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Volumn 6, Issue 2, 2012, Pages 475-494

Optimal strategy for controlling the spread of HIV/AIDS disease: A case study of South Africa

Author keywords

antiretroviral treatment; basic reproduction number; disease incidence; disease prevalence; optimal control; optimality system; Pontryagin's maximum principle

Indexed keywords

ACQUIRED IMMUNE DEFICIENCY SYNDROME; ARTICLE; BIOLOGICAL MODEL; EPIDEMIOLOGY; HUMAN; INCIDENCE; POPULATION DYNAMICS; PREVALENCE; SOUTH AFRICA;

EID: 84868311099     PISSN: 17513758     EISSN: 17513766     Source Type: Journal    
DOI: 10.1080/17513758.2011.628700     Document Type: Article
Times cited : (48)

References (33)
  • 1
    • 77952674174 scopus 로고    scopus 로고
    • Backward bifurcation and optimal control in transmission dynamics of the West Nile virus
    • Blayneh, K. W., Gumel, A. B., Lenhart, S. and Clayton, T. 2010. Backward bifurcation and optimal control in transmission dynamics of the West Nile virus. Bull. Math. Biol., 72: 1006-1028.
    • (2010) Bull. Math. Biol. , vol.72 , pp. 1006-1028
    • Blayneh, K.W.1    Gumel, A.B.2    Lenhart, S.3    Clayton, T.4
  • 4
    • 0036845274 scopus 로고    scopus 로고
    • Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    • Driessche, P. V. and Watmough, J. 2002. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci., 180: 29-48.
    • (2002) Math. Biosci. , vol.180 , pp. 29-48
    • Driessche, P.V.1    Watmough, J.2
  • 5
    • 34447571170 scopus 로고    scopus 로고
    • Immunotherapy: An optimal control theory approach
    • Fister, K. R. and Donnelly, J. H. 2005. Immunotherapy: An optimal control theory approach. Math. Biosci. Eng., 2: 499-510.
    • (2005) Math. Biosci. Eng. , vol.2 , pp. 499-510
    • Fister, K.R.1    Donnelly, J.H.2
  • 7
    • 70349647743 scopus 로고    scopus 로고
    • Optimal control applied to vaccination and treatment strategies for various epidemiological models
    • Gaff, H. and Schaefer, E. 2009. Optimal control applied to vaccination and treatment strategies for various epidemiological models. Math. Biosci. Eng., 6: 469-492.
    • (2009) Math. Biosci. Eng. , vol.6 , pp. 469-492
    • Gaff, H.1    Schaefer, E.2
  • 8
    • 36349004703 scopus 로고    scopus 로고
    • Survival and mortality of people infected with HIV in low and middle income countries: Results from the extended ALPHA network
    • Ghys, P. D., Basia, Z. and Prins, M. 2007. Survival and mortality of people infected with HIV in low and middle income countries: Results from the extended ALPHA network. AIDS, 21(Suppl. 6): S1-S4.
    • (2007) AIDS , vol.21 , Issue.SUPPL. 6.
    • Ghys, P.D.1    Basia, Z.2    Prins, M.3
  • 10
    • 58149097694 scopus 로고    scopus 로고
    • Universal voluntary HIV testing with immediate antiretroviral therapy as a strategy for elimination of HIV transmission: A mathematical model
    • The Lancet published online 26 November (2008), doi:10.1016/S0140-6736(08)61697-9
    • Granich, R. M., Gilks, C. F., Dye, C., De Cock, K. M. and Williams, B. G. "Universal voluntary HIV testing with immediate antiretroviral therapy as a strategy for elimination of HIV transmission: A mathematical model". The Lancet. published online 26 November (2008), doi:10.1016/S0140-6736(08)61697-9
    • Granich, R.M.1    Gilks, C.F.2    Dye, C.3    de Cock, K.M.4    Williams, B.G.5
  • 11
    • 44849101593 scopus 로고    scopus 로고
    • Mathematical models of infectious disease transmission
    • Grassly, N. C. and Fraser, C. 2008. Mathematical models of infectious disease transmission. Nat. Rev. Microbiol., 6: 477-487.
    • (2008) Nat. Rev. Microbiol. , vol.6 , pp. 477-487
    • Grassly, N.C.1    Fraser, C.2
  • 13
    • 0034486891 scopus 로고    scopus 로고
    • The Mathematics of Infectious Diseases
    • Hethcote, H. W. 2000. The Mathematics of Infectious Diseases. SIAM Rev., 42: 599-653.
    • (2000) SIAM Rev. , vol.42 , pp. 599-653
    • Hethcote, H.W.1
  • 14
    • 0035401181 scopus 로고    scopus 로고
    • The effect of density-dependent treatment and behaviour change on the dynamics of HIV transmission
    • Hsieh, Y. and Sheu, S. 2001. The effect of density-dependent treatment and behaviour change on the dynamics of HIV transmission. J. Math. Biol., 43: 69-80.
    • (2001) J. Math. Biol. , vol.43 , pp. 69-80
    • Hsieh, Y.1    Sheu, S.2
  • 15
    • 58849115144 scopus 로고    scopus 로고
    • Modeling the effect of information campaign on the HIV epidemic in Uganda
    • Joshi, H., Lenhart, S., Albright, K. and Gipson, K. 2008. Modeling the effect of information campaign on the HIV epidemic in Uganda. Math. Biosci. Eng., 5: 757-770.
    • (2008) Math. Biosci. Eng. , vol.5 , pp. 757-770
