Backward bifurcation in a model for HTLV-I infection of CD4+ T cells
- 157 Downloads
Human T-cell Lymphotropic Virus Type I (HTLV-I) primarily infects CD4+ helper T cells. HTLV-I infection is clinically linked to the development of Adult T-cell Leukemia/Lymphoma and of HTLV-I Associated Myelopathy/Tropical Spastic Paraparesis, among other illnesses. HTLV-I transmission can be either horizontal through cell-to-cell contact, or vertical through mitotic division of infected CD4+ T cells. It has been observed that HTLV-I infection has a high proviral load but a low rate of proviral genetic variation. This suggests that vertical transmission through mitotic division of infected cells may play an important role.We consider and analyze a mathematical model for HTLV-I infection of CD4+ T cells that incorporates both horizontal and vertical transmission. Among interesting dynamical behaviors of the model is a backward bifurcation which raises many new challenges to effective infection control.
Unable to display preview. Download preview PDF.
- Brauer, F., Noel, J.A., 1968. Qualitative Theory of Ordinary Differential Equations. Benjamin, New York.Google Scholar
- Cann, A.J., Chen, I.S.Y., 1996. Human T-cell leukemia virus types I and II. In: Fieds, B.N., Knipe, D.M., Howley, P.M. et al. (Eds.), Fields Virology, 3rd edn. Lippincott-Raven Publishers, Philadelphia, pp. 1849–1880.Google Scholar
- Gómez-Acevedo, H., Li, M.Y., 2002. Global dynamics of a mathematical model for HTLV-I infection of T cells. Canad. Appl. Math. Quart. 10, 71–86.Google Scholar
- Grant, C., Barmak, K., Alefantis, T., Yao, J., Jacobson, S., Wigdahl, B., 2002. Human T cell leukemia virus type I and neurologic disease: events in bone marrow, peripheral blood, and central nervous system during normal immune surveillance and neuroinflammation. J. Cell. Phys. 190, 133–159.CrossRefGoogle Scholar
- Hale, J.K., 1969. Ordinary Differential Equations. John Wiley&Sons, New York.Google Scholar
- Nowak, M.A., May, R.M., 2000. Virus Dynamics. Oxford University Press, Oxford.Google Scholar
- Perelson, A.S., 1989. Modeling the interaction of the immune system with HIV. In: Castillo-Chavez, C. (Ed.), Mathematical and Statistical Approaches to AIDS Epidemiology. Lect. Notes Biomath, vol. 83. Springer, Berlin, pp. 350–370.Google Scholar
- Wattel, E., Vartanian, J.-P., Pannetier, C., Wain-Hobson, S., 1995. Clonal expansion of human T-cell leukemia virus type I-infected cells in asymptomatic and symptomatic carriers without malignancy. J. Virol. 69, 2863–2868.Google Scholar