Dynamical analysis of a network-based SIR model with saturated incidence rate and nonlinear recovery rate: an edge-compartmental approach

Fang Wang; Juping Zhang; Maoxing Liu; Fang Wang; Juping Zhang; Maoxing Liu

doi:10.3934/mbe.2024239

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 4: 5430-5445. doi: 10.3934/mbe.2024239

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Research article

Dynamical analysis of a network-based SIR model with saturated incidence rate and nonlinear recovery rate: an edge-compartmental approach

1.
School of Big Data, North University of China, Taiyuan 030051, China
2.
College of General Education, Shanxi College of Technology, Shuozhou 036000, China
3.
Complex Systems Research Center, Shanxi University, Taiyuan 030006, China
4.
School of Science, Beijing University of Civil Engineering and Architecture, Beijing 102616, China

Received: 28 December 2023 Revised: 12 February 2024 Accepted: 27 February 2024 Published: 14 March 2024

A new network-based SIR epidemic model with saturated incidence rate and nonlinear recovery rate is proposed. We adopt an edge-compartmental approach to rewrite the system as a degree-edge-mixed model. The explicit formula of the basic reproduction number $\mathit{\boldsymbol{R_{0}}}$ is obtained by renewal equation and Laplace transformation. We find that $\mathit{\boldsymbol{R_{0}}} < 1$ is not enough to ensure global asymptotic stability of the disease-free equilibrium, and when $\mathit{\boldsymbol{R_{0}}} > 1$ , the system can exist multiple endemic equilibria. When the number of hospital beds is small enough, the system will undergo backward bifurcation at $\mathit{\boldsymbol{R_{0}}} = 1$ . Moreover, it is proved that the stability of feasible endemic equilibrium is determined by signs of tangent slopes of the epidemic curve. Finally, the theoretical results are verified by numerical simulations. This study suggests that maintaining sufficient hospital beds is crucial for the control of infectious diseases.

Keywords:

Citation: Fang Wang, Juping Zhang, Maoxing Liu. Dynamical analysis of a network-based SIR model with saturated incidence rate and nonlinear recovery rate: an edge-compartmental approach[J]. Mathematical Biosciences and Engineering, 2024, 21(4): 5430-5445. doi: 10.3934/mbe.2024239

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Abstract

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