Complex Stability Analysis of Therapeutic Actions in a Fractional Reaction Diffusion Model of Tumor

Abstract

Separate administration of either chemotherapy or immunotherapy has been studied and applied to clinical experiments but however, this administration has shown some side effects such as increased acidity which gives a selective advantage to tumor cell growth. We introduce a model for the combined action of chemotherapy and immunotherapy using fractional derivatives. This model with non-integer derivative was analysed analytically and numerically for stability of the disease free equilibrium. The analytic result shows that the disease free equilibrium exist and if the prescriptions of food and drugs are followed strictly (taken at the right time and right dose) and in addition if the basic tumor growth factor, ���� 21≥1 then the only realistic steady state is the disease free steady state. We also show analytically that this steady state is stable for some parameter values. Our analytical results were confirmed with a numerical simulation of the full non linear fractional diffusion system.