PERIOD-DOUBLING BIFURCATION ANALYSIS AND STABILITY OF EPIDEMIC MODEL

This study is concerned with finding the threshold parameter that determines the status of infected individuals in a discrete-time SIS disease model transmitting the infection to other individuals and determining the number of individuals catching the infection. In this study, we firstly examined the equilibrium points of the model, and we determined the presence of a single positive equilibrium point depending on the number of diseased individuals. Then, based on the threshold parameter, we investigated the local asymptotic stability conditions. Moreover, we provided a topological classification of these equilibria. Finally, we obtained the condition providing the emergence of "period-doubling bifurcation" in the given model. The theoretical results that were obtained were verified with numerical examples by using the Mathematica software.