Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence
Physica A: Statistical Mechanics and its Applications, Volume 476, Year 2017
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In this paper, we consider a stochastic SEIR epidemic model with standard incidence. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution to the model. Our result does not depend on the positive endemic equilibrium E∗ of the deterministic system, which improves the previous result to a greater extent. Moreover, we also establish sufficient conditions for extinction of the disease.