Bifurcations on a discrete–time SIS–epidemic model with saturated infection rate

In this paper, we explore the complex dynamics of a discrete-time SIS (Susceptible-Infected-Susceptible)-epidemic model. The population is assumed to be divided into two compartments: susceptible and infected populations where the birth rate is constant, the infection rate is saturated, and each recovered population has a chance to become infected again. Two types of mathematical results are provided namely the analytical results which consist of the existence of fixed points and their dynamical behaviors, and the numerical results, which consist of the global sensitivity analysis, bifurcation diagrams, and the phase portraits. Two fixed points are obtained namely the disease-free and the endemic fixed points and their stability properties. Some numerical simulations are provided to present the global sensitivity analysis and the existence of some bifurcations. The occurrence of forward and period-doubling bifurcations has confirmed the complexity of the solutions.