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\begin{document}

\title{Optimal control model of immunotherapy for autoimmune diseases}



\author[1]{M. Fernanda Costa}%
\author[1]{M. Piedade Ramos}%
\author[1]{Carolina Ribeiro}%
\author[1]{Ana Soares}%
\affil[1]{University of Minho}%


\vspace{-1em}



  
  \date{May 20, 2024}


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\begin{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.%
\end{abstract}%



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