Threshold dynamics of a switching diffusion SIR model with logistic growth and healthcare resources

Shuying Wu; Sanling Yuan; Shuying Wu; Sanling Yuan

doi:10.3934/mbe.2024260

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 4: 5881-5899. doi: 10.3934/mbe.2024260

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Threshold dynamics of a switching diffusion SIR model with logistic growth and healthcare resources

Shuying Wu ,
Sanling Yuan ^,

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Academic Editor: Xueying Wang

Received: 13 February 2024 Revised: 16 April 2024 Accepted: 22 April 2024 Published: 14 May 2024

In this article, we have constructed a stochastic SIR model with healthcare resources and logistic growth, aiming to explore the effect of random environment and healthcare resources on disease transmission dynamics. We have showed that under mild extra conditions, there exists a critical parameter, i.e., the basic reproduction number $ R_0^s $, which completely determines the dynamics of disease: when $ R_0^s < 1 $, the disease is eradicated; while when $ R_0^s > 1 $, the disease is persistent. To validate our theoretical findings, we conducted some numerical simulations using actual parameter values of COVID-19. Both our theoretical and simulation results indicated that (1) the white noise can significantly affect the dynamics of a disease, and importantly, it can shift the stability of the disease-free equilibrium; (2) infectious disease resurgence may be caused by random switching of the environment; and (3) it is vital to maintain adequate healthcare resources to control the spread of disease.
- stochastic SIR epidemic model,
- switching diffusion,
- threshold,
- backward bifurcation,
- logistic growth
Citation: Shuying Wu, Sanling Yuan. Threshold dynamics of a switching diffusion SIR model with logistic growth and healthcare resources[J]. Mathematical Biosciences and Engineering, 2024, 21(4): 5881-5899. doi: 10.3934/mbe.2024260

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Abstract

In this article, we have constructed a stochastic SIR model with healthcare resources and logistic growth, aiming to explore the effect of random environment and healthcare resources on disease transmission dynamics. We have showed that under mild extra conditions, there exists a critical parameter, i.e., the basic reproduction number $ R_0^s $, which completely determines the dynamics of disease: when $ R_0^s < 1 $, the disease is eradicated; while when $ R_0^s > 1 $, the disease is persistent. To validate our theoretical findings, we conducted some numerical simulations using actual parameter values of COVID-19. Both our theoretical and simulation results indicated that (1) the white noise can significantly affect the dynamics of a disease, and importantly, it can shift the stability of the disease-free equilibrium; (2) infectious disease resurgence may be caused by random switching of the environment; and (3) it is vital to maintain adequate healthcare resources to control the spread of disease.

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