 A linear optimal control model of immunotherapy for recurrent autoimmune diseaseK. Azib, M.P. Machado Ramos and C. Ribeiro Chaos, Solitons & Fractals, 2025, vol. 198, issue C Abstract: In this work, we improve a recent mathematical model for evaluating the effects of drug treatments in autoimmune diseases, incorporating the natural death of all cell populations due to interactions with cells in the host environment and taking into account a constant input of self-antigen presenting cells, due to external environmental factors that are believed to trigger autoimmunity in people with susceptibility to this disease. We derive macro-analogies of the kinetic model and demonstrate the positivity and well-posedness of the solution. We then examine the equilibrium of the corresponding dynamical system and its stability. We show that continuous oscillations occur due to the existence of a Hopf bifurcation. We formulate a linear optimal control problem relevant to the model such that the number of self-reactive T cells and the amount of interleukin-2 cytokines that is administrated are simultaneously minimized. Numerical simulations of the model show the effectiveness of the therapeutic strategies. Keywords: Mathematical biology; Autoimmune disease; Immunotherapy; Dynamical systems in biology; Linear optimal control; Integro-differential equations (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:198:y:2025:i:c:s0960077925004965 DOI: 10.1016/j.chaos.2025.116483 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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