Analysis of Multi-scale Infectious Disease Model Under the Influence of Limited Medical Resources

WANG Miao, WANG Yaping, NIE Linfei

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Journal of Shanxi University(Natural Science Edition) ›› 2025, Vol. 48 ›› Issue (3) : 445-455. DOI: 10.13451/j.sxu.ns.2023159
Mathematics and Applied Mathematics

Analysis of Multi-scale Infectious Disease Model Under the Influence of Limited Medical Resources

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Abstract

Considering the influence of the viral load in the host and limited medical resources on the transmission of infectious diseases, a multi-scale infectious disease model with saturated treatment rate coupling within-host and between-host dynamics is proposed. Firstly, for the between-host disease transmission model, the basic reproduction number is obtained, and a criterion describing the existence and stability of the disease-free and endemic equilibrium for the coupled model is given. Particularly, when the basic reproduction number is less than 1, the model has two endemic equilibria, one of which is locally asymptotically stable and the other is unstable. When the basic reproduction number is greater than 1, the model has a unique endemic equilibrium, which is global asymptotically stable under specific conditions. In addition, The existence of forward/backward bifurcation caused by limited medical resources is analyzed. This means that the elimination or prevalence of the disease no longer depends on the basic reproduction number but is closely related to the initial state of infected humans and the supply of medical resources. Finally, the main theoretical results of this paper are explained by numerical simulation.

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multi-scale infectious disease model / basic reproduction number / equilibrium / asymptotic stability / forward/backward bifurcation

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WANG Miao , WANG Yaping , NIE Linfei. Analysis of Multi-scale Infectious Disease Model Under the Influence of Limited Medical Resources. Journal of Shanxi University(Natural Science Edition). 2025, 48(3): 445-455 https://doi.org/10.13451/j.sxu.ns.2023159

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