We set immunotherapy control as a target control problem under state-control constraints, taking into account a general tumor dynamics. Then we use a set-valued approach based on viability theory to build feedback protocol laws by which cancer cells are asymptotically destroyed. An immunotherapy model is examined in order to illustrate our approach.
The aim of the paper is to study a cancer model based on anti-angiogenic therapy and radiotherapy. A set-valued analysis is carried out to control the tumor and carrying capacity of the vasculature, so in order to reverse tumor growth and augment tumor repair. The viability technique is used on an augmented model to solve the control problem. Obtained control is a selection of set-valued map of regulation and reduces tumor volume to around zero. A numerical simulation scheme with graphical representations and biological interpretations are given.
Mathematical model of ordinary differential equations is considered to analyze pharmacokinetics of multi chemotherapeutic drugs, and their pharmacodynamic effects on homogeneous tumors. Set-valued analysis is used to design protocols of drugs administration, and applied to decrease tumors density under their carrying capacity of Gompertz growth and converges to zero.
In this paper we set-valued analyze the problem of asymptotic stabilizing the tumor size. A mathematical model of exponential tumor growing caused by carcinogenic substance is considered, with chemotherapy, immunotherapy, and radiotherapy effects. We control the model to be viable in therapeutic domains, and reverse the exponential growing of the tumor size. The obtained controls derive from the derivative cone of therapeutic domains as solution of minimizing problem.
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