An optimal strategy for leukemia therapy: A multi-objective approachстатья
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Дата последнего поиска статьи во внешних источниках: 24 ноября 2021 г.
Аннотация:We introduce a multi-objective optimization problem using the example of a leukemia treatment model. We believe that treatment affects not only leukemia cells, but also the healthy cells. The treatment effect is modelled as a therapy function. The optimization problem consists of two objective functions that are in conflict: on the one hand, minimizing the leukemia cells and on the other hand, maximizing the number of healthy cells. We reduce this multi-objective problem by using the ε-constraint method. With the aid of Pontryagin’s maximum principle we give an analytical solution to this reduced problem. In order to solve the problem using the epsilon-constraint-method, the restriction of a threshold value for the number of healthy cells is separately considered as an optimization problem with a new extended objective function. For the most relevant parameters the maximum dose of chemotherapeutics should be administered as long as the predetermined restrictions are not violated. Furthermore, the case in which singular control may occur during the therapy process is analysed. In this case, the optimal control is also determined.