考虑人口异质性的丙型肝炎模型的构建和动力学分析
Construction and Dynamic Analysis of a Class of Hepatitis C Model with Population Heterogeneity
摘要: 依据丙型肝炎的传播机理，为了研究不同人群传染率系数和急性转变至慢性的比率的异质性因素对丙型肝炎传播的影响，建立了一类具有人口异质性的传染病模型。计算了系统的控制再生数，并对模型进行敏感性分析和数值模拟。研究结果表明：对高危人群增加急性丙型肝炎感染者的筛查和治疗，并且降低两类人群中急性转变至慢性的比例，可以有效地控制丙型肝炎的蔓延。
Abstract: Based on the transmission mechanism of hepatitis C, a class of epidemic model of hepatitis C trans-mission with population heterogeneity is developed in order to study the influnce of heterogeneous factors on the spread of hepatitis C, including the transmission rate in different populations and the conversion ratio from the acute to the chronic. The control reproduction number is calculated, and the sensitivity analysis and numerical simulations are performed. The results indicate that in-creasing screening and treatment of acute hepatitis C infection in high-risk populations and reduc-ing the transition proportion from the acute to the chronic can effectively control the spread of hep-atitis C.
文章引用：郭德玉, 王晓静, 陈靖宜, 刘堃, 王丽娜, 李欣. 考虑人口异质性的丙型肝炎模型的构建和动力学分析[J]. 应用数学进展, 2023, 12(11): 4665-4671. https://doi.org/10.12677/AAM.2023.1211458

参考文献

[1] 赵文群. 肝病养生保健知识1288问[M]. 上海: 上海科学技术文献出版社, 2012.
[2] 邓存良. 传染病防治科普读本[M]. 成都: 四川科学技术出版社, 2019.
[3] Hu, H.J., Yuan, X.P., Huang, L.H., et al. (2019) Global Dynamics of an SIRS Model with Demographics and Transfer from Infectious to Susceptible on Heterogeneous Networks. Math-ematical Biosciences and Engineering, 16, 5729-5749. [Google Scholar] [CrossRef] [PubMed]
[4] Cui, J.A., Zhang, Y.N. and Feng, Z.L. (2019) Influence of Non-Homogeneous Mixing on Final Epidemic Size in a Meta-Population Model. Journal of Biological Dynamics, 13, 31-46. [Google Scholar] [CrossRef] [PubMed]
[5] 桑梓. 异质性传染病模型的动力学分析和控制措施效果评估[D]: [博士学位论文]. 南京: 南京理工大学, 2012.
[6] Lu, L.Q. and Ouyang, Y.F. (2019) Dynamic Vaccination Game in a Heterogeneous Mixing Population. Physica A: Statistical Mechanics and Its Applications, 533, Article 122032. [Google Scholar] [CrossRef] 
[7] 陈靖宜, 王晓静, 郭松柏, 等. 一类具有早期筛查的丙型肝炎传染病模型分析[J]. 北京建筑大学学报(自然科学版), 2023, 39(3): 97-104. /j.2096-9872.2023.03.12 [Google Scholar] [CrossRef] 
[8] 马知恩, 周义仓, 李承治. 常微分方程定性与稳定性方法(第2版) [M]. 北京: 科学出版社, 2015.
[9] van den Driessche, P. and James, W. (2002) Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission. Mathematical Biosciences and Engineering, 180, 29-48. [Google Scholar] [CrossRef] 
[10] Hassard, B.D., Kazarinoff, N.D. and Wan, Y.H. (1981) Theory and Applications of Hopf Bifurcation. Cambridge University Press, Cambridge.
[11] Nakul, C., James, M.H. and Jim, M.C. (2008) Determining Important Parameters in the Spread of Malaria through the Sensitivity Analysis of a Mathematical Model. Bulletin of Mathematical Biology, 70, 1272-1296. [Google Scholar] [CrossRef] [PubMed]

为你推荐