Free Access
Issue
Math. Model. Nat. Phenom.
Volume 5, Number 6, 2010
Ecology (Part 2)
Page(s) 70 - 95
DOI https://doi.org/10.1051/mmnp/20105604
Published online 08 April 2010
  1. R. M. Anderson. The role of mathematical models in the study of HIV transmission and the epidemiology of AIDS. J. AIDS, 1 (1988), 241–256. [Google Scholar]
  2. R. M. AndersonR. M. May. Population Biology of Infectious Diseases. Part I. Nature, 280 (1979), 361–367. [CrossRef] [PubMed] [Google Scholar]
  3. R. M. Anderson, G. F. Medly, R. M. MayA. M. 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. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  4. M. BacharA. Dorfmayr. HIV treatment models with time delay. C.R. Biologies, 327 (2004), 983–994. [CrossRef] [Google Scholar]
  5. BBC News (BBC). HIV reduces infection. September 2009, http://news.bbc.co.uk/2/hi/health/8272113.stm. [Google Scholar]
  6. S. Blower. Calculating the consequences: HAART and risky sex. AIDS, 15 (2001), 1309–1310. [CrossRef] [PubMed] [Google Scholar]
  7. F. Brauer. Models for the disease with vertical transmission and nonlinear population dynamics. Math. Biosci., 128 (1995), 13–24. [CrossRef] [PubMed] [Google Scholar]
  8. S. Busenberg, K. Cooke. Vertically transmitted diseases. Springer, Berlin, 1993. [Google Scholar]
  9. L. M. Cai, X. Li, M. GhoshB. Guo. Stability of an HIV/AIDS epidemic model with treatment. J. Comput. Appl. Math., 229 (2009), 313–323. [CrossRef] [MathSciNet] [Google Scholar]
  10. V. Capasso. Mathematical structures of epidemic systems, Lectures Notes in Biomathematics, Vol. 97. Springer-Verlag, Berlin, 1993. [Google Scholar]
  11. Centers for Disease Control and Prevention. HIV and its transmission. Divisions of HIV/AIDS Prevention, 2003. [Google Scholar]
  12. C. Connell McCluskey. A model of HIV/AIDS with staged progression and amelioration. Math. Biosci., 181 (2003), 1–16. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  13. R. V. CulshawS. Ruan. A delay-differential equation model of HIV infection of CD4 + T-cells. Math. Biosci., 165 (2000), 27–39. [CrossRef] [PubMed] [Google Scholar]
  14. J. M. Cushing. Integrodifferential equations and delay models in population dynamics. Spring, Heidelberg, 1977. [Google Scholar]
  15. O. Diekmann, J. A. P. Heesterbeek. Mathematical epidemiology of infectious diseases: model building, analysis, and interpretation. John Wiley and Sons Ltd., Chichester, New York, 2000. [Google Scholar]
  16. E. H. ElbashaA. B. Gumel. Theoretical assessment of public health impact of imperfect prophylactic HIV-1 vaccines with therapeutic benefits. Bull. Math. Biol., 68 (2006), 577–614. [CrossRef] [PubMed] [Google Scholar]
  17. J. EsparzaS. Osmanov. HIV vaccine: a global perspective. Curr. Mol. Med., 3 (2003), 183–193. [CrossRef] [PubMed] [Google Scholar]
  18. K. Gopalsamy. Stability and oscillations in delay-differential equations of population dynamics. Kluwer, Dordrecht, 1992. [Google Scholar]
  19. D. Greenhalgh, M. DoyleF. Lewis. A mathematical treatment of AIDS and condom use . IMA J. Math. Appl. Med. Biol., 18 (2001), 225–262. [CrossRef] [PubMed] [Google Scholar]
  20. A. B. Gumel, C. C. McCluskeyP. van den Driessche. Mathematical study of a staged-progression HIV model with imperfect vaccine. Bull. Math. Biol., 68 (2006), 2105–2128. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  21. J. K. Hale, S. M. V. Lunel. Introduction to functional differential equations. Springer-Verlag, New York, 1993. [Google Scholar]
  22. A. V. M. Herz, S. Bonhoeffer, R. M. Anderson, R. M. MayM. A. Nowak. Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay. Proc. Nat. Acad. Sci. USA, 93 (1996), 7247–7251. [CrossRef] [Google Scholar]
  23. G. HerzongR. Redheffer. Nonautonomous SEIRS and Thron models for epidemiology and cell biology. Nonlinear Anal.: RWA, 5 (2004), 33–44. [CrossRef] [Google Scholar]
  24. H. W. Hethcote, J. W. Van Ark. Modelling HIV transmission and AIDS in the United States, in: Lect. Notes Biomath., vol. 95. Springer, Berlin, 1992. [Google Scholar]
  25. Y. H. HsiehC. H. Chen. Modelling the social dynamics of a sex industry: Its implications for spread of HIV/AIDS. Bull. Math. Biol., 66 (2004), 143–166. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  26. Y. H. HsiehK. Cooke. Behaviour change and treatment of core groups: its effect on the spread of HIV/AIDS. IMA J. Math. Appl. Med. Biol., 17 (2000), 213–241. [CrossRef] [PubMed] [Google Scholar]
