Stability and Hopf Bifurcation Analysis of a SIS Epidemic Model with Time Delay

Abstract

This research is being carried out within the framework of a SIS pandemic with a saturating incidence rate and a latent latency. Immediate and urgent attention is given to ensuring the stability of the model's disease-free and endemic equilibrium. To determine whether Hopf bifurcation takes place, one must first analyse the situation and, using the elapsed time as a metric, derive the bifurcation parameter. In order to help shed light on the results that were achieved, examples and simulations are provided. This paper investigates the dynamics of an SIS (Susceptible-Infectious-Susceptible) epidemic model incorporating a time delay to represent the period between infection and recovery. The analysis focuses on understanding how the time delay influences the system's stability and leads to the emergence of Hopf bifurcations. This study highlights the critical role of time delay in shaping the spread of infectious diseases and provides insights for developing effective control strategies.