Analysis of Convergence of Block Methods in Simulating Epidemic Diseases

Abstract

This research delves into a comprehensive examination of the application and convergence analysis of a newly developed block method for simulating epidemic models. The focal point of this study revolves around the derivation and implementation of a novel scheme, crafted through the utilization of power series polynomials, ensuring the fulfilment of essential properties. The formulation of the new scheme was rooted in the power series polynomial, a mathematical construct known for its versatility and precision. The rigorous validation process confirmed that the derived scheme satisfied the requisite properties, thereby establishing its theoretical soundness. The crux of the investigation lies in the practical application of this innovative scheme to simulate an epidemic model. Through meticulous simulations, the results yielded compelling evidence of the new method's superiority over existing approaches considered in this research. The comparative analysis demonstrated a notable enhancement in both accuracy and convergence speed, highlighting the efficacy of the newly proposed scheme in capturing and predicting the dynamics of epidemics. The observed advantages of the new scheme are particularly noteworthy, showcasing its potential to revolutionize the field of epidemiological modelling. By outperforming established methods, the new approach not only contributes to the theoretical underpinnings of epidemic modelling but also holds significant promise for practical applications, such as forecasting disease spread and optimizing intervention strategies.