Stability and bifurcation analysis of the SIS epidemic model

This thesis study is concerned with finding the threshold parameter that determines the status of transmission of the individuals who have the infection in a difference-time SIS disease model and the number of individuals who have the infection accordingly. In this study, we first investigated the equilibrium points of the model and determined the existence of the only positive equilibrium point that depends on the number of diseased individuals. Then, we examined the local asymptotic stability conditions depending on the threshold parameter. Moreover, we have given a topological classification of these equilibrium points. Finally, we achieved the condition that led to the emergence of "period doubling bifurcation" in the given model. Numerical examples for the theoretical results obtained were validated using the SageMath program.