Optimal chemotherapy and immunotherapy schedules for a cancer-obesity model with Caputo time fractional derivative
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ID: 281546
2018
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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.
| Reference Key |
baleanu2018optimal
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|---|---|
| Authors | Tuğba Akman Yıldız; Sadia Arshad; Dumitru Baleanu |
| Journal | arXiv |
| Year | 2018 |
| DOI |
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