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

doi:10.1007/s10473-020-0617-4

Acta mathematica scientia,Series B ›› 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

Qixing HAN^1,2, Daqing JIANG^3,4

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.

Abstract

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

CLC Number:

92D30

Qixing HAN, Daqing JIANG. DYNAMIC FOR A STOCHASTIC MULTI-GROUP AIDS MODEL WITH SATURATED INCIDENCE RATE[J].Acta mathematica scientia,Series B, 2020, 40(6): 1883-1896.

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References

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

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