Application of the Variational Iteration Method in Modelling Tumour–Immune System Interactions Involving White Blood Cell Dynamics
DOI:
https://doi.org/10.63561/jmns.v2i4.1119Keywords:
Tumor-immune modeling, white blood cells, Partial differential equations, MATLAB simulation, Variational Iteration MethodAbstract
Understanding how tumour cells interact with the immune system is a key focus in modern mathematical oncology, especially given cancer’s continuing global impact. This study presents a mathematical framework designed to explore how white blood cell (WBC) activity influences tumour progression. The model uses a coupled nonlinear reaction diffusion system to capture both the spatial and temporal dynamics of tumour immune interactions. To solve this complex system, the Variational Iteration Method (VIM) is applied, providing efficient semi-analytical approximations, while stability analysis identifies conditions for tumour elimination or persistence. Numerical simulations show that WBC concentration plays a pivotal role: low immune cell counts lead to rapid tumour growth, whereas higher levels slow tumour expansion. The model also reveals a two-phase tumour behaviour, with an initial period of immune-mediated suppression followed by gradual mass increase, reflecting the transition from immune control to tumour dominance. Overall, this approach highlights the delicate balance between tumour proliferation, immune response, and microenvironmental influences. These findings underscore the potential of mathematical modelling to inform treatment strategies and contribute to the advancement of precision oncology.
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