Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 125, pp. 1-120.

Title: Dynamic behavior of a stochastic SIR epidemic model with vertical transmission

Authors:  Xiao-Bing Zhang (Lanzhou Univ. of Technology, Lanzhou, Gansu,  China)
                Su-Qin Chang      (Lanzhou Univ. of Technology, Lanzhou, Gansu,  China)
                Hai-Feng Huo      (Lanzhou Univ. of Technology, Lanzhou, Gansu,  China)

Abstract:
  This article concerns the dynamic behavior of a stochastic SIR epidemic
 model with vertical transmission. We present sufficient conditions which can
 determine the extinction and persistence in mean of the epidemic.
 Also we discuss the asymptotic behavior of the stochastic model around
 the endemic equilibrium of the corresponding model. Moreover,
 sufficient conditions for the existence of stationary distribution are
 established. The results are illustrated by numerical simulations.
 
Submitted July 21, 2018. Published November 25, 2019.
Math Subject Classifications:  34A37, 34D05, 92D30.
Key Words: Stochastic SIR model; extinction; persistence;  stationary distribution.