Program and Positional Control Strategies for the Lotka–Volterra Competition Model

CAR T-cell immunotherapy is a new development in the treatment of leukemia, promising a new era in oncology. Although so far, this procedure only helps 50–90% of patients and, like other cancer treatments, has serious side effects. In this work, we have proposed a controlled model for leukemia treatment to explore possible ways to improve immunotherapy methodology. Our model is described by four nonlinear differential equations with two bounded controls, which are responsible for the rate of injection of chimeric cells, as well as for the dosage of the drug that suppresses the so-called “cytokine storm”. The optimal control problem of minimizing the cancer cells and the activity of the cytokine is stated and solved using the Pontryagin maximum principle. The five possible optimal control scenarios are predicted analytically using investigation of the behavior of the switching functions. The optimal solutions, obtained numerically using BOCOP-2.2.0, confirmed our analytical findings. Interesting results, explaining, why therapies with rest intervals (for example, stopping injections in the middle of the treatment interval) are more effective (within the model), rather than with continuous injections, are presented. Possible improvements to the mathematical model and method of immunotherapy are discussed.

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“…Adding to them following from (15) and (16) new initial conditions, we find the corresponding adjoint system:…”

Section: Lemmamentioning

confidence: 99%

“…In turn, for an organism weakened by radio-or chemotherapy, CAR T-cells are not very active or specific and the competition model for all three types of cells seems more suitable. The model of the latter type is considered in this work, which is the continuation of our studies presented in [15][16][17].…”

mentioning

confidence: 99%