Politecnico di Torino
Conventional mathematical models of tumor growth exist in the framework of continuum mechanics. In this framework the system is modeled with diffusion equations, considering an accidental and/or directed spread of tumor cells depending on the state of the disease.
The interaction between the tumor cells, the host environment and the immune cells occurs at a cellular level. Models considering these interactions at a microscopic level with the goal to derive macroscopic observables, such as tumor size can be derived from kinetic theory.
We will present a model for the competition between tumor cells and the immune system in the form of an initial value problem for a non linear system of integro-differential equations. The integral term stems from the averaging over the various states of the cells within the tumor or immune cell population, while the differential operator describes the evolution of the system.1998-1999 Mathematics in Biology