Bifurcation and Stability of an Discrete-time SIS Epidemic Model with Treatment

Abstract

Mathematical models are useful in examining the effect of an infection on populations. Conditions involving the spread and control of the disease are calculated by analyzing mathematical models, so that it is possible to have information about the behavior of the infection. This article includes the dynamic behavior of a discrete-time SIS epidemic model with treatment. Existence conditions of the fixed points of the model are obtained, and stability analysis is performed for these fixed points. The stability and bifurcation conditions of the obtained endemic fixed point are investigated. Depending on the infection coefficient, the flip bifurcation condition is obtained. At the same time, it is determined in which situation Neimark Sacker bifurcation may occur depending on the step size, and bifurcation is controlled. Rich dynamic behaviors are given to support our theoretical results.