Effects of Viral and Cytokine Delays on Dynamics of Autoimmunity

Farzad Fatehi, Yuliya N. Kyrychko and Konstantin B. Blyuss
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Farzad Fatehi: Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK
Yuliya N. Kyrychko: Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK
Konstantin B. Blyuss: Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK

Mathematics, 2018, vol. 6, issue 5, 1-24

Abstract: A major contribution to the onset and development of autoimmune disease is known to come from infections. An important practical problem is identifying the precise mechanism by which the breakdown of immune tolerance as a result of immune response to infection leads to autoimmunity. In this paper, we develop a mathematical model of immune response to a viral infection, which includes T cells with different activation thresholds, regulatory T cells (Tregs), and a cytokine mediating immune dynamics. Particular emphasis is made on the role of time delays associated with the processes of infection and mounting the immune response. Stability analysis of various steady states of the model allows us to identify parameter regions associated with different types of immune behaviour, such as, normal clearance of infection, chronic infection, and autoimmune dynamics. Numerical simulations are used to illustrate different dynamical regimes, and to identify basins of attraction of different dynamical states. An important result of the analysis is that not only the parameters of the system, but also the initial level of infection and the initial state of the immune system determine the progress and outcome of the dynamics.

Keywords: mathematical model; immune response; autoimmunity; time delays (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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