Mathematical Modeling of the Tumour Cell Growth and Immune System Interactions

Date of Award

Spring 4-2014

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

First Advisor

Fathalla Ali Rihan


This dissertation is concerned with mathematical modeling of the dynamics of tumour cells and immune system interactions. The models are based on a class of ordinary and delay differential equations with discrete time-lags. The main objectives are to examine the role of delay terms in the dynamics and investigate the qualitative behaviors of such models, using the stability of existing steady states and bifurcations analysis.

The main novelty of this study is to fit the suggested delay differential model to a class of observed data, of the B-cell lymphoma (BCL1) tumour cells growth that developed in the spleen of chimeric mice (in vivo), in order to evaluate the model parameters. The sensitivity functions are used to analyse the sensitivity of the number of tumour cells population with respect to the time delay, the normal source rate of effector cells (cytotoxic T-cells and natural killer cells), the death rate of effector cells, and the initial number of effector cells. Sensitivity analysis is an important tool for understanding a particular model, which is considered as an issue of stability with respect to the structural perturbations in the model. In addition, the immune-tumour interactions with the presence of HIV infection of CD4+ T-cells are considered.

In the model, the analysis is extended to include immunotherapy/chemotherapy treatments. The numerical simulations and obtained results are consistent with real cases and give a better understanding of cancer immunity.

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