Stationary distribution and probability density function of a stochastic SIRSI epidemic model with saturation incidence rate and logistic growth

Bingtao Han, Daqing Jiang, Baoquan Zhou, Tasawar Hayat and Ahmed Alsaedi

Chaos, Solitons & Fractals, 2021, vol. 142, issue C

Abstract: Focusing on the results of Rajasekar (2020) and the continuous dynamics of stochastic differential equation (SDE) developed by Mao (1997), a stochastic SIRSI epidemic model with saturation incidence rate and logistic growth is investigated in this paper. First, we propose and prove that the unique solution of stochastic model is globally positive. By constructing some suitable Lyapunov functions, the sufficient condition R0h>1 is obtained for the unique stationary distribution which has ergodicity property. Next, by solving the corresponding Fokker-Planck equation, we derive the approximate probability density function around the quasi-endemic equilibrium of the stochastic system. The above stationary distribution and density function can reveal all statistical properties of the disease persistence. In addition, by comparison with other existing articles, our developed theoretical results and some numerical simulations are introduced at the end of this paper.

Keywords: Stochastic SIRSI epidemic model; Ergodicity; Stationary distribution; Fokker-Planck equation; Probability density function (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920309115

DOI: 10.1016/j.chaos.2020.110519

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