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Optimal control model of immunotherapy for autoimmune diseases
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  • M. Fernanda Costa,
  • M. Piedade Ramos,
  • Carolina Ribeiro,
  • Ana Soares
M. Fernanda Costa
University of Minho
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M. Piedade Ramos
University of Minho
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Carolina Ribeiro
University of Minho
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Ana Soares
University of Minho
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Abstract

In this work, we develop a new mathematical model to evaluate the impact of drug therapies on autoimmunity disease. We describe the immune system interactions at the cellular level, using the kinetic theory approach, by considering self-antigen presenting cells, self-reactive T cells, immunosuppressive cells and Interleukin-2 (IL-2) cytokines. The drug therapy consists of an intake of Interleukin-2 cytokines which boosts the effect of immunosuppressive cells on the autoimmune reaction. We also derive the macroscopic model relative to the kinetic system and study the wellposedness of the Cauchy problem for the corresponding system of equations. We formulate an optimal control problem relative to the model so that the quantity of both the self-reactive T cells that are produced in the body and the Interleukin-2 cytokines that are administrated is simultaneously minimized. Moreover, we perform some numerical tests in view of investigating optimal treatment strategies and the results reveal that the optimal control approach provides good-quality approximate solutions and shows to be a valuable procedure in identifying optimal treatment strategies.

Peer review status:ACCEPTED

19 Aug 2020Submitted to Mathematical Methods in the Applied Sciences
21 Aug 2020Submission Checks Completed
21 Aug 2020Assigned to Editor
08 Sep 2020Reviewer(s) Assigned
22 Dec 2020Review(s) Completed, Editorial Evaluation Pending
26 Dec 2020Editorial Decision: Revise Minor
01 Feb 20211st Revision Received
01 Feb 2021Submission Checks Completed
01 Feb 2021Assigned to Editor
01 Feb 2021Editorial Decision: Accept