Stationary distribution of a hybrid stochastic Zika model with saturated incidence under Markov switching

Abstract

In this paper, we propose a hybrid stochastic Zika virus model with saturation incidence, which is interfered with by white noise and telegraph noise. By constructing an appropriate Lyapunov function, we derive a critical value $R_0^s$ and conclude that if $R_0^s>1$, the model has a unique ergodic stationary distribution that means the persistence of Zika disease. Finally, numerical simulations are carried out to illustrate the theoretical results.