Asymptotic properties of an HIV/AIDS model with a time delay

Journal of Mathematical Analysis and Applications

Volumn 330, Issue 2, 2007, Pages 916-933

  Mukandavire, Z ^a   Garira, W ^a   Chiyaka, C ^a  

^a NATIONAL UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Zimbabwe)

Author keywords

Delay; Global stability; HIV AIDS model; Incubation; Lyapunov functional; Persistence

Indexed keywords

EID: 33847642648     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.07.102     Document Type: Article

References (40)

1. Z. Mukandavire, W. Garira, HIV/AIDS model for assessing the effects of prophylactic sterilizing vaccines, condoms and treatment with amelioration, J. Biol. Syst. 14 (3) (2006), in press
2. Genik L., and van den Driessche P. An epidemic model with recruitment-death demographics and discrete delays. Fields Inst. Commun. 21 (1991) 238-249
3. Hyman J.M., and Stanley E.A. Using mathematical models to understand the AIDS epidemic. Math. Biosci. 90 (1998) 415-473
4. May R.M., and Anderson R.M. The transmission dynamics of Human Immunodeficiency Virus (HIV). Philosophical Trans. Roy. Soc. London Ser. B Biological Sciences (1998) 565-607
5. Alfonseca M., Martinez-Bravo M.T., and Torrea J.L. Mathematical models for the analysis of Hepatitis B and AIDS epidemics. Simulation, 0037-5497/00 74 (2000) 219-226 (Simulation Councils, Technical Article)
6. Luboobi L.S. Mathematical models for the dynamics of the AIDS epidemic. In: Patel M.S., and Noke S. (Eds). Biometry for Development (1991), ICIPE, Science Press, Nairobi 76-83
7. J.Y.T. Mugisha, The mathematical dynamics of HIV/AIDS epidemic in age-structured population, in: V.G. Masanja (Ed.), Proceedings of XI SAMSA Symposium on the Potential of Mathematical Modeling of Problems from the SAMSA Region, 1997, pp. 8-23
8. Srinivasa A.S.R. Mathematical modelling of AIDS epidemic in India. Current Science 84 9 (2003) 1193-1197
9. Hsu Schmitz S.F. Effects of genetic heterogeneity on HIV transmission in homosexual populations. In: Castillo-Chavez C., Blower S., van den Driessche P., Kirschner D., and Yakubu A.-A. (Eds). Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods and Theory (2002), Springer 45-260
10. Hsu Schmitz S.F. A mathematical model of HIV transmission in homosexuals with genetic heterogeneity. J. Theor. Med. 2 (2000) 285-296
11. Brauer F. Age of infection in epidemiology models. Electron. J. Differential Equations (Conf.) 12 (2005) 29-37
12. Arino J., and van den Driessche P. Time delays in epidemic models: Modeling and numerical aspects. http://www.math.mcmaster.ca/arino/papers/ArinoVdD2003-marrakech.pdf accessed 2005
13. Busenberg S., and Cooke K. Vertically Transmitted Diseases Models and Dynamics. Biomathematics vol. 23 (1993), Springer
14. + T-cells. Math. Biosci. 165 (2000) 27-39
15. Dixit N.M., and Perelson A.S. Complex patterns of viral load decay under antiretroviral therapy: Influence of pharmacokinetics and intracellular delay. J. Theor. Biol. 226 (2003) 95-109
16. C.T.H. Baker, G.A. Bocharov, F.A. Rihan, A report on the use of delay differential equations in numerical modelling in the biosciences, Numerical Analysis Report 343 (1999)
17. Thieme H.R. Global Asymptotic Stability in Epidemic Models. Lecture Notes in Math. vol. 1017 (1983), Springer
18. Beretta E., and Kuang Y. Modeling and analysis of marine bacteriophage infection with latency period. Nonl. Anal. B 2 1 (2001) 35-74
19. Berreta E., and Kuang Y. Geometric stability switch criteria in delay differential systems with delay dependent parameters. SIAM J. Math. Anal. 33 5 (2002) 1144-1165
20. Kuang Y., and So J.W.-H. Analysis of a two-stage population model with space-limited recruitment. SIAM J. Appl. Math. 55 6 (1995) 1675-1696
21. Kuang Y. Delay Differential Equations with Applications in Population Biology (1993), Academic Press, New York
22. Wendi W., and Zhien M. Global dynamics of an epidemic model with time delay. Nonlinear Anal. Real World Appl. 3 (2002) 365-373
23. Kyrychko Y.N., and Blyuss K.B. Global properties of a delayed SIR model with temporary immunity and nonlinear incidence rate. Nonlinear Anal. Real World Appl. 6 (2005) 495-507
24. Ma W., and Takeuchi Y. Asymptotic properties of a delayed SIR epidemic model with density dependent birth rate. Discrete Contin. Dyn. Syst. Ser. B 4 3 (2004) 671-678
25. Qui Z., Yu J., and Zou Y. The asymptotic behaviour of a chemostat model. Discrete Contin. Dyn. Syst. Ser. B 4 3 (2004) 721-727
26. Brauer F., and Castillo-Chavez C. Mathematical Models in Population Biology and Epidemiology (2001), Springer
27. 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28 (1990) 365-382
28. van den Driessche P., and Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180 (2002) 29-48
29. May R.M., and Anderson R.M. Transmission dynamics of HIV infection. Nature 326 (1987) 137-142
30. Kribs-Zaleta C.M., and Velasco-Hernandez J.X. A simple vaccination model with multiple endemic states. Math. Biosci. 164 (2000) 183-201
31. Kribs-Zaleta C.M. Structured models for heterosexual disease transmission. Math. Biosci. 160 (1999) 83
32. Thieme H.R. Uniform persistence and permanence for nonautonomous semiflows in population biology. Math. Biosci. 166 (2000) 173-201
33. Thieme H.R. Persistence under relaxed point-dissipativity (with application to an endemic model). SIAM J. Math. Anal. 24 2 (1993) 405-435
34. Jordan D.W., and Smith P. Nonlinear Ordinary Differential Equations (1999), Oxford University Press pp. 348-388
35. USAID. Country profile. http://www.usaid.gov accessed 2005
36. Ministry Of Health And Child Welfare Zimbabwe. CDC Zimbabwe and UNAIDS (2003), Zimbabwe National HIV and AIDS Estimates
37. Hyman J.M., Li J., and Stanley E.A. The differential infectivity and staged progression models for the transmission of HIV. Math. Biosci. 155 (1999) 77-109
38. Anderson R.M., Gupta S., and May R.M. Potential of community-wide chemotherapy or immunotherapy to control the spread of HIV-1. Nature 350 (1991) 350-356
39. Hsu Schmitz S.F. Effects of treatment or/and vaccination on HIV transmission in homosexuals with genetic heterogeneity. Math. Biosci. 167 (2000) 1-18
40. Baggaley R.F., Ferguson N.M., and Garnett G.P. The epidemiological impact of antiretroviral use predicted by mathematical models: A review. Emerging Themes in Epidemiology (2005). http://www.biomedcentral.com/1742-7622/2/9