[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 |