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

doi:10.1007/s10473-020-0617-4

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

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

韩七星^1,2, 蒋达清^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

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 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.

摘要/Abstract

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

韩七星, 蒋达清. DYNAMIC FOR A STOCHASTIC MULTI-GROUP AIDS MODEL WITH SATURATED INCIDENCE RATE[J]. 数学物理学报(英文版), 2020, 40(6): 1883-1896.

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.

参考文献

[1] UNAIDS/WHO, 2007 AIDS epidemic update, December 2007
[2] Blythe S P, Anderson R M. Distributed incubation and infections periods in models of transmission dynamics of human immunodeficiency virus (HIV). Ima J Math Appl Med Biol, 1988, 5(1):1-19
[3] Hyman J, Li J. An intuitive formulation for the reproductive number for the spread of diseases in heterogeneous populations. Math Biosci, 2000, 167(1):65-86
[4] Mukandavire Z, Garira W, Chiyaka C. Asymptotic properties of an HIV/AIDS model with a time delay. J Math Anal Appl, 2007, 330(2):916-933
[5] Huo H F, Feng L X. Global stability for an HIV/AIDS epidemic model with different latent stages and treatment. Appl Math Model, 2013, 37(3):1480-1489
[6] Gomes M G M, White L J, Medley G F. The reinfection threshold. J Theor Biol, 2005, 236(1):111-113
[7] Wang W, Ruan S. Bifurcation in epidemic model with constant removal rate infectives. J Math Anal Appl, 2004, 291(2):775-793
[8] Hyman J, Li J, Ann Stanley E. The differential infectivity and staged progression models for the transmission of HIV. Math Biosci, 1999, 155(2):77-109
[9] Ma Z, Liu J, Li J. Stability analysis for differential infectivity epidemic models. Nonlinear Anal Real World Appl, 2003, 4(5):841-856
[10] Capasso V, Serio G. A generalization of the Kermack-McKendrick deterministic epidemic model. Math Biosci, 1978, 42(1/2):43-61
[11] Wang W, Cai Y, Ding Z, et al. A stochastic differential equation SIS epidemic model incorporating OrnsteinUhlenbeck process. Phys A, 2018, 509:921-936
[12] Cai Y, Kang Y, Banerjee M, et al. A stochastic SIRS epidemic model with infectious force under intervention strategies. J Differential Equations, 2015, 259(12):7463-7502
[13] Fu J, Jiang, D, Shi N, et al. Qualitative analysis of a stochastic ratio-dependent Holling-Tanner system. Acta Math Sci, 2018, 38B(2):429-440
[14] Mao X. Stationary distribution of stochastic population systems. Syst Control Lett, 2011, 60(6):398-405
[15] Hu G, Liu M, Wang K. The asymptotic behaviours of an epidemic model with two correlated stochastic perturbations. Appl Math Comput, 2012, 218(21):10520-10532
[16] Settati A, Lahrouz A. Stationary distribution of stochastic population systems under regime switching. Appl Math Comput, 2014, 244:235-243
[17] Gray A, Greenhalgh D, Hu L, et al. A Stochastic differential equation SIS epidemic model. SIAM J Appl Math, 2011, 71(3):876-902
[18] Dalal N, Greenhalgh D, Mao X. A stochastic model of AIDS and condom use. J Math Anal Appl, 2007, 325(1):36-53
[19] Ding Y, Xu M, Hu L. Asymptotic behavior and stability of a stochastic model for AIDS transmission. Appl Math Comput, 2008, 204(1):99-108
[20] Liu H, Yang Q, Jiang D. The asymptotic behavior of stochastically perturbed DI SIR epidemic models with saturated incidences. Automatica, 2012, 48(5):820-825
[21] Liu Q, Jiang D, Hayat T, et al. Dynamical behavior of stochastic multigroup S-DI-A epidemic models for the transmission of HIV. J Franklin Inst, 2018, 355(13):5830-5865
[22] Mao X. Stochastic Differential Equations and Their Applications. Chichester:Horwood, 1997
[23] Gard T. Introduction to Stochastic Differential Equations. New York:Marcel Dekker, 1988
[24] Khasminskii R. Stochastic Stability of Differential Equations. 2nd ed. Berlin Heidelberg:Springer-Verlag, 2012
[25] Zhao Y, Jiang D. The threshold of a stochastic SIS epidemic model with vaccination. Appl Math Comput, 2014, 243:718-727
[26] Higham D. An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev, 2001, 43(3):525-546

