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. 2010 Apr;72(3):681-96.
doi: 10.1007/s11538-009-9465-z. Epub 2009 Dec 30.

Multistability in a model for CTL response to HTLV-I infection and its implications to HAM/TSP development and prevention

Horacio Gómez-Acevedo  1 , Michael Y Li, Steven Jacobson
Affiliations

Multistability in a model for CTL response to HTLV-I infection and its implications to HAM/TSP development and prevention

Horacio Gómez-Acevedo et al. Bull Math Biol. 2010 Apr.

Abstract

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.

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Figures

Fig. 1
Fig. 1
Transfer diagram for the CTL response to HTLV-I infection.
Fig. 2
Fig. 2
Graphic illustration of the uniqueness of the chronic-infection equilibrium P2 with CTL response.
Fig. 3
Fig. 3
Numerical simulations demonstrate three distinct outcomes of system (1). In (a), R0 ≤ 1, all solutions converge to the infection-free equilibrium P0 = (λ/μ1, 0, 0). In (b), R1 < 1 < R0, all interior solutions converge to the carrier equilibrium P1 = (x̄, ȳ, 0). In (c), R1 > 1, all interior solutions converge to the HAM/TSP equilibrium P2 = (x*, y*, z*).
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