Multistability in a Model for CTL Response to HTLV-I Infection and Its Implications to HAM/TSP Development and Prevention

Human T-cell leukaemia/lymphoma virus type I (HTLV-I) is a retrovirus that has been identified as the causative agent of HTLV-I-associated myelopathy/tropical spastic paraparesis (HAM/TSP) and other illnesses. HTLV-I infects primarily CD4⁺ T cells and the transmission occurs through direct cell-to-cell contact. HAM/TSP patients harbor higher proviral loads in peripheral blood lymphocytes than asymptomatic carriers. Also, HAM/TSP patients exhibit a remarkably high number of circulating HTLV-I-specific CD8⁺ cytotoxic T lymphocytes (CTLs) in the peripheral blood. While CTLs have a protective role by killing the infected cells and lowering the proviral load, a high level of CTLs and their cytotoxicity are believed to be a main cause of the development of HAM/TSP. A mathematical model for HTLV-I infection of CD4⁺ T cells that incorporates the CD8⁺ cytotoxic T-cell (CTL) response is investigated. Our mathematical analysis reveals that the system can stabilize at a carrier steady-state with persistent viral infection but no CTL response, or at a HAM/TSP steady-state at which both the viral infection and CTL response are persistent. We also establish two threshold parameters R ₀ and R ₁, the basic reproduction numbers for viral persistence and for CTL response, respectively. We show that the parameter R ₁ can be used to distinguish asymptomatic carriers from HAM/TSP patients, and as an important control parameter for preventing the development of HAM/TSP.