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] [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. [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. [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. [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. [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. [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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.