Stationary distribution of a double epidemic stochastic model driven by saturated incidence rates

Abstract

The double epidemic study is one of the critical studies in recent times as humankind experiences various simultaneous spreads of diseases. Reproduction numbers are important, which helps to derive sufficient conditions for extinction, persistence and co-persistence of diseases. This work aims to establish the stationary distribution of a stochastic double epidemic model comprised of SIR and SIRS transmission hypothesis through saturated incidence rate, with the aid of Markov semigroup theory. By constructing a suitable Lyapunov functional, the required result is sufficient by conditions on reproduction numbers.