and a greater number of anopheles are found in pollution, elevation lowers ambient temperature, rural areas, the initial immune and contaminated making it an unsuitable mosquito habitat. We consequently say that the highest probability of malaria infection is in ‘land’, and degressively in: road; city; Baume and Kachur (1999) stress the importance of and mountain. No contamination occurs in a hospital educating the population with the recognition of or school. This stochastic order abides to the malaria symptoms and the gravity of not acting information given on such habitats (Baudon 2000), see consequently. We have introduced this facet of the problem by creating an ‘education scale’ where agents have education points ranging from 1 to 20. Points Table 1 : Mosquito Contamination Probabilities represent the time agents take to attribute existing symptoms to malaria, where a contaminated agent with 1 education point ‘waits’ longer before heading Land 2% towards a hospital than its counterpart with 20 points, Road 1% who as soon as it is contaminated seeks medical City 0.66% attention. The maximum ‘waiting’ period is 29 days, because 30 days after contamination, an agent outside a Micro-environments not included are those with 0% probabilities hospital dies. Points are cumulative only. Schools are distributed throughout our Haiti map, both in rural and EXPERIMENTS AND RESULTS
urban areas. The utility of a school lies in that agents moving randomly arrive at a school and leave with Our model, described attempts to encompass the more malaria awareness. They enter the school, if they present malaria situation in Haiti, in addition to do not have 20 points and are not contaminated. They information we have deemed relevant to the parasite remain for a period of three days, after which they gain problem. We ran simulations with 3 different scenarios: environment changes in our model. Henceforth, our 3 scenarios will be denominated in the The model emulates the contamination process following manner: Experiment A (3 hospitals); stochastically through its environment. Only those Experiment B (3 hospitals and 20 schools); and agents whose state is safe can be contaminated when in Experiment C (5 hospitals and 20 schools). Each a micro-environment and according to the probabilities. experiment constitutes 10 simulations, whose duration Contaminated agents are to ‘wait’ an amount of time, depending on the education they have, as discussed Three Hospitals, no Schools (Experiment A)
above. If a contaminated agent has a maximum education of 20, the shortest distance between itself This experiment is our benchmark. We have obtained and the existing hospitals will be calculated. results from running simulations of our original model. Subsequently the agent will start heading towards medical attention. As a contaminated agent, the speed Three Hospitals, 20 Schools (Experiment B)
at which it proceeds is diminished by 50% (due to weakness caused by the parasite. Those contaminated Our aim is to observe the effect of adding schools to who have reached a hospital in time, will remain there the model environment. We therefore ran a further 10 for a period of 20 days, the average malaria recovery simulations with 20 schools, distributed randomly in time (Malaria Foundation International 2000), and the environment. These represent malaria education subsequently the agent’s state changes to immune initiatives that could be adopted, in order to reduce (during 1 year). Education’s role is seen in the model when the contaminated agent, because of lack of malaria awareness, does not recognise symptoms in Our hypothesis, of education having a significant time and hence cannot reach a hospital. In our model positive effect on controlling malaria deaths, yielded death strikes when a period of 30 days has elapsed after mediocre results: not improving the present Haiti symptoms appear, the average interval (Malaria situation. Each curve in Fig. 3 is an average taken from the 10 simulations in each experiment, with corresponding standard deviations. The goal is to The sex of an agent is not explicit. This factor only minimise this curve. Graphically we can note minimal affects our model when breeding occurs. We have difference from Experiment A to Experiment B. embodied it by using a random number generator However, taking the area under each curve (AUC) allowing an agent to reproduce 50% of the time, as the pointed to a slight improvement with Experiment B: male to female ratio is approximately 1:1 in Haiti. The above condition in combination with the following must be satisfied before an agent can reproduce: minimum age of 14 years; maximum age of 49 years; not have reproduced more than 6 times; and have at least an interval of 1 year after reproduction. (WHO 2001) As well as death caused by malaria, we have included natural deaths. The average life span for men and women in Haiti is 50.6 and 55.1 years respectively (WHO 2001). In order to accommodate these data, bearing in mind that our agent population is sex-less, we have set a maximum age of 55 years. If an agent survives malaria