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

Diletta Burini; Elena De Angelis; Miroslaw Lachowicz

doi:10.2478/caim-2018-0018

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

Communications in Applied and Industrial Mathematics

Volume 9 (2018): Issue 2 (December 2018)

By: Diletta Burini, Elena De Angelis and Miroslaw Lachowicz

Open Access

|Dec 2018

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.

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Articles in this issue

DOI: https://doi.org/10.2478/caim-2018-0018 | Journal eISSN: 2038-0909

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Language: English

Page range: 106 - 118

Submitted on: Dec 1, 2017

Accepted on: Feb 5, 2018

Published on: Dec 19, 2018

Published by: Italian Society for Applied and Industrial Mathemathics

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Continuous--time Markov chain,

Related subjects:

Numerical and computational mathematics,

Applied mathematics

© 2018 Diletta Burini, Elena De Angelis, Miroslaw Lachowicz, published by Italian Society for Applied and Industrial Mathemathics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 9 (2018): Issue 2 (December 2018)