Stability Analysis and Simulations of the Discrete-Time Cancer Epidemic Model

Year 2025, Volume: 8 Issue: 3, 148 - 160, 30.09.2025

Kemal Türk , Mehmet Gümüş

https://doi.org/10.33401/fujma.1696954

Abstract

Cancer is a major health problem worldwide. Mathematical models play a critical role in understanding the spread of the disease and the effects of treatment. In this study, a discrete version of a cancer model is developed using the Euler method. The conditions necessary for the discretized model's solutions to be non-negative and bounded are obtained. Six different equilibria are identified, and the feasibility conditions for these equilibria are established. Furthermore, the local asymptotic stability of each equilibrium is rigorously proved. Restrictions on the time-step size $h$ were derived to ensure the validity of the results, and simulations were performed to verify the stability behavior and the influence of the time-step size. The study established essential conditions for the discretization of mathematical models so as to preserve biological relevance and dynamical consistency. Moreover, the discrete formulation offers a flexible framework for the computational analysis of cancer dynamics and has the potential to inform future research directions.

Keywords

Cancer model , Euler method , Dynamical consistency , Stability , Numerical simulation

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