Mathematical models of cancer drug resistance

Drug resistance is a primary obstacle in cancer treatment. In many patients who first respond well to treatment, relapse occurs within months. The question how to overcome drug resistance is currently explored in many clinical trials, by using combination of drugs, or by changing protocols of treatment. Mathematical model can be useful in explaining how resistance to cancer drug develops, and then suggesting how to overcome it with In this talk I will give several such examples. The mathematical models are represented by dynamical systems of PDEs for variables which are cells densities, concentrations of proteins (cytokines) and drugs, within a tumor; the tumor boundary is evolving in time, it is a free boundary, unknown in advance. The model is validated by comparison the simulations of the model with mice data. The drugs we shall consider are mostly immunotherapy, PD-1 and CTLA-4 inhibitors; these drugs, which were developed a few years ago, revolutionized the treatment of melanoma , lung cancer and other cancers, but have been associated with resistance.

Please email Veronica Ciocanel (ciocanel@math.duke.edu) for zoom link and password.