一类具有两针疫苗接种的传染病模型的稳定性分析
Stability Analysis of an Epidemic Model with Two Doses of Vaccination
DOI: 10.12677/aam.2026.158358, PDF,    科研立项经费支持
作者: 王来全：昌吉职业技术学院公共基础教育学院，新疆 昌吉
关键词: 基本再生数；全局渐近稳定；Lyapunov函数；接种策略；Basic Reproduction Number； Global Asymptotically Stable； Lyapunov Function； Vaccination Strategy
摘要: 考虑了一类具有两针疫苗接种和潜伏期的传染病模型，得到了基本再生数 R 0 ，讨论了地方病平衡点存在的条件，运用Lyapunov函数讨论了平衡点的全局稳定性，通过数值模拟验证了所得结论的有效性，说明了增强第一针和第二针疫苗接种对传染病预防的效果。
Abstract: We considered a kind of transmission model with two doses of vaccination and the incubation period. The basic reproduction number R 0 and some conditions for the existence of the endemic equilibrium point were obtained. Throughout the paper, we investigated the global asymptotic of the disease-free equilibrium and the endemic equilibrium point by using the Lyapunov function. Furthermore, we investigated the effect of the one vaccination and two vaccinations on the prevention of epidemic. Lastly, numerical simulations are given to present the effectiveness of the obtained results.
文章引用：王来全. 一类具有两针疫苗接种的传染病模型的稳定性分析[J]. 应用数学进展, 2026, 15(8): 347-356. https://doi.org/10.12677/aam.2026.158358

参考文献

[1] 武文斌, 任雪, 张冉. 具有时滞的离散扩散疫苗接种模型的行波解[J]. 数学物理学报, 2025, 45(3): 858-874.
[2] Delacruz, W.P., Savona, M.R., Thornton, J.A. and Danaher, P.J. (2020) Evidence of Vaccinia Dissemination despite Lack of Major Reaction Following Smallpox Vaccination. Vaccine, 38, 1589-1592.
https://doi.org/10.1016/j.vaccine.2019.12.046
[3] Agaba, G.O., Kyrychko, Y.N. and Blyuss, K.B. (2017) Dynamics of Vaccination in a Time-Delayed Epidemic Model with Awareness. Mathematical Biosciences, 294, 92-99.
https://doi.org/10.1016/j.mbs.2017.09.007
[4] 薛春荣. 一类具有脉冲免疫和潜伏的SEIR传染病模型的全局分析[J]. 西北大学学报(自然科学版), 2013, 43(3): 367-370.
[5] Lu, Z., Chi, X. and Chen, L. (2002) The Effect of Constant and Pulse Vaccination on SIR Epidemic Model with Horizontal and Vertical Transmission. Mathematical and Computer Modelling, 36, 1039-1057.
https://doi.org/10.1016/s0895-7177(02)00257-1
[6] 张真真, 李盈科, 赵睿轩. 具有疫苗接种和年龄结构的疟疾传播模型的动力学行为[J]. 淮阴师范学院学报(自然科学版), 2024, 23(4): 288-296.
[7] 韩梦洁, 刘俊利. 具有不完全接种的反应扩散禽流感模型[J]. 山东大学学报(理学版), 2023, 58(10): 106-121.
[8] 刘胜强, 刘泽含, 骈晓宇. 具有媒体信息和不完善疫苗的传染病模型[J]. 广西师范大学学报(自然科学版), 2026, 44(2): 164-174.
[9] Lv, W., Ke, Q. and Li, K. (2020) Dynamical Analysis and Control Strategies of an SIVS Epidemic Model with Imperfect Vaccination on Scale-Free Networks. Nonlinear Dynamics, 99, 1507-1523.
https://doi.org/10.1007/s11071-019-05371-1
[10] Zhao, Z., Pang, L. and Chen, Y. (2015) Nonsynchronous Bifurcation of SIRS Epidemic Model with Birth Pulse and Pulse Vaccination. Nonlinear Dynamics, 79, 2371-2383.
https://doi.org/10.1007/s11071-014-1818-y
[11] Verguet, S., Johri, M., Morris, S.K., Gauvreau, C.L., Jha, P. and Jit, M. (2015) Controlling Measles Using Supplemental Immunization Activities: A Mathematical Model to Inform Optimal Policy. Vaccine, 33, 1291-1296.
https://doi.org/10.1016/j.vaccine.2014.11.050
[12] Chen, Z.W. and Xu, Z.T. (2019) A Delayed Diffusive Influenza Model with Two-Strain and Two Vaccinations. Applied Mathematics and Computation, 349, 439-453.
https://doi.org/10.1016/j.amc.2018.12.065
[13] 马知恩, 周义仓, 王稳地, 等. 传染病动力学的数学建模与研究[M]. 北京: 科学出版社, 2006.
[14] Hu, L., Wang, S.F., Zheng, T.T., Hu, Z., Kang, Y., Nie, L., et al. (2022) The Effects of Migration and Limited Medical Resources of the Transmission of SARS-CoV-2 Model with Two Patches. Bulletin of Mathematical Biology, 84, Article No. 55.
https://doi.org/10.1007/s11538-022-01010-w
[15] Kaymakamzade, B. and Hincal, E. (2018) Two-Strain Epidemic Model with Two Vaccinations and Two Time Delayed. Quality & Quantity, 52, 695-709.
https://doi.org/10.1007/s11135-017-0647-8

为你推荐