Modelos epidemiológicos em tempo discreto

Abstract

In an endemics, an infeccious disease remains prevalent, in low levels, in a population. In this work, three discrete time mathematical models for an endemic disease are studied: the SIR, the SEIR and SEIRS models. For the qualitative analysis of the models, Discrete Dynamical Systems techniques are used, through which the equilibrium solutions and their stability and the Basic Reproductive Number of each model are determined. In addition, the results are illustrated through numerical simulations. A careful comparison of the properties of the models reveals that they all exhibit damped oscillations as the number of susceptible, infectious, and recovered approaches the endemic equilibrium. In the SEIR model, the latency period slows down the spread of infection compared to the SIR model. When there is loss of immunity (SEIRS model) the levels of infectious are higher.