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Mathematical Analysis of an Autoimmune Diseases Model: Kinetic Approach

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  • Mikhail Kolev

    (Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Słoneczna 54, 10-710 Olsztyn, Poland)

Abstract

A new mathematical model of a general autoimmune disease is presented. Basic information about autoimmune diseases is given and illustrated with examples. The model is developed by using ideas from the kinetic theory describing individuals expressing certain functions. The modeled problem is formulated by ordinary and partial equations involving a variable for a functional state. Numerical results are presented and discussed from a medical view point.

Suggested Citation

  • Mikhail Kolev, 2019. "Mathematical Analysis of an Autoimmune Diseases Model: Kinetic Approach," Mathematics, MDPI, vol. 7(11), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1024-:d:281679
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    References listed on IDEAS

    as
    1. Carlo Bianca & Caterina Mogno, 2018. "Modelling pedestrian dynamics into a metro station by thermostatted kinetic theory methods," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 24(2), pages 207-235, March.
    2. Masurel, Léon & Bianca, Carlo & Lemarchand, Annie, 2018. "On the learning control effects in the cancer-immune system competition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 462-475.
    Full references (including those not matched with items on IDEAS)

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