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- 2018
基于饱和发生率的随机HIV模型的动力学研究
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Abstract:
建立了一个带饱和发生率的随机HIV模型.首先分析了全局正解的存在性和有界性,进一步通过构造Lyapunov函数得到了病毒灭绝和持续的条件.
In this paper, a stochastic HIV model with saturation rate is established. First, the existence and boundedness of the global positive solutions are proved. Then, by constructing Lyapunov function, the conditions of extinction and persistence for the stochastic HIV model with saturation rate are obtained
[1] | NOWAK M A, BONHOEKER S, HILL A M, et al. Viral Dynamics in Hepatities B Virus Infection[J]. Proc Natl Acad Sci USA, 1996, 93(9): 4398-4402. DOI:10.1073/pnas.93.9.4398 |
[2] | HUANG G, TAKEUCHI Y, KOROBEINIKOV A. HIV Evolution and Progression of the Infection to AIDS[J]. Journal of Theoretical Biology, 2012, 307: 149-159. DOI:10.1016/j.jtbi.2012.05.013 |
[3] | ELAIW A M. Global Properties of a Class of HIV Models[J]. Nonlinear Analysis: Real World Applications, 2010, 11(4): 2253-2263. DOI:10.1016/j.nonrwa.2009.07.001 |
[4] | MAO X R. Stability of Stochastic Differential Equations with Markovian Switching[M]. Stochastic Processes and Their Applications, 2007. |
[5] | 李巧玲. 具有饱和发生率的时滞HIV-1感染模型动力学研究[D]. 长沙: 湖南大学, 2011. http://cdmd.cnki.com.cn/article/cdmd-10532-1012328185.htm |
[6] | WEI F Y, CHEN F X. Stochastic Permanence of an SIQS Epidemic Model with Saturated Incidence and Independent Random Perturbations[J]. Physica A, 2016, 453: 99-107. DOI:10.1016/j.physa.2016.01.059 |
[7] | ZHAO Y N, JIANG D Q. The Threshold of a Stochatic SIS Epidemic Model with Vaccination[J]. Applied Mathematics and Computation, 2014, 243: 718-727. DOI:10.1016/j.amc.2014.05.124 |
[8] | DALAL N, GREENHALGH D. MAO X R, A Stochastic Model for Internal HIV Dynamics[J]. Journal of Mathematical Analysis and Applications, 2008, 341(2): 1084-1101. DOI:10.1016/j.jmaa.2007.11.005 |
[9] | 付瑞, 王稳地, 陈虹燕, 等. 一类考虑饱和发生率的HIV感染模型的稳定性分析[J]. 西南大学学报(自然学科版), 2015, 37(3): 76-81. |
[10] | JIANG D Q, LIU Q, SHI N Z. Dynamics of a Stochastic HIV-1 Infection Model with Logistic Growth[J]. Physica A, 2017, 469: 706-717. DOI:10.1016/j.physa.2016.11.078 |