메뉴 건너뛰기




Volumn 229, Issue 1, 2009, Pages 313-323

Stability analysis of an HIV/AIDS epidemic model with treatment

Author keywords

Basic reproduction number; Global stability; HIV AIDS; Hopf bifurcation; Time delay

Indexed keywords

BASIC REPRODUCTION NUMBER; BIFURCATION PARAMETERS; DELAY MODELS; DISCRETE TIME DELAYS; DISEASE-FREE EQUILIBRIUMS; EPIDEMIC MODELS; GLOBAL DYNAMICS; GLOBAL STABILITY; GLOBALLY ASYMPTOTICALLY STABLES; HIV/AIDS; INFECTIOUS DISEASE; MATHEMATICAL ANALYSIS; NUMERICAL SIMULATIONS; STABILITY ANALYSIS; TREATMENT EFFECTS; TREATMENT METHODS;

EID: 67349136420     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2008.10.067     Document Type: Article
Times cited : (148)

References (30)
  • 1
    • 0027531918 scopus 로고
    • Pathogenesis of human immunodeficiency virus infection
    • Levy J.A. Pathogenesis of human immunodeficiency virus infection. Microbiol. Rev. 57 (1993) 183-289
    • (1993) Microbiol. Rev. , vol.57 , pp. 183-289
    • Levy, J.A.1
  • 3
    • 0024274733 scopus 로고
    • The role of mathematical models in the study of HIV transmission and the epidemiology of AIDS
    • Anderson R.M. The role of mathematical models in the study of HIV transmission and the epidemiology of AIDS. J. AIDS. 1 (1988) 241-256
    • (1988) J. AIDS. , vol.1 , pp. 241-256
    • Anderson, R.M.1
  • 4
    • 77957175423 scopus 로고
    • A preliminary study of the transmission dynamics of the Human Immunodeficiency Virus (HIV), the causative agent of AIDS
    • Anderson R.M., Medly G.F., May R.M., and Johnson A.M. 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
    • (1986) IMA J. Math. Appl. Med. Biol. , vol.3 , pp. 229-263
    • Anderson, R.M.1    Medly, G.F.2    May, R.M.3    Johnson, A.M.4
  • 5
    • 0023091646 scopus 로고
    • Transmission dynamics of HIV infection
    • May R.M., and Anderson R.M. Transmission dynamics of HIV infection. Nature 326 (1987) 137-142
    • (1987) Nature , vol.326 , pp. 137-142
    • May, R.M.1    Anderson, R.M.2
  • 6
    • 8744234876 scopus 로고    scopus 로고
    • HIV treatment models with time delay
    • Bachar M., and Dorfmayr A. HIV treatment models with time delay. C. R. Biologies 327 (2004) 983-994
    • (2004) C. R. Biologies , vol.327 , pp. 983-994
    • Bachar, M.1    Dorfmayr, A.2
  • 7
    • 0035816373 scopus 로고    scopus 로고
    • Calculating the consequences: HAART and risky sex
    • Blower S. Calculating the consequences: HAART and risky sex. AIDS 15 (2001) 1309-1310
    • (2001) AIDS , vol.15 , pp. 1309-1310
    • Blower, S.1
  • 8
    • 0037210843 scopus 로고    scopus 로고
    • A model of HIV/AIDS with staged progression and amelioration
    • Connell~McCluskey C. A model of HIV/AIDS with staged progression and amelioration. Math. Biosci. 181 (2003) 1-16
    • (2003) Math. Biosci. , vol.181 , pp. 1-16
    • Connell McCluskey, C.1
  • 9
    • 0002915678 scopus 로고
    • Modelling HIV Transmission and AIDS in the United States
    • Springer, Berlin
    • Hethcote H.W., and Van~Ark J.W. Modelling HIV Transmission and AIDS in the United States. Lect. Notes Biomath. vol. 95 (1992), Springer, Berlin
    • (1992) Lect. Notes Biomath. , vol.95
    • Hethcote, H.W.1    Van Ark, J.W.2
  • 10
    • 0842349503 scopus 로고    scopus 로고
    • Modelling the social dynamics of a sex industry: Its implications for spread of HIV/AIDS
    • Hsieh Y.-H., and Chen C.H. Modelling the social dynamics of a sex industry: Its implications for spread of HIV/AIDS. Bull. Math. Biol. 66 (2004) 143-166
    • (2004) Bull. Math. Biol. , vol.66 , pp. 143-166
    • Hsieh, Y.-H.1    Chen, C.H.2
  • 11
    • 0041474671 scopus 로고    scopus 로고
    • Virus dynamics: A global analysis
    • Leenheer P.D., and Smith H.L. Virus dynamics: A global analysis. SIAM J. Appl. Math. 63 (2003) 1313-1327
    • (2003) SIAM J. Appl. Math. , vol.63 , pp. 1313-1327
    • Leenheer, P.D.1    Smith, H.L.2
  • 12
    • 0001918317 scopus 로고    scopus 로고
    • Mathematical analysis of HIV-1 dynamics in vivo
    • Perelson A.S., and Nelson P.W. Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev. 41 1 (1999) 3-44
