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

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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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Authors and Affiliations

  1. Department of Pediatrics, University of Arkansas for Medical Sciences, Little Rock, AR, 72202, USA

    Horacio Gómez-Acevedo

  2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada

    Michael Y. Li

  3. Viral Immunology Section, Neuroimmunology Branch NINDS/NIH, Bethesda, MD, 20892, USA

    Steven Jacobson

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  1. Horacio Gómez-Acevedo
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  2. Michael Y. Li
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  3. Steven Jacobson
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Correspondence to Michael Y. Li.

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Gómez-Acevedo, H., Li, M.Y. & Jacobson, S. Multistability in a Model for CTL Response to HTLV-I Infection and Its Implications to HAM/TSP Development and Prevention. Bull. Math. Biol. 72, 681–696 (2010). https://doi.org/10.1007/s11538-009-9465-z

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  • DOI: https://doi.org/10.1007/s11538-009-9465-z

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