In this paper we are concerned with numerical methods to solve stochastic differential
equations (SDEs), namely the Euler-Maruyama (EM) and Milstein methods. These methods …

In this paper, we discuss a multigroup SIR model with stochastic perturbation. We deduce
the globally asymptotic stability of the disease-free equilibrium when R0≤ 1, which means …

In this article, we discuss an SIR model with stochastic perturbation. We show that there is a
nonnegative solution that belongs to a positively invariant set. Then, by stochastic Lyapunov …

In this paper, we discuss the persistence and extinction of a delayed vaccinated SIR
epidemic model with temporary immunity and Lévy jumps. Firstly, we study the existence …

A stochastic ratio-dependent predator–prey model is investigated in this paper. By the
comparison theorem of stochastic equations and Itô's formula, we obtain the global …

In this paper, we introduce stochasticity into a multigroup SIR (susceptible, infective, and
recovered) model. The stochasticity in the model is introduced by parameter perturbation …

This paper is concerned with the asymptotic properties of a stochastic delayed SIR epidemic
model with temporary immunity. Sufficient conditions for extinction and persistence in the …

In this paper, a class of stochastic SIS epidemic models with nonlinear incidence rate is
investigated. It is shown that the extinction and persistence of the disease in probability are …

In this paper, we investigate the threshold dynamics of a stochastic delayed SIS epidemic
model with vaccination and double diseases which make the research more difficult. We …

Stochastic differential equations (SDEs) models play a prominent role in many application
areas including biology, epidemiology and population dynamics, mostly because they can …