    • Joshi, H.1    Lenhart, S.2    Albright, K.3    Gipson, K.4
  • 16
    • 77951691230 scopus 로고    scopus 로고
    • Optimal control methods applied to disease models
    • Joshi, H., Lenhart, S., Li, M. Y. and Wang, L. 2006. Optimal control methods applied to disease models. Contemp. Math., 410: 187-207.
    • (2006) Contemp. Math. , vol.410 , pp. 187-207
    • Joshi, H.1    Lenhart, S.2    Li, M.Y.3    Wang, L.4
  • 17
    • 33846888513 scopus 로고    scopus 로고
    • The effects of vertical transmission on the spread of HIV/AIDS in the presence of treatment
    • Kgosimore, M. and Lungu, E. M. 2006. The effects of vertical transmission on the spread of HIV/AIDS in the presence of treatment. Math. Biosci. Eng., 3: 297-312.
    • (2006) Math. Biosci. Eng. , vol.3 , pp. 297-312
    • Kgosimore, M.1    Lungu, E.M.2
  • 18
    • 0031204179 scopus 로고    scopus 로고
    • Optimal control of the chemotherapy of HIV
    • Kirschner, D., Lenhart, S. and Serbin, S. 1997. Optimal control of the chemotherapy of HIV. J. Math. Biol., 35: 775-792.
    • (1997) J. Math. Biol. , vol.35 , pp. 775-792
    • Kirschner, D.1    Lenhart, S.2    Serbin, S.3
  • 21
    • 34248351113 scopus 로고    scopus 로고
    • Sex-structured HIV/AIDS model to analyse the effects of condom use with application to Zimbabwe
    • 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.
    • (2007) J. Math. Biol. , vol.54 , pp. 669-699
    • Mukandavire, Z.1    Garira, W.2
  • 22
    • 35248819749 scopus 로고    scopus 로고
    • Optimal control of treatment in a mathematical model of chronic myelogenous leukemia
    • Nanda, S., Moore, H. and Lenhart, S. 2007. Optimal control of treatment in a mathematical model of chronic myelogenous leukemia. Math. Biosci, 210: 143-156.
    • (2007) Math. Biosci , vol.210 , pp. 143-156
    • Nanda, S.1    Moore, H.2    Lenhart, S.3
  • 23
    • 33746253677 scopus 로고    scopus 로고
    • Modelling the spread of AIDS epidemic with vertical transmission
    • Naresh, R., Tripathi, A. and Omar, S. 2006. Modelling the spread of AIDS epidemic with vertical transmission. Appl. Math. Comput., 178: 262-272.
    • (2006) Appl. Math. Comput. , vol.178 , pp. 262-272
    • Naresh, R.1    Tripathi, A.2    Omar, S.3
  • 25
    • 76549135399 scopus 로고    scopus 로고
    • HIV/AIDS epidemic in India and predicting the impact of the national response: Mathematical modeling and analysis
    • Rao, A. S., Thomas, K., Sudhakar, K. and Maini, P. K. 2009. HIV/AIDS epidemic in India and predicting the impact of the national response: Mathematical modeling and analysis. Math. Biosci. Eng., 6: 779-813.
    • (2009) Math. Biosci. Eng. , vol.6 , pp. 779-813
    • Rao, A.S.1    Thomas, K.2    Sudhakar, K.3    Maini, P.K.4
  • 26
    • 84974873238 scopus 로고
    • Optimal control of some simple deterministic epidemic models
    • Sethi, S. P. and Staats, P. W. 1978. Optimal control of some simple deterministic epidemic models. J. Oper. Res. Soc., 29: 129-136.
    • (1978) J. Oper. Res. Soc. , vol.29 , pp. 129-136
    • Sethi, S.P.1    Staats, P.W.2
  • 27
    • 62549125432 scopus 로고    scopus 로고
    • Lyapunov function for a dengue disease transmission model
    • Tewa, J. J., Dimi, J. L. and Bowong, S. 2009. Lyapunov function for a dengue disease transmission model. Chaos Solitons Fractals, 39: 936-941.
    • (2009) Chaos Solitons Fractals , vol.39 , pp. 936-941
    • Tewa, J.J.1    Dimi, J.L.2    Bowong, S.3
  • 29
    • 77951065603 scopus 로고    scopus 로고
    • UNAIDS/WHO, Available at or www.who.int/hiv
    • UNAIDS/WHO. AIDS epidemic update: November 2009 Available at www.unaids.org or www.who.int/hiv
    • AIDS epidemic update: November 2009
  • 31
    • 79952613782 scopus 로고    scopus 로고
    • Optimal Control of heterogeneous systems: Basic theory
    • Vladimir, M. V. 2008. Optimal Control of heterogeneous systems: Basic theory. J. Math. Anal. Appl., 346: 227-242.
    • (2008) J. Math. Anal. Appl. , vol.346 , pp. 227-242
    • Vladimir, M.V.1
  • 32
    • 39449089740 scopus 로고    scopus 로고
    • Optimal quarantine and isolation strategies in epidemics control
    • Yan, X., Zou, Y. and Li, J. 2007. Optimal quarantine and isolation strategies in epidemics control. World J. Model. Simul., 3: 202-211.
    • (2007) World J. Model. Simul. , vol.3 , pp. 202-211
    • Yan, X.1    Zou, Y.2    Li, J.3
  • 33
    • 48049122424 scopus 로고    scopus 로고
    • Stability analysis and optimal vaccination of an SIR epidemic model
    • Zaman, G., Kang, Y. H. and Jung, I. H. 2008. Stability analysis and optimal vaccination of an SIR epidemic model. BioSystems, 93: 240-249.
    • (2008) BioSystems , vol.93 , pp. 240-249
    • Zaman, G.1    Kang, Y.H.2    Jung, I.H.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.