Stability and sensitivity analysis of tumor-induceimmune suppression with time delay

Abstract

Emerging biomedical evidences suggest that tumor has capacity not only to secrete immunesuppression but also attack effector cells. In this work, we present a delay model to study the dynamics of tumor, effector cells and TGF-β interaction with incorporation of tumor-derived macrophages for counterattack. The existence of stationary solutions of the model and their long time behaviors are obtained analytically. The analytical results reveal that tumor-free stationary solution is stable if the body cells do not proliferate excessively, and tumor-present stationary solution is asymptotically stable if the proliferation rate of effector cells is greater than its suppression by TGF-β otherwise is unstable. For an unstable scenario, we examine the sensitivity of model parameters to ascertain their role in tumor-immune escape. This effort indicates the reducing function for effector cells suppression and increasing functions for tumors elimination. The numerical results validate all the analytical results and reveal the optimum tumor elimination strategies with amplifying effect on effector cells performance.