Stochastic dynamics of an SEIS epidemic model

In this paper, we investigate the stochastic disease dynamics of an SEIS epidemic model with latent patients and active patients. The two parameters R₀ˢ and R₀* are identified as the disease-free and endemic dynamics of the model. More specifically, we give the almost surely exponential stability of the disease-free equilibrium in terms of R₀ˢ , and stochastic endemic dynamics in terms of R₀* . The theoretical and numerical results may be useful for studying the dynamics of disease spreading in a randomly fluctuating environment.