Stability Analysis of an SIR Infectious Disease Model

Abstract

The paper investigates the stability of the SIR mathematical model of transmission of an infectious disease with delay. First, the study investigates local stability of the positive steady state of an infectious disease model by analyzing the linearised system where more general stability criteria with delay and model parameters are obtained. Secondly, the study shows that the model exhibits Hopf bifurcation on choosing the delay as a bifurcation parameter. Conditions for existence of qualitative behaviour for positive steady state are identified. Finally, numerical simulation of results and biological interpretations were verified using MATLAB software for the delay model. The study supplements theoretical improvement to earlier results obtained in the literature.