it dies when attaining that age. Figure 3 : Ratio of Malaria Deaths to Total Population population, see Fig. 4. It exposes the proportion, for We found that despite a net improvement in average the three experiments, of contaminated agents education as the simulation progressed (see Table 2), receiving medical attention. Calculating individual the malaria awareness acquired was not sufficient in decreasing malaria deaths, see Fig. 3. We attribute this AUC(B)=3.17; AUC(C)=3.65. There is a noticeable to the great distances between some contaminated increase from Experiment A, to B and finally C. The agents (aware of their malaria state) and the closest implication of this is explained in the Discussion hospital to them. Regardless of having maximum education, the symptom appearance interval elapsed before the agent could reach medical assistance. These preliminary results drove us to experiment with increasing the number of hospitals to five, one for each city. Table 2 : Average Education We present the average education of initial and final simulation populations for each experiment. Standard deviations refer to the spread of the 10 experiments (within each experiment group). Figure 4 : Ratio of Contaminated Agents in Hospital to Entire Five Hospitals, 20 Schools (Experiment C)
This experiment was composed of modifying further Observing population dynamics was achieved by our modelled environment, by adding 2 hospitals. By plotting them individually, see Figs. 5-7. Here the doing so, distances between certain contaminated number of safe, contaminated and immune agents is agents and a hospital are reduced, thereby increasing recorded so as to examine whether differences exist the possibility of them obtaining medical attention. between such states throughout the three experiments. When analysing results for Experiments A and B in The ratio of malaria deaths to total population in Fig. 3, comparison to Experiment C, the immune and safe decreases in Experiment C, where AUC(C)=1.13, a populations display a considerable increase for the lower value, as expected, than AUC(A) and AUC(B). latter. This, however, cannot be said for the contaminated population where we observe minimal In order to help us have a deeper insight into the impact variations between experiments, due to the factors of education, we plot the ratio of contaminated agents influencing it not varying across experiments. in hospital with respect to the entire contaminated Figure 5 : Safe Agent Population Figure 6 : Contaminated Agent Population Figure 7 : Immune Agent Population Figure 8 : Total Agent Population Individual and total population variations. The figures represent averages of 10 simulation runs within each experiment, and their corresponding standard deviations. Temporal population variations when observing the in a hospital obtaining medical attention. There is a clear entire agent population, see Fig. 8, show a clear improvement in Experiment C where its temporal increase in experiment C with respect to experiments A variations surpass those of experiments A and B. This visual observation is confirmed when calculating AUCs DISCUSSION
To corroborate the above results we can observe Our results demonstrate the impact of education on individual population variations in Figs. 5-7. The malaria deaths. We have seen in Table 2 the changes contaminated population is very similar in all three in average education throughout the entire agent experiments, which is to be expected as the population for all three experiments. In Experiment A, contamination algorithm was not modified. However, the despite the absence of schools, hence no ‘learning’ same cannot be said for the number of safe and immune occurring, there was an increase in final education. agents (Figs. 7 and 5), as well as the entire population This can be explained through natural selection. Those (Fig. 8). There is a significant increase in Experiment C agents with a lower education level had not enough in comparison to both A and B. The state cycle (see Fig. time to obtain medical assistance and consequently 2) is such that an immune agent must be previously a died. However, in the case of Experiments B and C, contaminated agent, unless it is a child of an immune there is a significantly higher final average education, agent (children of immune agents are also immune up to not only because of natural selection, but also due to 1 year after birth). This implies that those immune agents must have visited a hospital, been cured and subsequently become immune. Intuitively, we can The effect of education was viewed from many facets therefore say that the increase in the immune population of our model. One of these is the ratio of malaria in Experiment C is due to a greater number of deaths to the entire population. The improvement contaminated agents having sufficient education and displayed by Experiment B, in comparison to being close enough to a hospital in order to rid Experiment A was not as pronounced as expected. Taking the area under the curve reflected a crisper In conclusion, we notice from the several experiment results described above that there is an improvement not Moreover, our new hypothesis (the positive impact of only when introducing schools but also increasing the adding schools and hospitals), is somewhat confirmed by observing the dynamic ratio of contaminated agents in hospital with respect to the entire contaminated FUTURE WORK
