# A stochastic SIRS epidemic model with infectious force under intervention strategies

Yongli Cai, Yun Kang, Malay Banerjee, Weiming Wang

Research output: Contribution to journalArticle

118 Citations (Scopus)

### Abstract

In this paper, we extend a classical SIRS epidemic model with the infectious forces under intervention strategies from a deterministic framework to a stochastic differential equation (SDE) one through introducing random fluctuations. The value of our study lies in two aspects. Mathematically, by using the Markov semigroups theory, we prove that the reproduction number R0S can be used to govern the stochastic dynamics of SDE model. If R0S1, under mild extra conditions, it has an endemic stationary distribution which leads to the stochastical persistence of the disease. Epidemiologically, we find that random fluctuations can suppress disease outbreak, which can provide us some useful control strategies to regulate disease dynamics.

Original language English (US) 7463-7502 40 Journal of Differential Equations 259 12 https://doi.org/10.1016/j.jde.2015.08.024 Published - Dec 15 2015

### Fingerprint

Stochastic Epidemic Models
Stochastic Equations
Differential equations
Fluctuations
Differential equation
Markov Semigroups
Reproduction number
Semigroup Theory
Epidemic Model
Stochastic Dynamics
Stationary Distribution
Persistence
Control Strategy
Strategy
Model

### Keywords

• Epidemic model
• Markov semigroups
• Reproduction number
• Stationary distribution

• Analysis

### Cite this

A stochastic SIRS epidemic model with infectious force under intervention strategies. / Cai, Yongli; Kang, Yun; Banerjee, Malay; Wang, Weiming.

In: Journal of Differential Equations, Vol. 259, No. 12, 15.12.2015, p. 7463-7502.

Research output: Contribution to journalArticle

Cai, Yongli ; Kang, Yun ; Banerjee, Malay ; Wang, Weiming. / A stochastic SIRS epidemic model with infectious force under intervention strategies. In: Journal of Differential Equations. 2015 ; Vol. 259, No. 12. pp. 7463-7502.
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