<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In the present paper we propose two mathematical models describing, respectively at the microscopic level and at the mesoscopic level, a system of interacting tumor cells and cells of the immune system. The microscopic model is in terms of a Markov chain defined by the generator, the mesoscopic model is developed in the framework of the kinetic theory of active particles. The main result is to prove the transition from the microscopic to mesoscopic level of description.</p></abstract>

In the present paper we propose two mathematical models describing, respectively at the microscopic level and at the mesoscopic level, a system of interacting tumor cells and cells of the immune system. The microscopic model is in terms of a Markov chain defined by the generator, the mesoscopic model is developed in the framework of the kinetic theory of active particles. The main result is to prove the transition from the microscopic to mesoscopic level of description.

A Continuous–Time Markov Chain Modeling Cancer–Immune System Interactions

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In the present paper we propose two mathematical models describing, respectively at the microscopic level and at the mesoscopic level, a system of interacting...

A Continuous–Time Markov Chain Modeling Cancer–Immune System Interactions

Publié en ligne: 19 déc. 2018

Pages: 106 - 118

Reçu: 01 déc. 2017

Accepté: 05 févr. 2018

DOI: https://doi.org/10.2478/caim-2018-0018

Mots clés
Continuous--time Markov chain, Microscopic models, Mesoscopic model, KTAP theory, Cancer cells, Immune system

© 2018 Diletta Burini, et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

A Continuous–Time Markov Chain Modeling Cancer–Immune System Interactions

Publié en ligne: 19 déc. 2018

Pages: 106 - 118

Reçu: 01 déc. 2017

Accepté: 05 févr. 2018

DOI: https://doi.org/10.2478/caim-2018-0018

Mots clésContinuous--time Markov chain, Microscopic models, Mesoscopic model, KTAP theory, Cancer cells, Immune system

© 2018 Diletta Burini, et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
Continuous--time Markov chain, Microscopic models, Mesoscopic model, KTAP theory, Cancer cells, Immune system