Unveiling Rift valley fever dynamics using fractional SEIRV models and Gegenbauer wavelet analysis

This study introduces a novel fractional-order SEIRV model to explore the transmission dynamics of Rift Valley Fever (RVF) by incorporating the complex interactions between human, animal, and mosquito populations. The model employs Caputo fractional derivatives to effectively capture the memory-dependent nature of disease spread, allowing a more realistic representation of temporal dynamics. A key methodological advancement in this work is the implementation of the Gegenbauer Wavelet Collocation Method (GWCM), which enables highly accurate and computationally efficient numerical solutions to the nonlinear system. A new operational matrix of integration is developed and utilized within this framework. The stability and accuracy of the method are validated through a rigorous convergence analysis. Comparative numerical simulations demonstrate that the proposed method outperforms traditional solvers in precision and error reduction. In addition to numerical validation, the model investigates the effects of various transmission pathways and intervention strategies, highlighting how fractional dynamics can alter disease control outcomes. The proposed approach provides a powerful and flexible framework for modeling vector-borne zoonotic diseases, integrating fractional calculus and wavelet-based numerical analysis.