Modelling Population Heterogeneity in Epidemics Using Cellular Automata

Abstract

Compartmental models are very popular in epidemiology. One of the reason for such popularity is the excellent results obtained when the populations satisfy the building hypotheses (large populations, individual uniformity and appropriate structure), while the complexity of the resulting model is low. Besides, the ease of analysis, the wide variety of analysis tools available and the "intuitive reasonableness" make this kind of models very attractive. However, in many situations they ignore important factors inherent to the problem, such as the nature of contacts between individuals and the heterogeneity of the population. Cellular models are adequate to describe natural systems consisting of a massive collection of simple objects. They are a special case of models based on individuals, which represent the global system behavior from the description of the behavior of individuals within it. In this paper we study the time evolution of a heterogeneous population through the various stages of disease resulting from the individuals interactions (epidemic). The objectives of this work are i) the development of a model that includes the effects of heterogeneity and individual contacts in the evolution of the epidemic, ii the implementation of the proposed model through a cellular automaton and iii its validation with data from the 1918 influenza pandemic in the Geneva.