Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment

Mathematical Biosciences and Engineering

Volumn 5, Issue 1, 2008, Pages 145-174

  Sharomi, Oluwaseun ^a   Podder, Chandra N ^a   Gumel, Abba B ^a   Song, Baojun ^b  

^a UNIVERSITY OF MANITOBA   (Canada)

^b MONTCLAIR STATE UNIVERSITY   (United States)

Author keywords

Bifurcation; Equilibria; HIV TB; Stability; Treatment

Indexed keywords

HUMAN IMMUNODEFICIENCY VIRUS; MYCOBACTERIUM TUBERCULOSIS;

EID: 45849102405     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2008.5.145     Document Type: Article

References (40)

1. R.M. Anderson and R.M. May, EDS., (1991). Infectious diseases of humans: Dynamics and control, Oxford Univ. Press, London/New York.
2. J. Arino, C.C. McCluskey and P. van den Driessche (2003). Global results for an epidemic model with vaccinaton that exihibits backward bifurcation. SIAM J. Appl. Math. 64: 260-276.
3. Averting HIV and AIDS (2006). AIDS, HIV & Tuberculosis (TB). http://www.avert.org/tuberc.htm.
4. F. Brauer (2004). Backward bifurcations in simple vaccination models. J. Math. Anal. and Appl. 298(2): 418-431.
5. Canada Communicable Disease Report: Pediatric tuberculosis in Canada (2003). Public Health Agency of Canada. http://www.phacaspc.gc.ca/publicat/ccdr- rmtc/03vol29/dr2916eb.html.
6. J. Carr (1981). Applications Centre Manifold Theory. Springer-Verlag, New York.
7. C. Castillo-Chavez, K. Cooke, W. Huang, and S. A. Levin (1989). Results on the dynamics for models for the sexual transmission of the human immunodeficiency virus. Appl. Math. Letters 2: 327-331.
8. C. Castillo-Chavez, K. Cooke, W. Huang, and S. A. Levin (1989). The role of long incubation periods in the dynamics of HIV/AIDS, part 2: Multiple group models, In Carlos Castillo-Chavez, ed., Mathematical ans statistical approaches to AIDS epidemiology. Lecture notes in Biomathematics. Springer-Verlag. 83: 200-217.
9. C. Castillo-Chavez and B. Song (2004). Dynamical models of tuberculosis and their applications. Math. Biosci. Engrg. 1(2): 361-404.
10. J. Dushoff, W. Huang, and C. Castillo-Chavez (1998). Backwards bifurcations and catastrophe in simple models of fatal diseases. J. Math. Biol. 36: 227-248.
11. E. H. Elbasha and A. B. Gumel (2006). Theoretical assessment of public health impact of imperfect prophylactic HIV-1 vaccines with therapeutic benefits. Bull. Math. Biol. 68: 577-614.
12. Z. Feng, C. Castillo-Chavez, and F. Capurro (2000). A model for tuberculosis with exogeneous reinfection. Theor. Pop. Biol. 57: 235-247.
13. + T cells. Bull. Math. Biol. 67(1): 101-114.
14. R. H. Gray, X. Li, M.J. Wawer, S.J. Gange, D. Serwadda, N.K. Sewankambo, R. Moore, F. Wabwire-Mangen, T. Lutalo, and T.C. Quinn (2003). Stochastic simulation of the impact of antiretroviral therapy and HIV vaccines on HIV trasmission. Rakai, Uganda. AIDS. 17(13): 1941-1951.
15. K. P. Hadeler and C. Castillo-Chavez (1995). A core group model for disease transmission. Math. Biosci. 128: 41-55.
16. J. K. Hale (1969). Ordinary Differential Equations. John Wiley and Sons, New York.
17. H. W. Hethcote (2000). The mathematics of infectious diseases. SIAM Review. 42(4): 599-653.
18. Y. Honda et al. (1998). Type I Interferon induces inhibitory 16-KDCCAAT/enhancer binding protein (C/EBP)β, repressing the HIV-1 long terminal repeat in macrophages: pulmonary tuberculosis alters C/EBP expression, enhancicng HIV-1 replication. The Journal Of Experimental Medicine. 188.7: 1255-1265.