    • (1999) SIAM Rev. , vol.41 , Issue.1 , pp. 3-44
    • Perelson, A.S.1    Nelson, P.W.2
  • 14
    • 27144540965 scopus 로고    scopus 로고
    • Viral infection model with periodic lytic immune response
    • Wang K., Wang W., and Liu X. Viral infection model with periodic lytic immune response. Chaos Solitons Fractals 28 1 (2006) 90-99
    • (2006) Chaos Solitons Fractals , vol.28 , Issue.1 , pp. 90-99
    • Wang, K.1    Wang, W.2    Liu, X.3
  • 17
    • 0024578161 scopus 로고
    • An epidemiological model with a delay and a nonlinear incidence rate
    • Hethcote H.W., Lewis M.A., and van~den~Driessche P. An epidemiological model with a delay and a nonlinear incidence rate. J. Math. Biol. 27 (1989) 49-64
    • (1989) J. Math. Biol. , vol.27 , pp. 49-64
    • Hethcote, H.W.1    Lewis, M.A.2    van den Driessche, P.3
  • 18
    • 0034108662 scopus 로고    scopus 로고
    • A delay-differential equation model of HIV infection of CD4+ T-cells
    • Culshaw R.V., and Ruan S. A delay-differential equation model of HIV infection of CD4+ T-cells. Math. Biosci. 165 (2000) 27-39
    • (2000) Math. Biosci. , vol.165 , pp. 27-39
    • Culshaw, R.V.1    Ruan, S.2
  • 19
    • 0036845274 scopus 로고    scopus 로고
    • Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    • van~den~Driessche P., and Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180 (2002) 29-48
    • (2002) Math. Biosci. , vol.180 , pp. 29-48
    • van den Driessche, P.1    Watmough, J.2
  • 20
    • 1042298863 scopus 로고    scopus 로고
    • Global results for an epidemic model with vaccination that exhibits backward bifurcation
    • Arino J., McCluskey C.C., and van~den~Driessche P. Global results for an epidemic model with vaccination that exhibits backward bifurcation. SIAM J. Appl. Math. 64 (2003) 260-276
    • (2003) SIAM J. Appl. Math. , vol.64 , pp. 260-276
    • Arino, J.1    McCluskey, C.C.2    van den Driessche, P.3
  • 23
    • 0039591930 scopus 로고
    • Persistence under relaxed point-dissipativity (with application to an endemic model)
    • Thieme R.H. Persistence under relaxed point-dissipativity (with application to an endemic model). SIAM J. Math. Anal. 24 (1993) 407-435
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 407-435
    • Thieme, R.H.1
  • 24
    • 0025112636 scopus 로고
    • Analysis of a disease transmission model in a population with varying size
    • Busenberg S., and van~den~Driessche P. Analysis of a disease transmission model in a population with varying size. J. Math. Biol. 28 (1990) 257-270
    • (1990) J. Math. Biol. , vol.28 , pp. 257-270
    • Busenberg, S.1    van den Driessche, P.2
  • 25
    • 0041519201 scopus 로고    scopus 로고
    • A mathematical study of a model for childhood diseases with non-permanent immunity
    • Moghadas S.M., and Gumel A.B. A mathematical study of a model for childhood diseases with non-permanent immunity. J. Comput. Appl. Math. 157 (2003) 347-363
    • (2003) J. Comput. Appl. Math. , vol.157 , pp. 347-363
    • Moghadas, S.M.1    Gumel, A.B.2
  • 26
    • 0037118226 scopus 로고    scopus 로고
    • Qualitative analyses of SIS epidemic model with vaccination varying total population
    • Li J., and Ma Z. Qualitative analyses of SIS epidemic model with vaccination varying total population. Math. Comput. Modelling 35 (2002) 1235-1243
    • (2002) Math. Comput. Modelling , vol.35 , pp. 1235-1243
    • Li, J.1    Ma, Z.2
  • 28
    • 0003375471 scopus 로고
    • Three-species food chain models with mutual interference and time delays
    • Erbe L.H., Rao V.S.H., and Freedman H. Three-species food chain models with mutual interference and time delays. Math. Biosci. 80 (1986) 57-80
    • (1986) Math. Biosci. , vol.80 , pp. 57-80
    • Erbe, L.H.1    Rao, V.S.H.2    Freedman, H.3
  • 29
    • 0003082201 scopus 로고
    • On zeroes of some transcendental equations
    • Cooke K.L., and van~den~Driessche P. On zeroes of some transcendental equations. Funkcial. Ekvac. 29 (1986) 77-90
    • (1986) Funkcial. Ekvac. , vol.29 , pp. 77-90
    • Cooke, K.L.1    van den Driessche, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.