Source_Data.zip

<b>Fully-discrete Lyapunov-consistent discretizations for the simulation of reaction-diffusion phenomena: applications to epidemiology and oncolytic virotherapy</b>Reaction-diffusion equations model various biological, physical, sociological, and environmental phenomena. Often, numerical simulations are used to understand and discover the dynamics of such systems. Following the extension of the nonlinear Lyapunov theory applied to some class of reaction-diffusion partial differential equations, we develop the first fully-discrete Lyapunov discretizations that are consistent with the stability properties of the continuous parabolic reaction-diffusion models. The new schemes are applied to solve systems of partial differential equations, which arise in epidemiology and oncolytic M1 virotherapy. In particular, the results of oncolytic M1 virotherapy reveal a significant reduction in tumor size, ultimately leading to its complete disappearance, potentially preventing the necessity for supplementary treatments like chemo-radiation or surgery. The new computational framework provides physically consistent and accurate results without exhibiting scheme-dependent instabilities and converging to unphysically solutions. The proposed algorithms represent a capstone for developing efficient, robust, and predictive technologies for simulating complex phenomena.