具有染病者筛查和性别结构的随机AIDS传染病模型分析
Analysis of a Stochastic Sex-Structured AIDS Epidemic Model with Effect of Screening of Infectives
摘要: 本文主要研究了具有染病者筛查和性别结构的随机AIDS传染病模型，利用ITO公式，讨论了该系统的动力学行为。首先，我们证明了该模型解的极限性质；其次，通过选取合适的对数函数，给出了疾病灭绝的充分条件；进一步，选取恰当的V函数，分析了系统唯一正的遍历平稳分布的存在性；最后，通过数值模拟，验证了本文的理论结果。
Abstract: In this paper, we study a stochastic model describing the sex-structured AIDS with effect of screening of infectives, and the dynamic behavior of the system is discussed by using the formula of ITO. First, we consider the limiting behaviors of the solution. Further, the sufficient condition guaranteeing the extinction of AIDS is obtained. Then, an appropriate V-function is selected to prove that the solution of the model has a unique ergodic stationary distribution. Finally, the theoretical results are verified by numerical simulations.
文章引用：赵晓琦, 董玲珍. 具有染病者筛查和性别结构的随机AIDS传染病模型分析[J]. 应用数学进展, 2021, 10(4): 1153-1167. https://doi.org/10.12677/AAM.2021.104125

参考文献

[1] Kirschner, D. (1996) Using Mathematics to Understand HIV Immune Dynamics. Notices of the American Mathematical Society, 43, 191-202.
[2] Lutambi, A.M. (2015) Modelling the Impact of Stages of HIV Progression on Estimates. Mathematical Biosciences, 5, 101-113. [Google Scholar] [CrossRef] 
[3] Cai, L., Li, X. and Ghosh, M. (2009) Stability Analysis of an HIV/AIDS Epidemic Model with Treatment. Journal of Computational and Applied Mathematics, 229, 313-323. [Google Scholar] [CrossRef] 
[4] Tripathi, A., Naresh, R. and Sharma, D. (2007) Modeling the Effect of Screening of Unaware Infectives on the Spread of HIV Infection. Applied Mathematics and Computation, 184, 1053-1068. [Google Scholar] [CrossRef] 
[5] Kaur, N., Ghosh, M. and Bhatia, S.S. (2012) Modeling the Spread of HIV in a Stage Structured Population: Effect of Awareness. International Journal of Biomathematics, 5, 129-146. [Google Scholar] [CrossRef] 
[6] Hasminskii, R.Z. (1980) Stochastic Stability of Differential Equations. The Netherlands: Sijthoff and Noordhoff, Alphen aan den Rijn.
[7] Higham, D.J. (2001) An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations. SIAM Review, 43, 525-546. [Google Scholar] [CrossRef] 
[8] Zhao, Y. and Jiang, D.Q. (2014) The Threshold of a Stochastic SIS Epidemic Model with Vaccination. Applied Mathematics Computation, 243, 718-727. [Google Scholar] [CrossRef] 
[9] Rathinasamy, A., Chinnaduraia, M. and Athithanc, S. (2021) Analysis of Exact Solution of Stochastic Sex-Structured HIV/AIDS Epidemic Model with Effect of Screening of Infective. Mathematics and Computers in Simulation, 179, 213-237. [Google Scholar] [CrossRef] [PubMed]
[10] Mao, X. (2008) Stochastic Differential Equations and Applications. 2nd Edition. Horwood, Chichester. [Google Scholar] [CrossRef] 
[11] Has’minskii, R. (1980) Stochastic Stability of Differential Equations. Sijthoff and Noordhoff, Alphen aan den Rijn.
[12] Kloeden, P.E. and Eckhard, P. (1995) Numerical Solution of Stochastic Differential Equations. Society for Industrial and Applied Mathematics, Matthias Gelbrich and Werner Romisch.

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