A Time Scale Approach for Analyzing Pathogenesis of ATL Development Associated With HTLV-1 Infection

Abstract

In this paper, mathematical modeling of the dynamics of Human T-cell lymphotropic virus type I (HTLV-1) infection and the development of adult T-cell leukemia (ATL) cells is investigated by a time scale approach. The proposed models, constructed by nonlinear systems of first-order difference equations and h-difference equations, characterize the relationship among uninfected, latently infected, actively infected CD4(+) cells, and ATL cells, where the growth of leukemia cells is described by discrete logistic curves. The stability results are established based on basic reproduction number R-0. When R-0<1, infected T-cells always die out and there exist two disease-free equilibria depending on the proliferation rate and the death rate of leukemia cells. When R-0>1, HTLV-1 infection becomes chronic and spreads, and there exists a unique endemic equilibrium point. The stability results of disease-free and endemic equilibrium points are obtained when R-0<1 and R-0>1, respectively. Furthermore, the sensitivity analysis discovers the key parameters of the models related to R-0. Estimated parameters are applied based on the experimental observation. The numerical analysis also shows the equilibrium level of ATL cell proliferation is higher when the HTLV-I infection of T-cells is chronic than when it is acute. Moreover, our mathematical modeling by a time scale approach yields a new parameter to an HTLV-1 infection model which determines data frequency.