Delay Differential Model for Tumour-Immune System With Chemo-therapy and Optimal Control

Abstract

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.

Keywords

• chemotherapy
• ddes
• hamiltonian
• immune system
• mathematical modeling
• optimal control
• time-lags