Density function and stationary distribution of a stochastic SIR model with distributed delay

In this paper, we first transfer a stochastic SIR model with strong kernel into an equivalent high-dimensional stochastic system. Then the stationary distribution of the model with the white noises is obtained by constructing a suitable Lyapunov function, which determines a critical value R* corresponding to the control reproduction number R-0 of the corresponding determined system. Particularly, we obtain an exact local expression of the density function of the stochastic model around the unique quasi-equilibrium. (C) 2022 Elsevier Ltd. All rights reserved.

Automated summary

In this paper, a stochastic SIR model with strong kernel is transformed into an equivalent high-dimensional stochastic system. The stationary distribution of the model with white noise is obtained by constructing a suitable Lyapunov function, which determines a critical value corresponding to the control reproduction number of the corresponding determined system. Furthermore, an exact local expression of the density function of the stochastic model around the unique quasi-equilibrium is derived.