Analysis of virotherapy in solid tumor invasion
type: Item
instance of: scholarly article
title: Analysis of virotherapy in solid tumor invasion
zbMATH Open document ID: 1328.35252
author: Joseph Malinzi
author: P. Sibanda
author: Hermane Mambili-Mamboundou
published in: Mathematical Biosciences
publication date: 2015-09-01T00:00:00Z
review text: In this paper, two mathematical models for the dynamics of tumour growth in the presence of oncolytic viruses and immune system cells (cytotoxic T-cells) are developed and analysed. First, the authors present a spatially homogeneous system of ordinary differential equations: \[ \dot x=\sigma-x+\frac{\gamma_1 x z}{\eta_1+z}-\nu xz\quad\text{(cytotoxic T-cells)}, \] \[ \dot y=\alpha_1 y(1-\alpha_2 y)-\frac{\theta_1 zy}{\eta_2+z}\quad\text{(uninfected tumour cells)}, \] \[ \dot z=\beta_1 z(1-\beta_2 z)+\frac{\theta_2 z y}{\eta_2+z}-\mu xz\quad\text{(infected tumour cells)}. \] A linear stability analysis of stationary states is made; in a nutshell, tumour-free steady states are unstable, whereas -- at least in a specific, biologically sensible parameter situation -- a steady state reflecting tumour dormancy is asymptotically stable. Numerical simulations are given. The ODE model is extended to a spatially heterogeneous framework including diffusion of tumour and immune system cells as well as chemotaxis of the latter towards increasing concentrations of a specific signalling substance. It is assumed that cytotoxic T-cells are supplied only in a specific spatial subdomain to invade the cancerous tissue afterwards. The dynamics of the resulting reaction-diffusion system in one spatial dimension are numerically simulated using finite differences. In a simplified setting (e.g. neglecting chemotactic effects), travelling wave solutions are derived analytically.
reviewed by: Jonathan Zinsl
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 92C17
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 6477283
zbMATH Keywords: virotherapy
zbMATH Keywords: tumor-virus-immune interactions
zbMATH Keywords: oncolytic virus
zbMATH Keywords: traveling wave analysis
MaRDI profile type: Publication
full work available at URL: j.mbs.2015.01.015
OpenAlex ID: W2042627536
Wikidata QID: Q42158774
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DOI: 10.1016/J.MBS.2015.01.015
description: scientific article; zbMATH DE number 6477283