Backward bifurcation in an HIV model with two target cells

Proceedings of the 29th Chinese Control Conference, CCC'10

Volumn , Issue , 2010, Pages 1397-1400

  Liu, Yongqi ^a   Sun, Zhendong ^a  

^a SOUTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Backward bifurcation; HIV model; Stability

Indexed keywords

ASYMPTOTICALLY STABLE; BACKWARD BIFURCATION; BASIC REPRODUCTION NUMBER; CD4 T-CELLS; DISEASE-FREE EQUILIBRIUM; ENDEMIC EQUILIBRIUM; HIV INFECTION; HIV MODELS; TARGET CELLS; TRANSMISSION DYNAMICS;

ASYMPTOTIC ANALYSIS; BIFURCATION (MATHEMATICS); VIRUSES;

DISEASES;

EID: 78650248896     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (20)

1. B. M. Adams, H. T. Banks, M. Da vidian, H.-D. Kwon, H. T. Tran, S. N. Wynne, E. S. Rosenberg. HIV dynamics: Modeling, data analysis, and optimal treatment protocols. Journal of Computational and Applied Mathematics. 184: 10-49, 2005.
2. M. A. Aziz-Alaoui. Study of a LeslieCGower-type tritrophic population model. Chaos, Solitons and Fractals. 14: 1275-1293, 2002.
3. D. S. Callaway, A. S. Perelson. HIV-1 infection and low steady state viral loads. Bulletin of Mathematical Biology. 64: 29-64, 2001.
4. C. Castillo-Chavez, B. Song. Dynamical model of Tuberclosis and their applications, Mathematical Biosciences and Engineering. 1(2): 361-404, 2004.
5. M. Dehghan, M. Nasri, M. R. Razvan. Global stability of a deterministic model for HIV infection in vivo. Chaos, Solitons and Fractals. 34: 1225-1238, 2007.
6. A. M. Elaiw. Global properties of a class of HIV models. Nonlinear Analysis: Real World Applications (to appear).
7. Z. Feng, C. Castillo-Chavez, A. F. Capurro. A model for Tuberculosis with exogenous reinfection. Theoretical Population Biology. 57: 235-247, 2000.
8. K. P. Hadeler, P. V. D. Driessche. Backward bifurcation in epidemic control. Mathematical Biosciences. 146: 15-35, 1997.
9. V. Herz, S. Bonhoeffer, R. Anderson, R. May, M. Nowak. Viral dynamics in vivo: Limitations on estimations on intra-cellular delay and virus decay. Proceedings of the National Academy of Sciences of the USA. 93: 7247-7251, 1996.
10. Z. Hu, S. Liu, H. Wang. Backward bifurcation of an epidemic model with standard incidence rate and treatment rate. Nonlinear Analysis: Real World Applications 9: 2302-2312, 2008.
11. D. Kirschner. Using mathematics to understand HIV immune dynamics. Notices-American Mathematical Society. 43: 191-202, 1996.
12. D. Kirschner. Dynamics of co-infection with M. tuberculosis and HIV-1. Theoretical Population Biology. 55: 94-109, 1999.
13. P. D. Leenheer, H. L. Smith, Virus dynamics: A global analysis, SIAM Journal on Applied Mathematics. 63: 1313-1327, 2003.
14. A. S. Perelson, P. W. Nelson. Mathematical analysis of HIV-1 dynamics in vivo. SIAM Review. 41: 3-44, 1999.
15. O. Sharomi, C. N. Podder, A. B. Gumel, E. H. Elbasha, J. Watmough. Role of incidence function in vaccine-induced backward bifurcation in some HIV models. Mathematical Biosciences. 210: 436-463, 2007.
16. + T cells. Mathematical Biosciences. 200: 44-57, 2006.
17. Y. Wang, Y. Zhou, J. Wu, J. Heffernan. Oscillatory viral dynamics in a delayed HIV pathogenesis model. Mathematical Biosciences. 219: 104-112, 2009.
18. D. Wodarz, A. L. Lloyd, V. Jansen, V. A. A. Jansen, M. A. Nowak. Dynamics of Macrophage and T cell infection by HIV. Journal of Theoretical Biology. 199: 101-113, 1999. (Pubitemid 29017553)
19. X. Xia. Modeling of HIV infection: Vaccine readiness, drug effectiveness and therapeutical failures. Journal of Process Control. 17: 253-260, 2007.
20. X. Zhang, X. Liu. Backward bifurcation of an epidemic model with saturated treatment function. Journal of Mathematical Analysis and Applications. 348: 433-443, 2008.