Abstract
This paper is to investigate the dynamics of a stochastic SIS epidemic model with saturated incidence rate and double epidemic diseases which make the research more complex. The environment variability in this study is characterized by white noise and jump noise. Sufficient conditions for the extinction and persistence in the mean of two epidemic diseases are obtained. It is shown that the two diseases can coexist under appropriate conditions. Finally, numerical simulations are introduced to illustrate the results developed.
•A stochastic SIS epidemic model with double epidemic diseases is considered.•Sufficient conditions for the persistence and extinction are obtained.•The two diseases can coexist under appropriate conditions.•Numerical simulations are introduced to illustrate the results.