Abstract
Human immunodeficiency virus and acquired immune deficiency syndrome (HIV/AIDS) is pandemic. It has affected nearly 60 million people since the detection of the disease in 1981 to date. In this paper basic deterministic HIV/AIDS model with mass action incidence function are developed. Stability analysis is carried out. And the disease free equilibrium of the basic model was found to be locally asymptotically stable whenever the threshold parameter (RO) value is less than one, and unstable otherwise. The model is extended by introducing two optimal control strategies namely, CD4 counts and treatment for the infective using optimal control theory. Numerical simulation was carried out in order to illustrate the analytic results.
REFERENCES
- 1.http//www.statistics-hiv/aids.com/. Accessed in November 2013.
- 2.http://www.pedaids.org/page/-/uploads/resources/GlobalStats_5.pdf. Accessed in November 2013.
- 3.Marchant D., Neil S. J. and McKnight A., Journal of General Virology 87, 411–418 (2006). 10.1099/vir.0.81391-0 [DOI] [PubMed] [Google Scholar]
- 4.Blayneh K. W., Gumel A. B., Lenhart S. and Clayton T., Bulletin of Mathematical Biology 72, 1006–1028 (2010). 10.1007/s11538-009-9480-0 [DOI] [PubMed] [Google Scholar]
- 5.Castilho C.. Electronic Journal of Differential Equations 125, 1–11 (2006). [Google Scholar]
- 6.Shirazian M., and Farahi M. H., Intelligent Control and Automation 1, 15–19 (2010). 10.4236/ica.2010.11002 [DOI] [Google Scholar]
- 7.Tchuenche J. M., Khamis S. A., Agusto F. B. and Mpeshe S. C., ActaBiotheoretica 59, 1–28 (2011). [DOI] [PubMed] [Google Scholar]
- 8.Joshi H. R., Lenhart S., Li M. Y. and Wang L.. Contemporary Mathematics 410, 187–208 (2006). 10.1090/conm/410/07728 [DOI] [Google Scholar]
- 9.Blayneh K., Cao Y. and Kwon H. D., Discrete and Continuous Dynamical Systems Series B 11, 587–611 (2009). 10.3934/dcdsb.2009.11.587 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 10.Lenhart S. and Workman J. T., Proceedings of Symposia in Applied Mathematics 64, pp. 85 (2007). 10.1090/psapm/064/2359650 [DOI] [Google Scholar]
- 11.Karrakchou J., Rachik M. and Gourari S., Applied Mathematics and Computation 177, 807–818 (2006). 10.1016/j.amc.2005.11.092 [DOI] [Google Scholar]
- 12.Lichtenstein K. A., Armon C., Buchacz K., Chmiel J. S., Moorman A. C., Wood K. C. and Brooks J. T.. Journal of Acquired Immune Deficiency Syndromes 47, 27–35 (2008). 10.1097/QAI.0b013e31815acacc [DOI] [PubMed] [Google Scholar]
- 13.HIV Classification: CDC and WHO Staging Systems hab.hrsa.gov > Clinical Guide Testing and Assessment
- 14.Diekmann O., Heesterbeek J. A. P., Metz J. A. P., Journal Math. Bio. 2, 265–382 (1990). [Google Scholar]
- 15.Hussaini N., “Mathematical modelling and analysis of HIV transmission dynamics”, Ph.D Thesis, Brunel University, 2010. [Google Scholar]
- 16.Yusuf T. T. and Benyah F., Journal of Biological Dynamics 6, 475–494 (2012). 10.1080/17513758.2011.628700 [DOI] [PubMed] [Google Scholar]
- 17.Okosun K. O., Makinde O. D. and Takaidza I., Applied Mathematical Modelling 37, 3802–3820 (2013). 10.1016/j.apm.2012.08.004 [DOI] [Google Scholar]
- 18.Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V. and Mishchenko E.F., Gordon and Breach Science Publishers, NewYork, (1986). [Google Scholar]
- 19.Ngwenya O., “The role of incidence functions on the dynamics of SEIR model”, PhD Thesis, South Africa, 2009. [Google Scholar]