  27. D. W. Jordan, P. Smith. Nonlinear ordinary differential equations. Oxford University Press, New York, 2004. [Google Scholar]
  28. W. O. KermackA. G. Mckendrick. Contributions to the mathematical theory of epidemics. Part I. Proc. R. Soc. A, 115 (1927), No. 5, 700–721. [CrossRef] [Google Scholar]
  29. Y. Kuang. Delay-differential equations with applications in population dynamics. Academic Press, New York, 1993. [Google Scholar]
  30. P. D. LeenheerH. L. Smith. Virus dynamics: a global analysis. SIAM. J. Appl. Math., 63 (2003), 1313–1327. [CrossRef] [MathSciNet] [Google Scholar]
  31. M. Y. Li, H. L. SmithL. Wang. Global dynamics of an SEIR epidemic with vertical transmission. SIAM. J. Appl. Math., 62 (2001), No. 1, 58–69. [CrossRef] [MathSciNet] [Google Scholar]
  32. M. C. I. Lipman, R. W. Baker, M. A. Johnson. An atlas of differential diagnosis in HIV disease. CRC Press-Parthenon Publishers, pp. 22-27, 2003. [Google Scholar]
  33. Z. Ma, Y. Zhou, W. Wang, Z. Jin. Mathematical modelling and research of epidemic dynamical systems. Science Press, Beijing, 2004. [Google Scholar]
  34. R. M. MayR. M. Anderson. Transmission dynamics of HIV infection. Nature, 326 (1987), 137–142. [CrossRef] [PubMed] [Google Scholar]
  35. Medical News Today, dated 9th February, 2007, East Sussex, TN 40 9BA, United Kingdom. [Google Scholar]
  36. X. Meng, L. ChenH. Cheng. Two profitless delays for the SEIRS epidemic disease model with nonlinear incidence and pulse vaccination. Appl. Math. Comput., 186 (2007), 516–529. [CrossRef] [MathSciNet] [Google Scholar]
  37. R. Naresh, A. TripathiS. Omar. Modelling the spread of AIDS epidemic with vertical transmission. Appl. Math. Comput., 178 (2006), 262–272. [MathSciNet] [Google Scholar]
  38. A. S. PerelsonP. W. Nelson. Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev., 41 (1999), No. 1, 3–44. [CrossRef] [MathSciNet] [Google Scholar]
  39. A. S. Perelson, A. U. Neumann, M. Markowitz, J. M. LeonardD. D. Ho. HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time. Science, 271 (1996), 1582–1586. [CrossRef] [PubMed] [Google Scholar]
  40. G. P. Samanta. Dynamic behaviour for a nonautonomous heroin epidemic model with time delay. J. Appl. Math. Comput., 2009, DOI 10.1007/s12190-009-0349-z. [Google Scholar]
  41. J. ShiverE. Emini. Recent advances in the development of HIV-1 vaccines using replication-incompetant adenovirus vectors. Ann. Rev. Med., 55 (2004), 355–372. [CrossRef] [Google Scholar]
  42. C. A. StoddartR. A. Reyes. Models of HIV-1 disease: A review of current status. Drug Discovery Today: Disease Models, 3 (2006), No. 1, 113–119. [CrossRef] [Google Scholar]
  43. Z. TengL. Chen. The positive periodic solutions of periodic Kolmogorov type systems with delays. Acta Math. Appl. Sin., 22 (1999), 446–456. [Google Scholar]
  44. H. R. Thieme. Uniform weak implies uniform strong persistence for non-autonomous semiflows. Proc. Am. Math. Soci., 127 (1999), 2395–2403. [CrossRef] [Google Scholar]
  45. H. R. Thieme. Uniform persistence and permanence for nonautonomous semiflows in population biology. Math. Biosci., 166 (2000), 173–201. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  46. UNAIDS. 2007 AIDS epidemic update. WHO, December 2007. [Google Scholar]
  47. L. WangM. Y. Li. Mathematical analysis of the global dynamics of a model for HIV infection of CD4+T-cells. Math. Biosci., 200 (2006), 44–57. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  48. K. Wang, W. WangX. Liu. Viral infection model with periodic lytic immune response. Chaos Solitons Fractals, 28 (2006), No. 1, 90–99. [CrossRef] [MathSciNet] [Google Scholar]
  49. Wikipedia. HIV vaccine. September, 2009, http://en.wikipedia.org/wiki/HIV_vaccine. [Google Scholar]
  50. T. ZhangZ. Teng. On a nonautonomous SEIRS model in epidemiology. Bull. Math. Biol., 69 (2007), 2537–2559. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  51. T. ZhangZ. Teng. Permanence and extinction for a nonautonomous SIRS epidemic model with time delay. Appl. Math. Model., 33 (2009), 1058–1071. [CrossRef] [MathSciNet] [Google Scholar]
  52. R. M. Zinkernagel. The challenges of an HIV vaccine enterprise. Science, 303 (2004), 1294–1297. [CrossRef] [Google Scholar]

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