Artificial neural networks for stability analysis and simulation of delayed rabies spread models

Rabies remains a significant public health challenge, particularly in areas with substantial dog populations, necessitating a deeper understanding of its transmission dynamics for effective control strategies. This study addressed the complexity of rabies spread by integrating two critical delay effects—vaccination efficacy and incubation duration—into a delay differential equations model, capturing more realistic infection patterns between dogs and humans. To explore the multifaceted drivers of transmission, we applied a novel framework using piecewise derivatives that incorporated singular and non-singular kernels, allowing for nuanced insights into crossover dynamics. The existence and uniqueness of solutions was demonstrated using fixed-point theory within the context of piecewise derivatives and integrals. We employed a piecewise numerical scheme grounded in Newton interpolation polynomials to approximate solutions tailored to handle singular and non-singular kernels. Additionally, we leveraged artificial neural networks to split the dataset into training, testing, and validation sets, conducting an in-depth analysis across these subsets. This approach aimed to expand our understanding of rabies transmission, illustrating the potential of advanced mathematical tools and machine learning in epidemiological modeling.