Dynamical analysis of tumor–dystrophin interaction model with impact of age of onset and staging

Abstract

In this research work, the authors present a mathematical model to study the biological interplay between tumor growth, dystrophin protein, and the impact of age of onset and staging through a system of ordinary differential equations (ODEs). An area that has not been thoroughly explored in mathematical biology. Initially, a simplified model examines the interplay between dystrophin and tumor growth, with analytical and numerical solutions verifying stability at equilibrium points. Subsequently, a more intricate model factoring in the age of onset and staging is developed, and stability is again demonstrated via analytical and numerical methods. In the final phase, a three-dimensional model is introduced, and the Picard–Lindelof theorem confirms the existence and uniqueness of solutions. Stability analysis demonstrates conditional stability at the equilibrium points. The Lyapunov function is used for global stability analysis to confirm that the system follows a predictable, stabilizing trajectory rather than being chaotic or oscillatory. Numerical simulations, executed using the fourth-order Rung–Kutta method, support the analytical results numerically as well as graphically.