数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (6): 1883-1896.doi: 10.1007/s10473-020-0617-4

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DYNAMIC FOR A STOCHASTIC MULTI-GROUP AIDS MODEL WITH SATURATED INCIDENCE RATE

韩七星1,2, 蒋达清3,4   

  1. 1. School of Mathematics, Changchun Normal University, Changchun 130032, China;
    2. School of Mathematics, Jilin University, Changchun 130012, China;
    3. Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;
    4. College of Science, China University of Petroleum(East China), Qingdao 266580, China
  • 收稿日期:2019-06-05 修回日期:2020-07-28 出版日期:2020-12-25 发布日期:2020-12-30
  • 通讯作者: Daqing JIANG,E-mail:daqingjiang2010@hotmail.com E-mail:daqingjiang2010@hotmail.com
  • 作者简介:Qixing HAN,E-mail:hanqixing123@163.com
  • 基金资助:
    The work was supported by NSF of China (11801041, 11871473), Foudation of Jilin Province Science and Technology Development (20190201130JC), Scientific Rsearch Foundation of Jilin Provincial Education Department (JJKH20181172KJ, JJKH20190503KJ) and Natural Science Foundation of Changchun Normal University.

DYNAMIC FOR A STOCHASTIC MULTI-GROUP AIDS MODEL WITH SATURATED INCIDENCE RATE

Qixing HAN1,2, Daqing JIANG3,4   

  1. 1. School of Mathematics, Changchun Normal University, Changchun 130032, China;
    2. School of Mathematics, Jilin University, Changchun 130012, China;
    3. Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;
    4. College of Science, China University of Petroleum(East China), Qingdao 266580, China
  • Received:2019-06-05 Revised:2020-07-28 Online:2020-12-25 Published:2020-12-30
  • Contact: Daqing JIANG,E-mail:daqingjiang2010@hotmail.com E-mail:daqingjiang2010@hotmail.com
  • Supported by:
    The work was supported by NSF of China (11801041, 11871473), Foudation of Jilin Province Science and Technology Development (20190201130JC), Scientific Rsearch Foundation of Jilin Provincial Education Department (JJKH20181172KJ, JJKH20190503KJ) and Natural Science Foundation of Changchun Normal University.

摘要: In this paper, a stochastic multi-group AIDS model with saturated incidence rate is studied. We prove that the system is persistent in the mean under some parametric restrictions. We also obtain the sufficient condition for the existence of the ergodic stationary distribution of the system by constructing a suitable Lyapunov function. Our results indicate that the existence of ergodic stationary distribution does not rely on the interior equilibrium of the corresponding deterministic system, which greatly improves upon previous results.

关键词: multi-group AIDS model, Lyapunov function, stationary distribution, persistence in the mean

Abstract: In this paper, a stochastic multi-group AIDS model with saturated incidence rate is studied. We prove that the system is persistent in the mean under some parametric restrictions. We also obtain the sufficient condition for the existence of the ergodic stationary distribution of the system by constructing a suitable Lyapunov function. Our results indicate that the existence of ergodic stationary distribution does not rely on the interior equilibrium of the corresponding deterministic system, which greatly improves upon previous results.

Key words: multi-group AIDS model, Lyapunov function, stationary distribution, persistence in the mean

中图分类号: 

  • 92D30