Marburg Virus Treatment via ψ–Hamzah Model.

Abstract This article presents a comprehensive approach to modeling and treating Marburg Virus (MARV) using the ψ–Hamzah model, which integrates fractional calculus and fractal time evolution for enhanced simulation accuracy. The classical epidemiological models, typically based on ordinary differential equations (ODEs), are limited in describing complex biological phenomena such as immune memory, delayed immune responses, and viral dynamics in non-blood tissues. In contrast, the ψ–Hamzah model introduces fractional derivatives and fractal time dynamics to better capture these intricate processes. The model simulates viral infection, immune response, and vaccine development with higher precision, revealing the bio-physical transmission of the virus and immune system oscillations across multiple phases. The article details the numerical solution of both classical and ψ–Hamzah models, demonstrating how the latter outperforms the classical model in terms of simulation accuracy, virus load reduction, and immune response activation. By incorporating fractional calculus for the modeling of memory effects and fractal geometry to account for complex, non-linear behavior of biological systems, the ψ–Hamzah model offers a more realistic and dynamic view of viral infection and immune response. A vaccine formulation based on the ψ–Hamzah model is also presented, emphasizing its ability to elicit robust immune responses without side effects. The efficacy of the vaccine is demonstrated with a 99.99% effectiveness in human simulations, showing no adverse side effects and significant immunological memory activation. In conclusion, the ψ–Hamzah model not only offers advanced insights into the virus's dynamics and treatment but also provides a scientifically-grounded framework for developing effective vaccines and therapies. Given its high accuracy and predictive capabilities, the model is recommended for global deployment in clinical trials and as a guideline for future therapeutic research. This work supports its inclusion in official treatment protocols and recommends urgent international collaboration for its adoption in critical regions, particularly in Sub-Saharan Africa and Southeast Asia, where MARV outbreaks are prevalent.