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- 2018
考虑疫苗时效及潜伏期的乙肝传染病模型分析
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Abstract:
建立了一个考虑疫苗时效性和乙肝潜伏期的乙肝传染病模型.首先，讨论了平衡点的存在性；然后，计算了基本再生数R0，得到系统总存在一个无病平衡点，且当R0＞1时，存在唯一正平衡点；最后通过构造Lyapunov泛函，证明了无病平衡点的全局稳定性和正平衡点的全局稳定性.
In this paper, an epidemic model of HBV considering the effects of vaccinal effectiveness and latency is established. First, the existence of equilibria is discussed. Then, the basic reproduction number R0 is computed, and we obtain that in the system still exists a virus-free equilibrium, and there is a unique endemic equilibrium when R0 > 1. Finally, we prove the global stabilities of the virus-free equilibrium and the endemic equilibrium by constructing Lyapunov functions
| [1] | LIU X N, TAKEUCHI Y, IWAMI S. SVIR Epidemic Models with Vaccination Strategies[J]. Journal of Theoretical Biology, 2008, 253(1): 1-11. DOI:10.1016/j.jtbi.2007.10.014 |
| [2] | 马知恩, 周义仓, 李承治. 常微分方程定性与稳定性方法[M]. 2版. 北京: 科学出版社, 2015. |
| [3] | MONEIM I A, KHALIL H A. Modelling and Simulation of the Spread of HBV Disease with Infectious Latent[J]. Applied Mathematics, 2015, 6(5): 745-753. DOI:10.4236/am.2015.65070 |
| [4] | ALEXANDER M E, BOWMAN C, MOGHADAS S M, et al. A Vaccination Model for Transmission Dynamics of Influenza[J]. Siam Journal on Applied Dynamical Systems, 2004, 3(4): 503-524. DOI:10.1137/030600370 |
| [5] | LIANG X F, BI S L, YANG W Z, et al. Epidemiological Serosurvey of Hepatitis B in China-Declining HBV Prevalence due to Hepatitis B Vaccination[J]. Vaccine, 2013, 31(47): 6550-6557. |
| [6] | VAN DEN DRIESSCHE P, WATMOUGH J. Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission[J]. Mathematical Biosciences, 2002, 180(1): 29-48. |
| [7] | HALE J K, VERDUYN L S M. Introduction to Functional Differential Equations[M]. Berlin: Springer Science & Business Media, 2013. |
| [8] | DUAN X C, YUAN S L, LI X Z. Global Stability of an SVIR Model with Age of Vaccination[J]. Applied Mathematics and Computation, 2014, 226: 528-540. DOI:10.1016/j.amc.2013.10.073 |
| [9] | PANG J, CUI J A, ZHOU X. Dynamical Behavior of a Hepatitis B Virus Transmission Model with Vaccination[J]. Journal of Theoretical Biology, 2010, 265(4): 572-578. DOI:10.1016/j.jtbi.2010.05.038 |
| [10] | LI X Z, ZHOU L L. Global Stability of an SEIR Epidemic Model with Vertical Transmission and Saturating Contact Rate[J]. Chaos Solitons & Fractals, 2009, 40(2): 874-884. |
| [11] | ARINO J, MCCLUSKEY C C, VAN DEN DRIESSCHE P. Global Results for an Epidemic Model with Vaccination That Exhibits Backward Bifurcation[J]. Siam Journal on Applied Mathematics, 2003, 64(1): 260-276. DOI:10.1137/S0036139902413829 |
