Stationary distribution, extinction and probability density function of a stochastic SEIV epidemic model with general incidence and Ornstein-Uhlenbeck process

Considering the great benefit of vaccination and the variability of environmental influence, a stochastic SEIV epidemic model with mean-reversion Ornstein-Uhlenbeck process and general incidence rate is investigated in this paper. First, it is theoretically proved that stochastic model has a unique global solution. Next, by constructing a series of suitable Lyapunov functions, we obtain a sufficient criterion Rs0> 1 for the existence of stationary distribution which means the disease will last for a long time. Then, the sufficient condition for the extinction of the infectious disease is also derived. Furthermore, an exact expression of probability density function near the quasi-endemic equilibrium is obtained by solving the corresponding four-dimensional matrix equation. Finally, some numerical simulations are carried out to illustrate the theoretical results.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

In this paper, a stochastic SEIV epidemic model with mean-reversion Ornstein-Uhlenbeck process and general incidence rate is investigated. The unique global solution of the stochastic model is theoretically proved. By constructing suitable Lyapunov functions, a sufficient criterion Rs0> 1 for the existence of stationary distribution and a sufficient condition for the extinction of the infectious disease are obtained. An exact expression of probability density function near the quasi-endemic equilibrium is also derived. Numerical simulations are conducted to illustrate the theoretical results.