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Time-delayed model of autoimmune dynamics

Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9QH, United Kingdom

Special Issues: Mathematical Methods in the Biosciences

Among various environmental factors associated with triggering or exacerbating autoimmune response, an important role is played by infections. A breakdown of immune tolerance as a byproduct of immune response against these infections is one of the major causes of autoimmune disease. In this paper we analyse the dynamics of immune response with particular emphasis on the role of time delays characterising the infection and the immune response, as well as on interactions between different types of T cells and cytokines that mediate their behaviour. Stability analysis of the model provides insights into how different model parameters affect the dynamics. Numerical stability analysis and simulations are performed to identify basins of attraction of different dynamical states, and to illustrate the behaviour of the model in different regimes
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Keywords immune response; mathematical model; time delay; autoimmunity; multi-stability

Citation: Farzad Fatehi, Yuliya N. Kyrychko, Konstantin B. Blyuss. Time-delayed model of autoimmune dynamics. Mathematical Biosciences and Engineering, 2019, 16(5): 5613-5639. doi: 10.3934/mbe.2019279


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