Optimal control of a sex‐structured HIV/AIDS model with condom use

References

• Adams , B.M. 2004 . Dynamic multidrug therapies for HIV: optimal and STI control approaches . J M.B.E., , 1 (2) : 223 – 241 .
   Google Scholar
• Briz , V. , Poveda , E. and Soriano , V. 2006 . HIV entry inhibitors: mechanisms of action and resistance pathways . J. Antimic. Chemo., , 57 : 619 – 627 . (doi:10.1093/jac/dkl027)
   PubMed Web of Science ®Google Scholar
• Fleming , W.H. and Rishel , R.W. 1975 . Deterministic and Stochastic Optimal Control. , New York : Spinger .
   Google Scholar
• Garira , W. , Musekwa , S.D. and Shiri , T. 2005 . Optimal control of combined therapy in a single strain HIV‐1 model . EJDE, , 52 : 1 – 22 .
   Google Scholar
• Greenhalgh , D. , Dolye , M. and Lewis , F. 2001 . A mathematical treatment of AIDS and condom use . IMA J. Math. Appl. Med. Biol., , 18 (3) : 225 – 262 . (doi:10.1093/imammb/18.3.225)
   PubMedGoogle Scholar
• Joshi , H.R. 2002 . Optimal control of an HIV immunology model . Opt. Control Appl. Meth., , 23 : 199 – 213 . (doi:10.1002/oca.710)
   Web of Science ®Google Scholar
• Kirschner , D. and Wedd , G.F. 1997 . A mathematical model of combined drug therapy of HIV infection . J. Theor. Med. , 1 : 25 – 34 .
   Google Scholar
• Kwon , H. 2007 . Optimal treatment strategies derived from a HIV model with drug resistant mutants . A. Math. Comp., , 188 (2) : 1193 – 1204 . (doi:10.1016/j.amc.2006.10.071)
   Google Scholar
• Lukes , D.L. 1982 . Differential Equations: Classical to controlled. , New York : Mathematical in Science and Engineering. Academic Press .
   Google Scholar
• Magombedze , G. , Garira , W. and Mwenje , E. 2008 . Modelling the immuno‐pathogenesis of HIV‐1 infection and the effect of mlti‐drug therapy: The role of Fusion inhibitors in HAART . Math. Biosc. Eng., , 5 (3) : 485 – 504 .
   PubMedGoogle Scholar
• Moghadas , S.M. , Gumel , A.B. , McLeod , R.G. and Gordon , R. 2003 . Could condoms stop the AIDS epidemic . J. Theor. Med., , 5 : 172 – 181 .
   Google Scholar
• Moore , J.P. and Doms , R.W. 2003 . The entry of entry inhibitors: A fusion of science and medicine . PNAS, , 100 (19) : 10598 – 10602 . (doi:10.1073/pnas.1932511100)
   PubMedGoogle Scholar
• Moyle , G. 2003 . Stopping HIV fusion with enfuvirtide: the first step to extracellular HAART . J. Antimic. Chemo., , 51 : 213 – 217 . (doi:10.1093/jac/dkg066)
   PubMed Web of Science ®Google Scholar
• Mukandavire , Z. and Garira , W. 2007 . Sex‐structured HIV/AIDS model to analyse the effects of condom use with application to Zimbabwe . J. Math. Biol., , 54 : 669 – 699 . (doi:10.1007/s00285–006–0063–5)
   PubMed Web of Science ®Google Scholar
• Mukandavire , Z. and Garira , W. 2006 . HIV/AIDS model for assessing the effects of prophylactic sterilizing vaccines, condoms and treatment with amelioration . Bio. Sys., , 14 (3) : 323 – 355 .
   Google Scholar
• Rockstroh , J.K. and Mauss , S. 2004 . Clinical perspective of fusion inhibitors for treatment of HIV . J. Antimic. Chemo., , 53 : 700 – 702 . (doi:10.1093/jac/dkh161)
   PubMedGoogle Scholar
• Shiri , T. , Garira , W. and Musekwa , S.D. 2005 . A two‐strain HIV‐1 mathematical model to assess the effects of chemotherapy on disease parameters . MBE Journal, , 2 : 811 – 832 .
   Google Scholar
• Tashima , T.K. 2003 . Fusion inhibition a major but costly step forward in the treatment of HIV‐1 . N. ENGL. J. MED., , 348 (22) : 2249 – 2250 . (doi:10.1056/NEJMe030042)
   PubMedGoogle Scholar
• Tumwiine , J. , Mugisha , J.Y.T. and Luboobi , L.S. 2008 . Threshold and stability results for a malaria model in a population with protective intervention among high‐risk groups . Math. Model. Anal., , 13 (3) : 443 – 460 . (doi:10.3846/1392–6292.2008.13.443–460)
   Google Scholar