Stability of the Epidemiological Model SIR with Loss of Immunity

Abstract

This study approaches the analysis of the stability of the epidemiological model SIR with loss of immunity. This is a model given by a system of ordinary differential equations. Initially, we present the model and its interpretation. Then we define the constants and elements that compose the model, so we present the results obtained using the qualitative theory of ordinary differential equations, especially the theory of planar systems related to the dynamics of fixed points. Finally, we show that the system representing the SIR model is globally stable and they have two types of dynamic that {depend on model constants}, and their meaning for epidemiology.

Keywords

• SIR model
• ordinary differential equations
• fixed points
• stability