A general framework for modeling tumor-immune system competition at the mesoscopic level |
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Authors: | M Lachowicz A Quartarone |
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Institution: | 1. Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland;2. Scienze Matematiche e Informatiche, Universitá di Messina, Dipartimento di Matematica, Viale F. Stagno D’Alcontres, 98166 Messina, Italy |
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Abstract: | We propose a class of nonlinear integro-differential equations that at the mesoscopic level models the competition between a tumor and the immune system. The model describes the evolution of a distribution function of the microscopic parameter referred to as activity of cells. The idea is somehow similar to the Enskog theory in kinetic theory. By averaging with respect to the parameter, the mesoscopic class of models reduces to the general class of macroscopic models introduced by A. d’Onofrio that may assess the effect of delays in stimulation of the immune system by tumor cells. The existence and uniqueness theory is developed. |
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