| Issue |
ITM Web Conf.
Volume 31, 2020
International Conference “Mathematical Modelling in Biomedicine” 2019
|
|
|---|---|---|
| Article Number | 04003 | |
| Number of page(s) | 8 | |
| Section | Methods of Modelling | |
| DOI | https://doi.org/10.1051/itmconf/20203104003 | |
| Published online | 09 March 2020 | |
Delay Differential Model for Tumour-Immune System With Chemo-therapy and Optimal Control
1 Department of Mathematical Sciences, College of Science, Al Ain, 15551, UAE University, UAE
2 Faculty of Medicine, Ain Shams University, Abbassyia 1156, Cairo, Egypt
∗ e-mail: frihan@uaeu.ac.ae
In this paper, we present a mathematical model of tumour-immune interactions in presence of chemotherapy treatment. The model is governed by a system of delay differential equations with optimal control variables. The control variables are included to justify the best strategy of treatments with minimum side effects, by reducing the production of new tumour cells and keeping the number of normal cells above the average of its carrying capacity. Existence of optimality and optimality conditions are also proved. The numerical simulations show that the optimal treatment strategy reduces the load of tumour cells and increases the effector cells after few days of therapy.
Key words: Chemotherapy / DDEs / Hamiltonian / Immune system / Mathematical modeling / Optimal control / Time-lags
© The Authors, published by EDP Sciences, 2020
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