Asymptotic behavior of a stochastic HIV model with Beddington–DeAngelis functional response

Advances in Difference Equations

Juan Zhao¹  Junxing Zhu¹  Xiaoli Ren²  Suxia Wang² 

[1] College of Computer Meteorology and Oceanography, National University of Defense Technology, Changsha, China;College of Computer Meteorology and Oceanography, National University of Defense Technology, Changsha, China;College of Computer Science and Technology, National University of Defense Technology, Changsha, China;

关键词: Stochastic HIV model;    Itô’s formula;    Asymptotic behavior;    Lyapunov;    Beddington–DeAngelis functional;   

DOI  :  10.1186/s13662-020-02911-7

来源: Springer

【 摘 要 】

In this paper, we study the dynamics property of a stochastic HIV model with Beddington–DeAngelis functional response. It has a unique uninfected steady state. We prove that the model has a unique global positive solution. Furthermore, if the basic reproductive number is not larger than 1, the asymptotic behavior of the solution is stochastically stable. Otherwise, it fluctuates randomly around the infected steady state of the corresponding deterministic HIV model. Finally, some numerical simulations are carried out to verify our results.

【 授权许可】

CC BY