Stability analysis of a SAIR epidemic model on scale-free community networks

Xing Zhang; Zhitao Li; Lixin Gao; Xing Zhang; Zhitao Li; Lixin Gao

doi:10.3934/mbe.2024204

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 3: 4648-4668. doi: 10.3934/mbe.2024204

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Stability analysis of a SAIR epidemic model on scale-free community networks

School of Mathematics and Physics, Wenzhou University, Wenzhou 325035, China

Academic Editor: Sereno Denis

Received: 19 October 2023 Revised: 19 January 2024 Accepted: 29 January 2024 Published: 29 February 2024

The presence of asymptomatic carriers, often unrecognized as infectious disease vectors, complicates epidemic management, particularly when inter-community migrations are involved. We introduced a SAIR (susceptible-asymptomatic-infected-recovered) infectious disease model within a network framework to explore the dynamics of disease transmission amid asymptomatic carriers. This model facilitated an in-depth analysis of outbreak control strategies in scenarios with active community migrations. Key contributions included determining the basic reproduction number, $ R_0 $, and analyzing two equilibrium states. Local asymptotic stability of the disease-free equilibrium is confirmed through characteristic equation analysis, while its global asymptotic stability is investigated using the decomposition theorem. Additionally, the global stability of the endemic equilibrium is established using the Lyapunov functional theory.
- SAIR,
- infectious disease model,
- network,
- basic reproduction number,
- stability
Citation: Xing Zhang, Zhitao Li, Lixin Gao. Stability analysis of a SAIR epidemic model on scale-free community networks[J]. Mathematical Biosciences and Engineering, 2024, 21(3): 4648-4668. doi: 10.3934/mbe.2024204

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Abstract

The presence of asymptomatic carriers, often unrecognized as infectious disease vectors, complicates epidemic management, particularly when inter-community migrations are involved. We introduced a SAIR (susceptible-asymptomatic-infected-recovered) infectious disease model within a network framework to explore the dynamics of disease transmission amid asymptomatic carriers. This model facilitated an in-depth analysis of outbreak control strategies in scenarios with active community migrations. Key contributions included determining the basic reproduction number, $ R_0 $, and analyzing two equilibrium states. Local asymptotic stability of the disease-free equilibrium is confirmed through characteristic equation analysis, while its global asymptotic stability is investigated using the decomposition theorem. Additionally, the global stability of the endemic equilibrium is established using the Lyapunov functional theory.

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