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

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

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	刘丽雅, 蒋达清, Tasawar HAYAT, Bashir AHMAD. DYNAMICS OF A HEPATITIS B MODEL WITH SATURATED INCIDENCE[J]. 数学物理学报(英文版), 2018, 38(6): 1731-1750.
[2]	付静, 蒋达清, 史宁中, Tasawar HAYAT, Ahmed ALSAEDI. QUALITATIVE ANALYSIS OF A STOCHASTIC RATIO-DEPENDENT HOLLING-TANNER SYSTEM[J]. 数学物理学报(英文版), 2018, 38(2): 429-440.
[3]	刘群, 蒋达清, 史宁中, Tasawar HAYAT, Ahmed ALSAEDI. DYNAMICAL BEHAVIOR OF A STOCHASTIC HBV INFECTION MODEL WITH LOGISTIC HEPATOCYTE GROWTH[J]. 数学物理学报(英文版), 2017, 37(4): 927-940.
[4]	R. AGARWAL, S. HRISTOVA, P. KOPANOV, D. O'REGAN. IMPULSIVE DIFFERENTIAL EQUATIONS WITH GAMMA DISTRIBUTED MOMENTS OF IMPULSES AND P-MOMENT EXPONENTIAL STABILITY[J]. 数学物理学报(英文版), 2017, 37(4): 985-997.
[5]	Alexander ALEKSANDROV, Elena ALEKSANDROVA, Alexey ZHABKO, 陈阳舟. PARTIAL STABILITY ANALYSIS OF SOME CLASSES OF NONLINEAR SYSTEMS[J]. 数学物理学报(英文版), 2017, 37(2): 329-341.
[6]	Yoshiaki MUROYA, Eleonora MESSINA, Elvira RUSSO, Antonia VECCHIO. COEXISTENCE FOR MULTIPLE LARGEST REPRODUCTION RATIOS OF A MULTI-STRAIN SIS EPIDEMIC MODEL[J]. 数学物理学报(英文版), 2016, 36(5): 1524-1530.
[7]	M. YOUSEFNEZHAD, S. A. MOHAMMADI. STABILITY OF A PREDATOR-PREY SYSTEM WITH PREY TAXIS IN A GENERAL CLASS OF FUNCTIONAL RESPONSES[J]. 数学物理学报(英文版), 2016, 36(1): 62-72.
[8]	M. SYED ALI. STOCHASTIC STABILITY OF UNCERTAIN RECURRENT NEURAL NETWORKS WITH MARKOVIAN JUMPING PARAMETERS[J]. 数学物理学报(英文版), 2015, 35(5): 1122-1136.
[9]	Yoshiaki MUROYA, Huaixing LI, Toshikazu KUNIYA. ON GLOBAL STABILITY OF A NONRESIDENT COMPUTER VIRUS MODEL[J]. 数学物理学报(英文版), 2014, 34(5): 1427-1445.
[10]	Yoshiaki MUROYA, Yoichi ENATSU, Toshikazu KUNIYA. GLOBAL STABILITY OF EXTENDED MULTI-GROUP SIR EPIDEMIC MODELS WITH PATCHES THROUGH MIGRATION AND CROSS PATCH INFECTION[J]. 数学物理学报(英文版), 2013, 33(2): 341-361.
[11]	Yoichi Enatsu, Yukihiko Nakata, Yoshiaki Muroya. GLOBAL STABILITY OF SIRS EPIDEMIC MODELS WITH A CLASS OF NONLINEAR INCIDENCE RATES AND DISTRIBUTED DELAYS[J]. 数学物理学报(英文版), 2012, 32(3): 851-865.
[12]	叶俊. QUASI-STATIONARY DISTRIBUTIONS FOR THE RADIAL ORNSTEIN-UHLENBECK PROCESSES[J]. 数学物理学报(英文版), 2008, 28(3): 513-522.
[13]	张瑜; 孙继涛. EVENTUAL STABILITY OF IMPULSIVE DIFFERENTIAL SYSTEMS[J]. 数学物理学报(英文版), 2007, 27(2): 373-380.
[14]	靳祯; 马知恩; 韩茂安. GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DELAYS[J]. 数学物理学报(英文版), 2006, 26(2): 291-306.
[15]	徐瑞, 陈兰荪,M.A.J. Chaplain. GLOBAL ASYMPTOTIC STABILITY IN N-SPECIES NONAUTONOMOUS LOTKA-VOLTERRACOMPETITIVE SYSTEMS WITH DELAYS[J]. 数学物理学报(英文版), 2003, 23(2): 208-.