On a Nonlinear System Modeling Darwinian Dynamics and the Immune Response to Cancer Evolution

Bellouquid, Abdelghani; Ch-Chaoui, Mohamed; Elena, De Angelis

doi:10.1142/9789813141919_0017

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“…We use a low proliferation rate of the immune cells (p 21 = 0.1) in the simulation. These parameters values were used in previous studies as well (Afraites, Atlas, Bellouquid, CH-Chaoui, 2012;Bellouquid & Delitala, 2006;Bellomo & Delitala, 2008;Bellouquid, CH-Chaoui, & De Angelis, 2015). All simulations are performed with the following nonzero initial conditions, unless otherwise noted:…”

Section: Numerical Studymentioning

confidence: 99%

Activation of the immune response by cytokines and its effect on tumour cells: a mathematical model

Ch-Chaoui¹,

Eladdadi

Mokni³

2018

Letters in Biomathematics

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In this paper, we present a mathematical model at the cellular level of the tumour-immune competition mediated by the cytokines. The model consists of a system of nonlinear differential equations describing the intracellular interactions between the tumour and the immune cells in the presence of the cytokines. A detailed phenomenological description of the model based on the kinetic theory for active particle approach is carried out to formulate the model. Well-posedness is presented to establish local and global existence. Numerical simulations are addressed to show how initial conditions and model parameters influence the output of the model. Under a suitable choice of the model's key parameters and the cytokines' initial activation levels, the simulation results show that the activated immune system is able to achieve a total elimination of the cancer cells.

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Section: Numerical Studymentioning

confidence: 99%