Bioinformatics and Hardware Group

1. Introduction
2. General options for simulation program
3. Epidemic evolution
4. Conclusions

SIMULATION OF AN EPIDEMIC PROCESS

INTRODUCTION

The Artificial Intelligence techniques (the neural networks, the genetic algorithms and the cellular automata) can be used for the viral epidemics simulations.

This project presents a program of simulation of a viral epidemic using cellular automata. Are analyzed the results obtained considering various parameters characterizing a measles epidemics in a close community (an orphanage with children having between 3 and 9 years).

Description of the simulation medium

The used model refers to a population, with a given number of individuals, but not the same, some of them are dying and other appearing in the community as newborns. That population, open structurally, is closed spatially, the immigration and the emigration being negligible.

The epidemic propagation is realized by the changes of the health states of the individuals of the population, placed in a bidimensional, finite and close space (the tridimensional image of this space is a torus) An elementary zone of that space corresponds to a spatial niche. Each niche can contain only an individual, whose elementary possible displacements are towards the neighbor niche, oriented only in the various cardinal directions from the starting niche (from the Von Neumann neighborhood).

The implementation of the model reflects the main used paradigms: the necessity of a cellular automata and of the moving (and changing the state) agents.

The individuals of the community can be, from the epidemiological point of view, in one of the following states: susceptibles (which were no infected till the considered moment, but can be contaminated in the future), contagious persons (source of contamination for the neighbor susceptible individuals), immunized (which make the virosis and gained the immunity against the respective virus). The contagiousness time can be considered for the measles as 7 days, or 14 t.u (the time unity being a half of day). For a simple virosis no other health states must be taken into account and the immunity is gained forever, the respective individuals, creating difficulties to the other persons displacements.

The used epidemiological model contains two local laws, describing the respective elementary processes: the individuals displacements and the epidemics propagation

The global evolution of the epidemic is the result of many independent, simultaneous elementary processes, in all the community.

The overall parameters of the model, established before the simulation, refer to the number of cells (niche) of the cellular automaton, the number of the individuals, the density DENS(D individuals/cell), the duration of the contagiousness period (T t.u), the probability of contamination (the contagiousness C), the natality (N/oo.ooo individuals) and the mortality (Mo/oo.ooo).

General options for simulation program

The initial aleatory distribution of the susceptible individuals. Windows with general options for simulation program.

Epidemic evolution

The evolution of the epidemic in a community with 414 individuals, with an initially contaminated person. The contagiosirty was 0.25. The blue, red and green circles in the cells represent individuals. which are susceptible, contaminated or immunized. In the left window is presented the individual distribution in the cellular automata. In the right window the red and green curves represent the evolution in time of the number of contagious and immunized individuals.

CONCLUSIONS

The cellular automata are a adequate concept for the micropopulational modeling of the aleatory interactions of the individuals of a community, during a viral epidemic propagation, which suppose various displacements and independent or reciprocally changes of the health states of the interacting individuals.

We use the Monte Carlo method for representing the various aleatory simultaneous and successive processes implied in the viral epidemic propagation. Averaging the results of repeated running, we obtain simulation of the overall evolution of simple viral epidemics, as the measles propagation in a community.

For different sets of specific parameters of the cellular automaton and of the elementary processes relating the viral epidemic propagation in a close community, we can obtain the temporal evolution of the morbidity. The used micropopulational model appears as representative, because there are no statistic significant difference between the simulation results and the observation data.

The types of the analyzed epidemics in this project are characterized by the overall parameters Nep (the maximal extension) and Tep (the epidemic duration), which are obtained as functions of the transmissibility k of the virosis (measles) and of the duration of the contagiousness TC:

• the relative extension of the epidemics Nep/NT increases monotonically, from 0 to - 1, in a small interval (ko-3Dko, ko+Dko); for ko, Nep/NT is 1/2 the ko value, the central one in the increase interval of Nep/NT, decreases when T increases;
• the epidemic duration Twep, for increasing k, attain a maximum Tep, max for an intermediary value of k, kmax; at values of k greater than kmax, Tep decreases, when k increases till to a minimal value Tep, min;
• the values Tep, max and Tep, min increases with TC; but kmax decreases when, T increases.