19. HIV-TB Coinfection-A Guide for Medical Officers (2006). National AIDS Control Organization. Ministry of Health & Family Welfare, Government of India, http://www.nacoonline.org/publication/12.pdf.
20. W. Huang, K. Cooke, and C. Castillo-Chavez (1992). Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission. SIAM J. Appl. Math. 52: 835-854.
21. L. E. Jones and A. S. Perelson (2005). Opportunistic infection as a cause of transient viremia in chronically infected HIV patients under treatment with HAART. Bulletin of Math. Bio. 67: 1227-1251.
22. C. Kribs-Zaleta and J. Valesco-Hernandez (2000). A simple vaccination model with multiple endemic states. Math Biosci. 164: 183-201.
23. D. Kirschner (1996). Using mathematics to understanding HIV immune dynamics. Notices of the AMS. 43: 191-202.
24. D. Kirschner (1999). Dynamics of coinfection with m. tuberculosis and HIV-1. Theoretical Population Biology. 55: 94-109.
25. V. Lakshmikantham, S. Leela, and A. A. Martynyuk (1989). Stability Analysis of Nonlinear Systems. Marcel Dekker, Inc., New York and Basel.
26. J. P. LaSalle (1976). The Stability of Dynamical Syatems. Regional Conference Series in Applied Mathematics. SIAM, Philedelphia.
27. R. Naresh and A. Tripathi (2005). Modelling and analysis of HIV-TB coinfection in a variable size population. Math. Model. Anal. 10(3): 275-286.
28. F. J. Palella (Jr.), K. M. Delaney, A. C. Moorman, N.O. Loveless, J. Fuher, G. A. Saten, D. J. Achman, and S. D. Homberg (1998). Declining morbidity and mortality among patients with advanced human immunodeficiency virus infection. HIV outpatients study investigators. New Engl. J. Med. 338(13): 853-860.
29. A. S. Perelson and P. W. Nelson (1999). Mathematical analysis of HIV-1 dynamics in vivo. SIAM Review. 41(1): 3-44.
30. R. B. Schinazi (2003). Can HIV invade a population which is already sick? Bull, Braz. Math. Soc. (N.S.) 34(3): 479-488.
31. C. P. Simon and J. A. Jacquez (1992). Reproduction numbers and the stability of equilibrium of SI models for heterogeneous populations. SIAM J. Appl. Math. 52: 541-576.
32. O. Sharomi, C. N. Podder, A. B. Gumel, E. H. Elbasha, and J. Watmough (2007). Role of incidence function in vaccine-induced backward bifurcation in some HIV models. Math. Biosci. 210(2): 436-463.
33. P. van den Driessche and J. Watmough (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences. 180: 29-48.
34. W. Wang (2006). Backward bifurcation of an epidemic model with treatment. Math. Biosci. 201(1-2): 58-71.
35. R. W. West and J. R. Thompson (1996). Modelling the impact of HIV on the spread of tubercolusis in the United States. Mathematical Biosciences. 143: 35-60.
36. J. E. Wigginton and D. Kirschner (2001). A model to predict cell mediated immunue regulatory mechanisms during human infection with mycobacterium tuberculosis. J. Immunol. 166(3): 1951.
37. B. G. Williams, R. Granich, L. S. Chauhan, N. S. Dharmshaktu, and C. Dye (2005). The impact of HIV/AIDS on the control of tuberculosis in India. PNAS. 102(27): 9619-9624.
38. World Health Organization (2005). Global tuberculosis control-surveillance, planning, and financing. http://www.who.int/tb/ publications/globaLreport/2005/en/.
39. World Health Organization (2006). TB/HIV. http://www.who.int/tb/hiv/en/.
40. Integrating HIV/AIDS and TB Efforts (2004). The challenge for the President's AIDS Initiative. Open Society Institute, New York Public Health Programs, http://www.soros.org/initiatives/health/articles-publications/ publications/integrating-tb-20040218.