具有有限医疗资源的手足口病模型分析
Analysis of Hand-Foot-Mouth Disease Models with Limited Medical Resources
DOI: 10.12677/aam.2025.147363, PDF,    科研立项经费支持
作者: 高永谦, 马扬军*：重庆交通大学数学与统计学院，重庆
关键词: 有限医疗资源；手足口病；基本再生数；疫苗接种；Limited Medical Resources； Hand-Foot-Mouth Disease； Basic Reproduction Number； Vaccination
摘要: 本文建立了一个具有有限医疗资源的手足口病传播模型，首先计算了模型的基本再生数，讨论了地方病平衡点的存在性，并分析了无病平衡点和地方病平衡点的稳定性，如果假定在治疗能力之内时治疗函数满足一个非线性函数，当染病者数量超过了治疗能力承受的界限时，治疗函数为某一常数形式。模拟发现，若治疗函数较小时，会出现后向分支，这表明基本再生数小于1不一定能够使疾病消除。最后结合2023年中国大陆手足口病月报告病例数据进行拟合，通过数值模拟来展示有限医疗资源对手足口病传播的影响。
Abstract: In this paper, we develop a model for the spread of HFMD with limited medical resources, first calculate the basic regeneration number of the model, discuss the existence of the endemic equilibrium point, and analyze the stability of the disease-free equilibrium point and the endemic equilibrium point, if it is assumed that the treatment function satisfies a nonlinear function when it is within the treatment capacity, and when the number of infected people exceeds the limit of the treatment capacity to withstand the treatment, the treatment function is a certain constant form. The simulation finds that backward branching occurs if the treatment function is small, which suggests that a basic regeneration number less than 1 does not necessarily lead to disease elimination. Finally, numerical simulations are fitted with the data of monthly reported cases of HFMD in mainland China in 2023 to demonstrate the impact of limited medical resources on the spread of HFMD.
文章引用：高永谦, 马扬军. 具有有限医疗资源的手足口病模型分析[J]. 应用数学进展, 2025, 14(7): 269-283. https://doi.org/10.12677/aam.2025.147363

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