Travelling wave analysis of a model of the immune response to cancer

Anastasios Matzavinos, Mark A. J. Chaplain

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)


In this paper we present a travelling-wave analysis of a mathematical model describing the growth of a solid tumour in the presence of an immune system response. From a modelling perspective, attention is focused upon the attack of tumour cells by tumour infiltrating cytotoxic lymphocytes (TICLs), in a small multicellular tumour, without necrosis and at some stage prior to (tumour-induced) angiogenesis. As we have shown in previous work, for a particular choice of parameters, the underlying reaction?diffusion?chemotaxis system of partial differential equations is able to simulate the well-documented phenomenon of cancer dormancy by depicting spatially heterogeneous tumour cell distributions that are characterized by a relatively small total number of tumour cells. This behaviour is consistent with several immunomorphological investigations. Moreover, the alteration of certain parameters of the model is enough to induce bifurcations into the system, which in turn result in tumour invasion in the form of a standard travelling wave. The work presented in this paper complements the bifurcation analysis undertaken by Matzavinos et al. [Math. Med. Biol. IMA 21 (2004) 1?34] and establishes the existence of travelling-wave solutions for the system under discussion by promoting the understanding of the geometry of an appropriate phase space
Original languageEnglish
JournalComptes Rendus Biologies
Issue number11
Publication statusPublished - 2004


  • Travelling waves
  • Mathematical modelling
  • Partial differential equations
  • Cancer dormancy
  • Tumour cells
  • Bifurcations


Dive into the research topics of 'Travelling wave analysis of a model of the immune response to cancer'. Together they form a unique fingerprint.

Cite this