Optimal Treatment Strategy for Cancer Based on Mathematical Modeling and Impulse Control Theory

Abstract

Adaptive therapy is a new type of cancer treatment in which time and dose are dynamically changed according to different individuals, which is very different from conventional cancer treatment strategies that use the maximum dose to kill the tumor cells. However, how to determine the time and dose of drug treatment is a challenging problem. In this paper, a competition model between drug-sensitive cells and drug-resistant cells was established, in which pulse intervention was introduced. In addition, based on the theory of pulse optimal control, three pulse optimal control strategies are proposed in the process of cancer treatment by controlling the pulse interval and dose, minimizing the number of tumor cells at the end of the day at minimal cost. Finally, three optimization strategies were compared, using numerical simulation, in terms of tumor burden and the effect on drug-resistant cells. The results show that the hybrid control strategy has the best effect. This work would provide some new ideas for the treatment of cancer.

Keywords

• pulse effect
• permanence
• global attractiveness
• optimal control