8 - Global stability of a diffusive HTLV-I infection model with mitosis and CTL immune response

Abstract

In this work, we first introduce an overview on HTLV-I infection models presented in the literature, then we propose and investigate an HTLV-I infection model with spatial dependence. The model describes the within-host interactions of uninfected CD4+T cells, latent HTLV-infected cells, Tax-expressing HTLV-infected cells, and HTLV-specific CTLs. HTLV-I has two modes of transmission: horizontal transmission through cell-to-cell contact and vertical transmission through mitosis of Tax-expressing HTLV-infected cells. In the beginning, the well-posedness of solutions, including the existence of global solutions and the boundedness, is justified. We calculate two threshold parameters, the basic infection reproduction number ℜ0 and the HTLV-specific CTL immunity reproduction number ℜ1, which completely determine the existence and stability of the three steady states of the model. We study the global stability of all steady states based on the construction of suitable Lyapunov functions and the usage of the Lyapunov-LaSalle asymptotic stability theorem. When ℜ0⩽1, the global asymptotic stability of the infection-free steady state is established. Further, when ℜ1⩽1<ℜ0, the persistent infection steady state with ineffective HTLV-specific CTL immune response is globally asymptotically stable. Furthermore, when ℜ1>1, the persistent infection steady state with effective HTLV-specific CTL immune response is globally asymptotically stable. Finally, numerical simulations are presented to verify the validity of our theoretical results.