Dynamic analysis of a SIS epidemic model with nonlinear incidence and ratio dependent pulse control

In this paper, a SIS epidemic model with nonlinear incidence and ratio dependent pulse control is proposed and analyzed. Firstly, for the system that ignores the effect of pulses, the basic reproductive number \(R_0\) $R_0$ is derived using the next-generation matrix method, and the stability of the equilibria of the system is analyzed. And then the dynamics of the system containing pulse effects was investigated. The existence of periodic solutions has been proven by constructing appropriate Poincaré mappings and using the fixed point theorem. We found that pulses have a significant impact on system dynamics. Under the influence of pulses, the system trajectory undergoes periodic oscillations, which are verified by numerical simulations.