Threshold behavior in a stochastic SIR epidemic model with Logistic birth

Qun Liu and Daqing Jiang

Physica A: Statistical Mechanics and its Applications, 2020, vol. 540, issue C

Abstract: In this paper, we consider a stochastic SIR epidemic model with Logistic birth. By using the stochastic Lyapunov function method, we show that the stochastic basic reproduction number R0S can be used to determine the threshold dynamics of the stochastic system. If R0S>1, we establish sufficient conditions for the existence of a stationary distribution of the positive solutions to the model. While if R0S<1, under some extra conditions, we obtain sufficient conditions for extinction of the disease. Finally, some examples and numerical simulations are provided to illustrate the theoretical results.

Keywords: SIR epidemic model; Threshold; Stationary distribution; Extinction; Logistic birth (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:540:y:2020:i:c:s0378437119319478

DOI: 10.1016/j.physa.2019.123488

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