Threshold dynamics of a stochastic SIHR epidemic model of COVID-19 with general population-size dependent contact rate

Tianfang Hou; Guijie Lan; Sanling Yuan; Tonghua Zhang; Tianfang Hou; Guijie Lan; Sanling Yuan; Tonghua Zhang

doi:10.3934/mbe.2022195

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 4: 4217-4236. doi: 10.3934/mbe.2022195

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Research article

Threshold dynamics of a stochastic SIHR epidemic model of COVID-19 with general population-size dependent contact rate

1.
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
2.
Department of Mathematics, Swinburne University of Technology, Hawthorn, VIC 3122, Australia

Academic Editor: Yang Kuang

Received: 23 December 2021 Revised: 25 January 2022 Accepted: 03 February 2022 Published: 21 February 2022

In this paper, we propose a stochastic SIHR epidemic model of COVID-19. A basic reproduction number $ R_{0}^{s} $ is defined to determine the extinction or persistence of the disease. If $ R_{0}^{s} < 1 $, the disease will be extinct. If $ R_{0}^{s} > 1 $, the disease will be strongly stochastically permanent. Based on realistic parameters of COVID-19, we numerically analyze the effect of key parameters such as transmission rate, confirmation rate and noise intensity on the dynamics of disease transmission and obtain sensitivity indices of some parameters on $ R_{0}^{s} $ by sensitivity analysis. It is found that: 1) The threshold level of deterministic model is overestimated in case of neglecting the effect of environmental noise; 2) The decrease of transmission rate and the increase of confirmed rate are beneficial to control the spread of COVID-19. Moreover, our sensitivity analysis indicates that the parameters $ \beta $, $ \sigma $ and $ \delta $ have significantly effects on $ R_0^s $.
- stochastic SIHR epidemic model,
- COVID-19,
- the basic reproduction number,
- extinction,
- stochastically permanent
Citation: Tianfang Hou, Guijie Lan, Sanling Yuan, Tonghua Zhang. Threshold dynamics of a stochastic SIHR epidemic model of COVID-19 with general population-size dependent contact rate[J]. Mathematical Biosciences and Engineering, 2022, 19(4): 4217-4236. doi: 10.3934/mbe.2022195

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Abstract

In this paper, we propose a stochastic SIHR epidemic model of COVID-19. A basic reproduction number $ R_{0}^{s} $ is defined to determine the extinction or persistence of the disease. If $ R_{0}^{s} < 1 $, the disease will be extinct. If $ R_{0}^{s} > 1 $, the disease will be strongly stochastically permanent. Based on realistic parameters of COVID-19, we numerically analyze the effect of key parameters such as transmission rate, confirmation rate and noise intensity on the dynamics of disease transmission and obtain sensitivity indices of some parameters on $ R_{0}^{s} $ by sensitivity analysis. It is found that: 1) The threshold level of deterministic model is overestimated in case of neglecting the effect of environmental noise; 2) The decrease of transmission rate and the increase of confirmed rate are beneficial to control the spread of COVID-19. Moreover, our sensitivity analysis indicates that the parameters $ \beta $, $ \sigma $ and $ \delta $ have significantly effects on $ R_0^s $.

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