A Thermostatted Kinetic Framework with Particle Refuge for the Modeling of Tumors Hiding

Abstract

Recently, thermostatted kinetic models have been proposed for the modeling of complex systems subjected to external force fields. This paper deals with the derivation of a generalized thermostatted k inetic framework, which incorporates particles refuge. From the qualitative viewpoint, the global in time existence and uniqueness of the so lution to the relative Cauchy problem, the time evolution of the moments of the solution, and the existence of stationary solutions are d iscussed. Applications refer to biological systems and especially to tumor-escape from immune system surveillance, indeed within this framework an mathematical model for the tumor- immune system competition is derived. Further research directions are outlined in the last section of the paper.