Analysis of tumour-immune evasion with chemo-immuno therapeutic treatment with quadratic optimal control

A simple mathematical model for the growth of tumour with discrete time delay in the immune system is considered. The dynamical behaviour of our system by analysing the existence and stability of our system at various equilibria is discussed elaborately. We set up an optimal control problem relative to the model so as to minimize the number of tumour cells and the chemo-immunotherapeutic drug administration. Sensitivity analysis of tumour model reveals that parameter value has a major impact on the model dynamics. We numerically illustrate how does these delay can change the stability region of the immune-control equilibrium and display the different impacts to the control of tumour. Finally, epidemiological implications of our analytical findings are addressed critically.