Modelos de autômatos celulares para febre amarela silvestre em bugios

Abstract

In this work, discrete mathematical models are proposed to analyze the dynamics of a population of howler monkeys stricken with periodic outbreaks of yellow fever. Using the cellular automata framework, the models describe the spatiotemporal evolution of the population inhabiting an isolated or a fragmented forest. Initially, in the time scale of the epizootic, a first cellular automaton model considering only the movement of mosquitoes and howler monkeys, the vital dynamics of the mosquitoes and the yellow fever dynamics in a fragmented and remote forest region is proposed. The probability of extinction of the population of howler monkeys is estimated for several parameters sets. The model is also applied to a fragmented forest region. Through this model, the probabilities of extinction are measured not only for the total population of howler monkeys but for populations living in different fragments of forest. A model for the vital dynamics of the population of howler monkeys is proposed, taking into account the probabilities of births and deaths of howler monkeys, as well as the probability of deaths due to intraspecific competition. The evolution of population size is obtained through several simulations. We observed that the number of individual reaches a constant value which depends on the intraspecific competition. Finally, we combine the model for the population vital dynamics with the cellular automata for the evolution of the population under a yellow fever outbreak to study the long-term survival of the species. We observed the persistence of the howler monkeys depends on the carrying capacity and on the transmission rates.