Explicit Representations of Solutions and Parameter Estimations Problems of Time Delay Tumor Cells Model

Abstract

We consider ordinary differentials of cancerous tumor cells model with time delay that illustrates and represents the interactions of the tumor cells with effector cells include immune response of natural, dendritic and cytotoxic cells. The time delay is incorporated here into the model to justify the time required to stimulate the effector cells. This also help to study the behavior of the system without using all kinds of treatments. We study the stability of the model that confirms a free tumor steady state and displays two equilibrium points. The numerical simulations show that growing of the tumor cells reduces and the effector cells increase after few days for different values of time delay up to , even without considering the treatment strategies in the model. We present an efficient numerical technique that shows how we can first represent the periodic solution of the tumor nonlinear equation and then effectively estimate the unknown parameters of the model.

Keywords

• Tumor cells
• Time delay differential equations
• Steady states of ODEs