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摘要
考虑到传染病传播过程中宿主体内病毒载量和医疗资源有限对疾病传播的影响，提出一类具有饱和治疗率的宿主体内和宿主之间耦合的多尺度传染病模型。首先，对于宿主之间疾病传播模型，通过计算得到基本再生数，并给出刻画其无病平衡点和地方病平衡点的存在性与稳定性的判别准则。特别地，当基本再生数小于1时，模型存在两个地方病平衡点，其中一个局部渐近稳定，另一个不稳定。当基本再生数大于1时，模型存在唯一的地方病平衡点，它在特定条件下是全局渐近稳定的。其次，探讨医疗资源有限导致的前向/后向分支的存在性，这意味着疾病的消除或流行不再取决于基本再生数，而是与感染者的初始状态以及医疗资源的供应密切相关。最后，通过数值模拟解释了本文的主要理论结果。
关键词
多尺度传染病模型
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基本再生数
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平衡点
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渐近稳定性
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前向/后向分支
Key words
multi-scale infectious disease model
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basic reproduction number
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equilibrium
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asymptotic stability
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forward/backward bifurcation
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王妙,王雅萍,聂麟飞.
有限医疗资源影响下的多尺度传染病模型研究[J].
山西大学学报(自然科学版), 2025, 48(03): 445-455 DOI:10.13451/j.sxu.ns.2023159
基金资助
国家自然科学基金(11961066)
新疆维吾尔自治区自然科学基金(2021D01E12)
京公网安备11010202008535号
