Estimation of the domain of attraction of free tumor equilibrium point of perturbed tumor immunotherapy model

Abstract

In this paper we are going to estimate domain of attraction of tumor-free equilibrium points in a perturbed cancer tumor model which is describing the tumor-immune system competition dynamics. The proposed method is based on solving an optimization problem for a chosen Lyapunov function that can be casted in terms of Linear Matrix Inequalities constraint and Taylor expansion of nonlinear terms. We will find a specific Lyapunov function in order to vanishing maximum perturbation of modeling error, aging or uncertainties which exist in this system. Using this method and appropriate Lyapunov function, we demonstrate there is an invariant polytope that for the set of perturbed initial conditions which belongs to such region, the convergence to the healthy state is guaranteed.