Mathematical Biomedicine: Examples

Mathematical biomedicine is an area of research where questions that arise in medicine are addressed by mathematical methods. Each such question needs first to be represented by a network with nodes that includes the biological entities that will be used to address the medical question. This network is then converted into a dynamical system for these entities, with parameters that need to be computed, or estimated. Simulations of the model are first used to validate the model, and then to address the specific question. I will give some examples, mostly from my recent work, including cancer drug resistance, side effects and metastasis, autoimmune diseases, and chronic and diabetic wounds, where the dynamical systems are PDEs. In each example, I will write explicitly the biological network, but will not the details of the corresponding PDE system.