Damped and Sustained Oscillations in SIR-models

Abstract

Different types of SIR-models are analysed for the existence of sustained oscillations. Techniques like linearisation around the endemic equilibrium and Hopf bifurcation theory are used for the analysis of these models. Out of the five different variations of SIR-models that were thoroughly analysed, only some have sustained oscillations. In two of the five models, there exist no sustained oscillations. In two other models sustained oscillations exist for some parameter values. In the last of the five models, sustained oscillations exist only when there is a sufficiently large delay in the waning of immunity.