Mathematical analysis of the global dynamics of a model for HTLV-I infection and ATL progression

Mathematical analysis is carried out that completely determines the global dynamics of a mathematical model for the transmission of human T-cell lymphotropic virus I (HTLV-1) infection and the development of adult T-cell leukemia (ATL). HTLV-1 infection of healthy CD4(+) T cells takes place through cell-to-cell contact with infected T cells. The infected T cells can remain latent and harbor virus for several years before virus production occurs. Actively infected T cells can infect other T cells and can convert to ATL cells, whose growth is assumed to follow a classical logistic growth function. Our analysis establishes that the global dynamics of T cells are completely determined by a basic reproduction number R-0. If R-0 less than or equal to 1, infected T cells always die out. If R-0 > 1, HTLV-1 infection becomes chronic, and a unique endemic equilibrium is globally stable in the interior of the feasible region. We also show that the equilibrium level of ATL-cell proliferation is higher when the HTLV-1 infection of T cells is chronic than when it is acute. (C) 2002 Published by Elsevier Science Inc.