A Delay Induced Cancer Model with the Effect of Logistic Approach Drug Administration

Authors

  • Anusmita Das, Hemanta Kr. Sarmah, Kaushik Dehingia

Abstract

In this paper, we have presented the effect of time delay on the dynamical behaviour of a mathematical model involving tumor, immune, and normal cells; first without and then with drug administration. Time delay is merged into the model to make it a more realistic one, as some amount of time is required to stimulate the immune cells so that they can fight against the tumor cells. In this study, we administered drug in logistic form rather than an optimal approach. We have studied the local asymptotic stability of the existing equilibrium of the system with delay equation in absence of drug administration and have shown that its stability can be lost through a Hopf bifurcation. Implicit function theorem is applied to characterize the existence of complex function in the neighborhood of delay term and we additionally show the existence of Hopf bifurcation when transversality condition is exerted. Later on, drug therapy is incorporated into the system to eradicate the tumor cells. Simulation with numerical data has been presented to show that the treatment scheme reduces the tumor cells.

Published

2020-11-01

Issue

Section

Articles