Global dynamics of a staged-progression model for HIV/AIDS with amelioration

Nonlinear Analysis: Real World Applications

Volumn 12, Issue 5, 2011, Pages 2529-2540

  Guo, Hongbin ^a   Li, Michael Y ^b  

^a YORK UNIVERSITY   (Canada)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Amelioration; Basic reproduction number; Global stability; HIV AIDS; Lyapunov functions; Staged progression

Indexed keywords

AMELIORATION; BASIC REPRODUCTION NUMBER; GLOBAL STABILITY; HIV/AIDS; LYAPUNOV; STAGED PROGRESSION;

DIFFERENTIAL EQUATIONS; LYAPUNOV FUNCTIONS; MATHEMATICAL MODELS;

DISEASES;

EID: 79957910156     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2011.02.021     Document Type: Article

References (33)

1. L. Wang, and M.Y. Li Mathematical analysis of the global dynamics of a model for HIV infection of CD4+T cells Math. Biosci. 200 2006 44 57
2. F. Wasserstein-Robbins A mathematical model of HIV infection: simulating T4, T8, macrophages, antibody, and virus via specific anti-HIV response in the presence of adaptation and tropism Bull. Math. Biol. 72 2010 1208 1253
3. A.M. Elaiw Global properties of a class of HIV models Nonlinear Anal. RWA 11 2010 2253 2263
4. K. Wang, A. Fan, and A. Torres Global properties of an improved hepatitis B virus model Nonlinear Anal. RWA 11 2010 3131 3138
5. I. Vieira, R. Cheng, P. Harper, and V. de Senna Small world network models of the dynamics of HIV infection Ann. Oper. Res. 178 2010 173 200
6. R.M. Anderson, R.M. May, G.F. Medley, and A. Johnson A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causative agent of AIDS IMA J. Math. Appl. Med. Biol. 3 1986 229 263
7. Z. Feng, and H.R. Thieme Endemic model with arbitrarily distributed periods of infection I. General theory SIAM J. Appl. Math. 61 2000 803 833 (Pubitemid 32672593)
8. A.B. Gumel, C.C. McCluskey, and P. van den Driessche Mathematical study of a staged progression HIV model with imperfect vaccine Bull. Math. Biol. 68 2006 2105 2128 (Pubitemid 44705861)
9. J.C. Hendriks, G.A. Satten, I.M. Longini, H.A. van Druten, P.T. Schellekens, R.A. Coutinho, and G.J. Gvan Griensven Use of immunological markers and continuous-time Markov models to estimate progression of HIV infection in homosexual men AIDS 10 1996 649 656 (Pubitemid 26162994)
10. H.W. Hethcote, J.W. Van Ark, and I.M. Longini Jr. A simulation model of AIDS in San Francisco: I. Model formulation and parameter estimation Math. Biosci. 106 1991 203 222
11. J.M. Hyman, J. Li, and E.A. Stanley The differential infectivity and staged progression models for the transmission of HIV Math. Biosci. 155 1999 77 109 (Pubitemid 129672419)
12. J.A. Jacquez, C.P. Simon, J. Koopman, L. Sattenspiel, and T. Perry Modelling and analyzing HIV transmission: the effect of contact patterns Math. Biosci. 92 1988 119 199 (Pubitemid 19046874)
13. X. Lin, H.W. Hethcote, and P. van den Driessche An epidemiological model for HIV/AIDS with proportional recruitment Math. Biosci. 118 1993 181 195
14. I.M. Longini, W.S. Clark, M. Haber, and R. Horsburgh The stages of HIV infection: waiting times and infection transmission probabilities C. Castillo-Chavez, Levin Shoemaker Mathematical and Statistical Approaches to AIDS Epidemiology Lecture Notes in Biomath. vol. 83 1989 Springer New York 111 137
15. C.C. McCluskey A model of HIV/AIDS with staged progression and amelioration Math. Biosci. 181 2003 1 16 (Pubitemid 35379443)
16. A. Perelson, and P. Nelson Mathematical analysis of HIV-1 dynamics in vivo SIAM Rev. 41 1999 3 44 (Pubitemid 129723746)
17. H.R. Thieme, and C. Castillo-Chavez How may infection-age dependent infectivity affect the dynamics of HIV/AIDS? SIAM J. Appl. Math. 53 1992 1447 1479
18. H. Guo, and M.Y. Li Global dynamics of a staged progression model with amelioration for infectious diseases J. Biol. Syst. 2 2008 154 168
19. H.W. Hethcote, and J.W. Van Ark Modeling HIV Transmission and AIDS in the United States Lecture Notes in Biomath. vol. 95 1992 Springer-Verlag
20. R.M. Anderson, and R.M. May Infectious Diseases of Humans: Dynamics and Control 1992 Oxford University Press Oxford
21. R 0 in models for infectious diseases in heterogeneous populations J. Math. Biol. 28 1990 365 382
22. P. van den Driessche, and J. Watmough Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission Math. Biosci. 180 2002 29 48 (Pubitemid 35304346)
23. J.P. LaSalle The Stability of Dynamical Systems Regional Conference Series in Applied Mathematics 1976 SIAM Philadelphia
24. H. Guo, and M.Y. Li Global dynamics of a staged progression model for infectious diseases Math. Biosci. Eng. 3 2006 513 525
25. M.Y. Li, J.R. Graef, L. Wang, and J. Karsai Global dynamics of a SEIR model with varying total population size Math. Biosci. 160 1999 191 213 (Pubitemid 29398860)
26. A. Iggidr, J. Mbang, G. Sallet, and J.J. Tewa Multi-compartment models Discrete Contin. Dyn. Syst. Supp. 2007 506 519
27. H.I. Freedman, and J.W.-H. So Global stability and persistence of simple food chains Math. Biosci. 76 1985 69 86
28. B.S. Goh Global stability in a class of preypredator models Bull. Math. Biol. 40 1978 525 533 (Pubitemid 8383403)
29. S.-B. Hsu Limiting behavior for competing species SIAM J. Appl. Math. 34 1978 760 763
30. V. Capasso Mathematical Structures of Epidemic Systems Lecture Notes in Biomath. vol. 97 1993 Springer-Verlag
31. H. Guo, M.Y. Li, and Z. Shuai Global stability of the endemic equilibrium of multigroup SIR epidemic model Canad. Appl. Math. Quart. 14 2006 259 284
32. A. Korobinikov, and P.K. Maini A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence Math. Biosci. Eng. 1 2004 57 60
33. R.A. Horn, and C.R. Johnson Topics in Matrix Analysis 1991 Cambridge University Press Cambridge