Global stability for an HIV/AIDS epidemic model with different latent stages and treatment

Applied Mathematical Modelling

Volumn 37, Issue 3, 2013, Pages 1480-1489

  Huo, Hai Feng ^a   Feng, Li Xiang ^a  

^a LANZHOU UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Basic reproduction number; Equilibrium; Global stability; HIV AIDS

Indexed keywords

ANALYTICAL RESULTS; BASIC REPRODUCTION NUMBER; DISEASE-FREE EQUILIBRIUM; ENDEMIC EQUILIBRIUM; EPIDEMIC MODELS; GLOBAL DYNAMICS; GLOBAL STABILITY; GLOBALLY ASYMPTOTICALLY STABLE; HIV/AIDS; INFECTIOUS DISEASE; MATHEMATICAL ANALYSIS;

EPIDEMIOLOGY; PHASE EQUILIBRIA;

DISEASES;

EID: 84870243997     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2012.04.013     Document Type: Article

References (25)

1. HIV & AIDS in South Africa. Available at: http://www.avert.org/aidssouthafrica.htm.
2. UNAIDS/WHO 2007 AIDS epidemic update, December 2007.
3. Samanta G.P. Permanence and extinction of a nonautonomous HIV/AIDS epidemic model with distributed time delay. Nonlinear Anal. Real World Appl. 2011, 12:1163-1177.
4. Centers for disease control and prevention, HIV and its transmission, Divisions of HIV/AIDS prevention, 2003.
5. Morgan D., Mahe C., Mayanja B., Okongo J.M., Lubega R., Whitworth J.A. HIV-1 infection in rural Africa: is there a difference in median time to AIDS and survival compared with that in industrialized countries?. AIDS 2002, 16:597-632.
6. Stoddart C.A., Reyes R.A. Models of HIV-1 disease: a review of current status. Drug Discov. Today: Disease Models 2006, 3:113-119.
7. Anderson R.M. The role of mathematical models in the study of HIV transmission and the epidemiology of AIDS. J. AIDS 1988, 1:241-256.
8. Anderson R.M., Medly G.F., May R.M., Johnson A.M. A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causative agent of AIDS. IMA J. Math. Appl. Med. Biol. 1986, 3:229-263.
9. May R.M., Anderson R.M. Transmission dynamics of HIV infection. Nature 1987, 326:137-142.
10. Bachar M., Dorfmayr A. HIV treatment models with time delay. C.R. Biologies 2004, 327:983-994.
11. Blower S. Calculating the consequences: HAART and risky sex. AIDS 2001, 15:1309-1310.
12. Cai L.M., Li X., Ghosh M., Guo B. Stability of an HIV/AIDS epidemic model with treatment. J. Comput. Appl. Math. 2009, 229:313-323.
13. Nyabadza F., Mukandavire Z., Hove-Musekwa S.D. Modelling the HIV/AIDS epidemic trends in South Africa: insights from a simple mathematical model. Nonlinear Anal. Real World Appl. 2011, 12:2091-2104.
14. Xu R. Global stability of an HIV-1 infection model with saturation infection and intracellular delay. J. Math. Anal. Appl. 2011, 375:75-81.
15. Song X., Neumann Avidan U. Global stability and periodic solution of the viral dynamics. J. Math. Anal. Appl. 2007, 329:281-297.
16. Wang K., Wang W., Pang H., Liu X. Complex dynamic behavior in a viral model with delayed immune response. Physica D 2007, 226:197-208.
17. Mukandavire Z., Garira W., Tchuenche J.M. Modelling effects of public health educational campaigns on HIV/AIDS transmission dynamics. Appl. Math. Model. 2009, 33:2084-2095.
18. Song X., Zhou X., Zhao X. Properties of stability and Hopf bifurcation for a HIV infection model with time delay. Appl. Math. Model. 2010, 34:1511-1523.
19. Zhang T., Jia M., Luo H., Zhou Y., Wang N. Study on a HIV/AIDS model with application to Yunnan province, China. Appl. Math. Model. 2011, 35:4379-4392.
20. Hethcote H.W., Van Ark J.W. Modelling HIV transmission and AIDS in the United States. Lecture Notes in Biomathematics 1992, vol. 95. Springer, Berlin.
21. van den Driessche P., Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 2002, 180:29-48.
22. Lakshmikantham V., Leela S., Martynyuk A.A. Stability Analysis of Nonlinear Systems 1989, Marcel Dekker Inc., New York.
23. Smith R.J., Blower S.M. Could disease modifying HIV vaccine cause population-level pervasity?. Lancet Infect. Dis. 2004, 4:636-639.
24. Li J., Yang Y., Zhou Y. Global stability of an epidemic model with latent stage and vaccination. Nonlinear Anal. Real World Appl. 2011, 12:2163-2173.
25. LaSalle J.P. The stability of dynamical systems. Regional Conference Series in Applied Mathematics 1976, SIAM, Philadelphia.