Mathematical Modelling of the Immune Response to Cancer

  • Iona Kirsten Tough

Student thesis: Doctoral ThesisDoctor of Philosophy


The immune system’s vitality and function is of the upmost importance in the human body. The ingenuity and performance of this defence mechanism also plays a role in the prevention of mutated, transformed cells becoming malig- nant tumours (cancers). More recently, the subject of cancer immunology has been concerned with examining the local effects the immune system has on a pre-angiogenic tumour site. A recent immunological review article - “The Three Es of Cancer Immunoediting” - discusses the way the immune system interacts with cancer cells: elimination, equilibrium, and escape. This bio- logical explanation underpins the mathematical modelling in this PhD thesis where mathematical models of pre-angiogenic immune-tumour interactions are presented and analysed. Chapter two develops an individual-based model of immune-cancer cell interactions using the computational simulation plat- form, CompuCell3D, to extend an earlier spatio-temporal model of tumour dormancy (Matzavinos et al. [2004]). Chapter three investigates and analyses an ODE model of the interaction of two immune cells and two tumour cells. This model is extended to include spatial movement terms for the tumour and immune cells (in both one and two dimensions) and investigates the rich heterogeneous spatio-temporal dynamics of the system in the presence of a limit cycle in the reaction kinetics. Finally, chapter four extends the models in the previous two chapters by examining an individual based model of two immune cell populations interacting with two tumour cell populations.
Date of Award2017
Original languageEnglish
SupervisorMark Chaplain (Supervisor) & Raluca Eftimie (Supervisor)


  • Immune response
  • Mathematics
  • Cancer modelling

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