Periodic Solution and Ergodic Stationary Distribution of SEIS Dynamical Systems with Active and Latent Patients

Abstract

This paper proposes two new stochastic non-autonomous SEIS epidemic dynamical models with latent and active patients. For the non-autonomous periodic system, we first obtain the sufficient conditions for the existence of nontrivial positive periodic solution by constructing some suitable stochastic Lyapunov functions with regime switching. Then we prove the existence of ergodic stationary distribution of the stochastic SEIS epidemic model with Markov conversion by using the stochastic qualitative theory. At last, some rigorous computer numerical simulations illustrate our theoretical results. The results show that the large random disturbance can destroy the periodic solution and the ergodic stationary distribution.