Modelo epidemiológico baseado em autômatos celulares probabilistas com população estruturada por grupos

Abstract

Epidemiological modeling of contact diseases generally considers physical contact between two individuals for a contagious infection to be spread in a population. Although for some diseases contact is in fact only made by two individuals, such as AIDS disease textit (Acquired Immunode ciency Syndrome), there are other contagious diseases that spread by contact between two or more individuals. Generally, these diseases are spread in public transportation system, residences or rooms in corporate environments. All of these situations are related to groups of individuals who may contract a disease due to the presence of one or more infected individuals in the group. In this paper, we present a population based epidemiological model structured by groups, where individuals move in a neighborhood forming groups in which the disease can be transmitted. The action of susceptible individuals is analyzed when they avoid the formation of groups with infected individuals, for fear of contracting the disease. The spatially distributed population model is modeled by two-dimensional probabilistic cellular automata in which each matrix cell represents an individual, and the disease is represented by the SIR model (Susceptible, Infected, Recovered), and is also described by ordinary di erential equations. The main results show that the individual's home delity (probability of staying in his cell in the movements) and a proposed measure we call lattice temperature are related to the number of new cases of the disease per time step. The control strategies used in this paper show that only a population with greatly reduced mobility can extinguish a contagious disease.