Optimal Control for a Mathematical Model of Cancer Disease via Dynamic Programming Approach

ABSTRACT The objective of this paper is to provide a comprehensive overview of optimal control models in the context of cancer treatment. We will explore how these mathematical models are used to optimize the administration of anticancer drugs. By understanding the principles behind optimal control models, we can appreciate their potential to revolutionize cancer treatment and contribute to personalized medicine. We utilize recent advancements in dynamic programming method to achieve a rigorous solution for a cancer disease model proposed by Neilan as an unsolved problem. Beginning with a certain refinement of Cauchy's method of characteristics for stratified Hamilton–Jacobi equations allows us to delineate a broad range of admissible trajectories. This, in turn, leads to the identification of a domain wherein the value function not only exists but is also generated by a certain admissible control. While the optimality is checked by using one of the well‐known verification theorems taken as sufficient optimality conditions. JEL Classification: 2000 MSC: 49J15, 49L20, 35F21