Estimation of domains of attraction in epidemiological models with constant removal rates of infected individuals

Abstract

ABSTRACT: The spread of infections is commonly represented through the so-called Susceptible – Infectious – Recovered models (SIR). Treatment based on isolation of infected individuals is often applied to decrease the spread of certain diseases. Such situation is considered in the SIR model through a constant removal rate term. It has been shown that in such cases, the outcome of the disease spread may depend on the position of the initial states for certain range of the model parameters. The estimation of the domains of attraction of the equilibrium points may therefore be useful to understand the dynamic behavior of the infection spread as a function of the initial population distribution. In this contribution, a Lyapunov based approach to estimate the domain of attraction of the endemic steady state point in SIR models is proposed