Optimization of HAP administration in cancer therapy

We study a mathematical model of a tumor described and investigated in Mathur et al. (2024). Hypoxia is often a factor that contributes to tumor resistance against anticancer treatments. However, the use of Hypoxia-Activated Prodrugs (HAPs) turns this challenge into an advantage, offering potential benefits in treatment. By specifically targeting hypoxic tumor regions, HAPs can enhance the efficacy of drug delivery, making hypoxia a beneficial aspect in the therapeutic approach. In Mathur et al. (2024) optimal schedules for different finite number of simulation of treatment combinations is study. Optimization is done by observation of tissue under treatment. We develop approximate sufficient optimality conditions for that mathematical model of cancer with controls on the boundary. It is a starting point to present numerical algorithm with verification theorem of approximate solution. Numerical calculations are performed to optimize the density of the active drug within the tissue. The results show that the maximum density of active drugs can be achieved by increasing the injection of the drug and reducing oxygen levels, with optimal control parameters set. We refer our result to the simulations done by other authors with direct treatments.