Epidemic characteristics of two classic SIS models with disease-induced death

The epidemic characteristics of two classic SIS epidemic models, including the epidemic size, peak and turning point, are investigated. The two SIS models are with bilinear and standard incidences, respectively. For the SIS models, the susceptible individuals generally can be divided into two classes. One consists of the individuals who had not been infected by the infection, the other are individuals who have been infected and recovered from the infection. Based on this fact, the classic SIS epidemic models need to be reformulated in order to analyze the turning points of the epidemic for various cumulative cases in detail. The obtained results illustrate how to determine the epidemic characteristics of the two models, and demonstrate their dependence on the initial conditions and the relative parameters of the models.