Optimal chemotherapy and immunotherapy schedules for a cancer-obesity model with Caputo time fractional derivative

TL;DR

This paper develops a fractional-order mathematical model to optimize combined chemotherapy and immunotherapy schedules for cancer treatment considering obesity effects, analyzing stability, and comparing strategies through simulations.

Contribution

It introduces a novel fractional-order cancer-obesity model with optimal control, analyzing treatment strategies and deriving optimal schedules.

Findings

Optimal treatment schedules identified for combined therapies

Fractional order affects treatment effectiveness and cost

Simulation results compare chemotherapy, immunotherapy, and their combination

Abstract

This work presents a new mathematical model to depict the effect of obesity on cancerous tumor growth when chemotherapy as well as immunotherapy have been administered. We consider an optimal control problem to destroy the tumor population and minimize the drug dose over a finite time interval. The constraint is a model including tumor cells, immune cells, fat cells, chemotherapeutic and immunotherapeutic drug concentrations with Caputo time fractional derivative. We investigate the existence and stability of the equilibrium points namely, tumor free equilibrium and coexisting equilibrium, analytically. We discretize the cancer-obesity model using L1-method. Simulation results of the proposed model are presented to compare three different treatment strategies: chemotherapy, immunotherapy and their combination. In addition, we investigate the effect of the differentiation order $\alpha$ and the value of the decay rate of the amount of chemotherapeutic drug to the value of the cost functional. We find out the optimal treatment schedule in case of chemotherapy and immunotherapy applied.