Chemo and immunotherapy effects on stability regions of tumor models

Abstract

This paper deals with the problem of estimating the regions of attraction (or Safe regions) of two well-known nonlinear tumor growth models by redefining each model as a set of independent artificial systems and utilizing the novel concept of individual invariance. The first model describes leukemia growth in the presence of chemotherapy where the stable tumor-free equilibrium point vanishes once the treatment is stopped, therefore, we define a safe region around the tumor-free equilibrium point. Then, we compute its region of attraction corresponding one treatment protocol. The second model, known as the Stepanova model, describes immune tumor interactions with chemo- and immunotherapy. First, an initial estimate of an invariant set around its tumor-free equilibrium without therapeutic effects is provided. The estimate is used in a second step to validate the invariant set for a higher-order model with chemo- and immunotherapy. Moreover, a parametric sensitivity analysis is carried out to study the effect of model parameter uncertainties on the size of the region of attraction (RoA) for both models. The proposed model restructuring and the associated analysis method prove to be accurate, scalable, and efficient. It allows for sensitivity analysis and an analytical description of the safe regions in tumor growth models giving an insightful look at the tumor dynamics in association with the treatment protocols.