Stable and transient periodic oscillations in a mathematical model for CTL response to HTLV-I infection.

London School of Economics-LSE, London, UK.
Journal of Mathematical Biology (Impact Factor: 2.39). 07/2011; 65(1):181-99. DOI: 10.1007/s00285-011-0455-z
Source: PubMed

ABSTRACT The cytotoxic T lymphocyte (CTL) response to the infection of CD4+ T cells by human T cell leukemia virus type I (HTLV-I) has previously been modelled using standard response functions, with relatively simple dynamical outcomes. In this paper, we investigate the consequences of a more general CTL response and show that a sigmoidal response function gives rise to complex behaviours previously unobserved. Multiple equilibria are shown to exist and none of the equilibria is a global attractor during the chronic infection phase. Coexistence of local attractors with their own basin of attractions is the norm. In addition, both stable and unstable periodic oscillations can be created through Hopf bifurcations. We show that transient periodic oscillations occur when a saddle-type periodic solution exists. As a consequence, transient periodic oscillations can be robust and observable. Implications of our findings to the dynamics of CTL response to HTLV-I infections in vivo and pathogenesis of HAM/TSP are discussed.

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Available from: John Lang, Apr 23, 2014
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    • "The evidence implies that cytotoxicity of the CTL is ultimately responsible for the demyelination of the central nervous system resulting in HAM/TSP [5]. Mathematical models have been formulated to describe the in-vivo infection process with the humoral immune response to HTLV-I infections [2] [6] [9] [11] [12] [16] [26] [25] [14] as well as to the human immunodeficiency virus (HIV) [13] [15] [19] [21] [24] [27]. In [6], Gómez-Acevedo et al consider the following mathematical model for the HTLV-I infection of CD4 + T cells that incorporates the CD8 + cytotoxic T-cell response: "
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    • "Chaotic like behavior is observed in Wang et al. (2007) for a three-dimensional delayed model, but with no bistability. We point out that sustained periodic oscillations and transient oscillations induced by nonlinearity have also been reported in ordinary differential equation models (Lang and Li 2012). The rest of this paper is organized as follows. "
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