A time scale approach for analyzing pathogenesis of ATL development associated with HTLV-1 infection

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 ℛ0. When ℛ01, 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 ℛ01, respectively. Furthermore, the sensitivity analysis discovers the key parameters of the models related to ℛ0. 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. •ATL development associated with HTLV-1 infection.•Mathematical modeling by a time scale approach.•The number of leukemia cells described by implicit discrete logistic curve.•Determining data frequency by h-difference equations.