Applied Mathematics & Information Sciences

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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 kinetic framework, which incorporates particles refuge. From the qualitative viewpoint, the global in time existence and uniqueness of the solution to the relative Cauchy problem, the time evolution of the moments of the solution, and the existence of stationary solutions are discussed. Applications refer to biological systems and especially to tumor-escape from immune system surveillance, indeed within this framework an mathematical model for the tumorimmune system competition is derived. Further research directions are outlined in the last section of the paper.

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