Mathematical and Numerical Modelling of Interference of Immune Cells in the Tumour Environment


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Sinha S., Singh P., Köksal M. E.

DISCRETE DYNAMICS IN NATURE AND SOCIETY, vol.2023, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2023
  • Publication Date: 2023
  • Doi Number: 10.1155/2023/9006678
  • Journal Name: DISCRETE DYNAMICS IN NATURE AND SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this article, the behaviour of tumour growth and its interaction with the immune system have been studied using a mathematical model in the form of partial differential equations. However, the development of tumours and how they interact with the immune system make up an extremely complex and little-understood system. A new mathematical model has been proposed to gain insight into the role of immune response in the tumour microenvironment when no treatment is applied. The resulting model is a set of partial differential equations made up of four variables: the population density of tumour cells, two different types of immune cells (CD4+ helper T cells and CD8+ cytotoxic T cells), and nutrition content. Such kinds of systems also occur frequently in science and engineering. The interaction of tumour and immune cells is exemplified by predator-prey models in ecology, in which tumour cells act as prey and immune cells act as predators. The tumour-immune cell interaction is expressed via Holling's Type-III and Beddington-DeAngelis functional responses. The combination of finite volume and finite element method is used to approximate the system numerically because these approximations are more suitable for time-dependent systems having diffusion. Finally, numerical simulations show that the methods perform well and depict the behaviour of the model.