|
|
具有隐性传染和有限医疗资源的手足口病模型分析
|
Abstract:
本文建立和分析了一类具有隐性传染和有限医疗资源的手足口病模型，计算了疾病的基本再生数，证明了无病平衡点的稳定性，讨论了地方病平衡点的存在性。通过利用中国大陆2022年1月至12月的手足口病月数据进行拟合，分析得到提高感染者的就医率和增加医院的床位数可有效控制疾病的传播。
This article establishes and analyzes a model of hand, foot, and mouth disease with recessive infection and limited medical resources, calculates the basic regeneration number of disease, proves the stability of the disease-free equilibrium point, and discusses the existence of endemic disease equilibrium points. By fitting the monthly data of HFMD in Chinese Mainland from January to December 2022, the analysis shows that improving the medical attendance rate of infected people and increasing the number of beds in hospitals can effectively control the spread of disease.
| [1] | 聂青和. 手足口病流行病学及其临床诊断与治疗[J]. 中国实用内科杂志, 2008, 28(8): 3. |
| [2] | Ma Y., Liu M., Hou Q., et al. (2013) Modelling Seasonal HFMD with the Recessive Infection in Shandong, China. Mathematical Biosciences and Engineering, 10, 1159-1171. https://doi.org/10.3934/mbe.2013.10.1159 |
| [3] | Wang J., Xiao Y. and Check R. (2016) Modelling the Effects of Contaminated Environments on HFMD Infections in Mainland China. Biosystems, 140, 1-7. https://doi.org/10.1016/j.biosystems.2015.12.001 |
| [4] | Wang J., Xiao Y. and Peng Z. (2016) Modelling Seasonal HFMD Infections with the Effects of Contaminated Environments in Mainland China. Applied Mathematics and Computation, 27, 615-627. https://doi.org/10.1016/j.amc.2015.11.035 |
| [5] | Shan, C. and Zhu, H. (2014) Bifurcations and Complex Dynamics of an SIR Model with the Impact of the Number of Hospital Beds. Journal of Differential Equations, 257, 1662-1688. https://doi.org/10.1016/j.jde.2014.05.030 |
| [6] | 刘单, 王艳, 任新志, 等. 具有媒体报道和有限医疗资源的传染病模型[J]. 应用数学和力学, 2023, 44(3): 333-344. |
| [7] | Van den Driessche, P. and Watmough, J. (2002) Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission. Mathematical Biosciences, 180, 29-48. https://doi.org/10.1016/S0025-5564(02)00108-6 |
| [8] | 马知恩, 周义仓, 李承治. 常微分方程定性与稳定性方法[M]. 北京: 科学出版社, 2015. |
| [9] | La Salle, J.P. (1994) The Stability of Dynamical Systems. Society for Industrial and Applied Mathematics, Philadelphia. |