population, see Fig. 4. We expected to witness an increase in this ratio as the simulation progressed, Our aim was to encapsulate epidemiological, whereby a greater number of contaminated agents are environmental and socio-economic factors in our model. However, we would like to attempt to include greater Baudon, D. 2000. “Les Paludismes en Afrique realism in our current efforts. This would be including Subsaharienne”. Afrique Contemporaine, Numéro rural population and climatic seasons. The latter spécial, La Santé en Afrique: Anciens et nouveaux défis, emulates the fluctuations in mosquito population and 195, July-Sept. La Documentation française, 36-45. hence in probabilities of malaria contamination. Our Baume, C. and S.P. Kachur. 1999. “Améliorer la Prise en Charge Communautaire du Paludisme Infantile: Comment intention is also to run simulations for a longer period. la Recherche Comportementale Peut-Elle Aider?”. Technical report Support for Analysis and Research in With respect to education, a future step could be Africa (SARA) Project. Academy for Educational modelling the loss of education points. This could be Development (AED), United States Agency for used to capture the idea that for example after 20 years, a person can forget what it has been taught or that the Carnahan, J.; S. Li; C. Costantini; Y.T. Toure; and C.E. Taylor. treatment will have progressed, therefore information 1997. “Computer Simulation of Dispersal by Anopheles acquired previously has become obsolete. Gambiae in West Africa”. In Artificial Life V. MIT Press, Gomez, R. and J.E. Rowe. 2003. “An Agent-Based As we have demonstrated, education was not sufficient Simulation of Crowd Movement.” In UK Simulation. D. in our model. We had to include more hospitals. This reflects the vast distances that some agents had to Hamagami, T.; S. Koakutsu; and H. Hirate. 2003. “A New travel. A future step could then be to simulate the Crowd Simulation Method by Using Multiagent on effect of improving road infrastructure and transport. Cellular Automata” In Artificial Life VIII. MIT Press. Jaeger, W. and M.A. Janssen. 2001. “Diffusion Processes in Our current model lacks realism in spatial constraints. Demographic Transitions: a Prospect on Using Multi For example with in real life hospitals there is a Agent Simulation to Explore the Role of Cognitive maximum patient capacity for every hospital. This Strategies and Social Interactions”. Technical report 01B40. SOM (Systems, Organisation and Management) could be achieved by applying a cellular automata layer Janssen, M.A. and W.J.M. Martens. 1997. “Modeling Malaria as a Complex Adaptive System”. In Artificial Life III. Finally, we can say that our model could be extended to produce a generic model adaptable to different Krogstad, D.J. 1996. “Malaria as a Reemerging Disease.” countries or geographical areas, with changes in certain Epidemiological Reviews, 18(1), 77-89. parameters. Only parameter changes are needed, as the mechanisms of the malaria problem, described in the Model section, are universal. This could be the basis PAHO (Pan American Health Organization). 2001. “Basic Country Health Profiles”. http://www.paho.org, May. Pavard, B. 2002. “Complexity Paradigm as a Framework for the Study of Cooperative Systems”. Lecture handouts, ACKNOWLEDGEMENTS
COSI Summer School on Modelling and Designing Complex Organisational Systems, Chania, Greece, June- Many thanks go to Dr. J. Dugdale for her help throughout the process and Dr. J. E. Rowe for his input Pavard, B. and J. Dugdale. 2002. “An introduction to in modelling malaria contamination. This work was complexity in social science”. Tutorial on complexity in social science, COSI project. funded by the EU Framework 5 (DG XII TMR) project http://www.irit.fr/COSI/training/complexity- Complexity in Social Sciences, RTN Contract Number HPRN-CT-2000-00068. See http://www.irit.fr/COSI/ Payne, D. 1987. “Spread of Chloroquine Resistance in Plasmodium Falciparum.” Parasitology Today, 3, 241- REFERENCES
WHO (World Health Organization). 2001. Annex Table 2: Basic Indicators for all Member States, World Health Report 2000. http://www.who.org. Aschan-Leygonie, C.; H. Mathian; and L. Saunders. 2000. WHO (World Health Organization). 1996. “Fighting Disease “A Spatial Microsimulation of Population Dynamics in Fostering Development”. The World Health Report, Southern France: a Model Integrating Individual Decisions and Spatial Constraints”. In Applications of Simulations to Social Sciences. Ballot, G. and G. Weisbuch (Eds.). HERMES Science Publishing ltd, 109-125. Bagni, R.; R. Berchi; and P. Cariello. 2002. “A Comparison of Simulation Models Applied to Epidemics.” Journal of Artificial Societies and Social Simulation, 5(3), June.

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