A stochastic model as a survival strategy for an infected population

Abstract

Complex Systems is a branch of Statistical Mechanics that has gained great notoriety in recent years. In particular, Cellular Automata are a simple way to represent complex dynamical systems in which space and time are discrete. In addition to the high degree of nonlinearity, the Boltzmann-Gibbs formalism fails due to the non-extensibility of the systems. In some cases, Complex Systems appear at the typical scale, such as stock market fluctuations for example. In the case of epidemic modeling, cellular automata are used in the description of contagion processes, such phenomena are complex and have large-scale correlations. In this sense, cellular automata present a robust and precise tool for quantifying the spread of diseases in a population provided. In our work, we reported the temporal evolution of an infection in the square network, counting process is to introduce an interaction between first neighbors and the population in which the infection acts remains constant. We obtained, through the fourth-order Binder's cumulative, the instant of time when the peak of the infection occurs, we also carried out the characterization of the type of passage through which the system goes through. We also analyzed the impact that the parameter causes on the temporal evolution of the infection.