Um modelo SIS com taxas de recuperação e infecção variáveis

Abstract

In this dissertation we present a qualitative theoretical study of modifications to the SIS epidemiological model for infectious diseases that do not confer immunity. We first study the classic SIS model, which considers constant infection and recovery rates. We then analyze a model in wich the recovery rate decreases rate with infectious individuals. This model assumes that recovery depends on a treatment that may become scarce as the infection spreads. Our results show that if the decline in the recovery rate is very steep, a threshold of infectious people appears. Above this threshold, the disease reaches the endemic level even with R0 < 1. In what follows, we analyze two models with infection rate that varies with the number of infectious people. We suppose that susceptible people adopt measures to prevent contagion when the density of infectious people increases, so that hte infection rate is a decreasinf function of infectious. We studied the effects of two types of behavior. In the first one, prevention measures begin as soon as the first infectious appear. In the second model, we assume that preventive measures are taken after the number of infectious people reaches an intermediate value. The results depend on R0. For a small R0, it is better to start contact reduction measures as soon as the first infectious are detected. On the other hand, when R0 is large, the best strategy, according to our results, is to start contact reduction more slowly and increase the reduction as the number of infectious people increases.