A Caputo fractional-order model for Foot-And-Mouth Disease with environmental transmission and intervention strategies

Abstract

This study develops a novel Caputo fractional-order model for Foot-and-Mouth Disease (FMD) that incorporates both direct animal-to-animal transmission and indirect environmental transmission pathways. The proposed SVEIQRB model integrates multiple intervention strategies, including vaccination, movement restriction, quarantine, biosecurity, surveillance, and culling. Using fractional-order derivatives, the model captures memory effects and hereditary properties inherent in disease dynamics, offering a more realistic representation than classical integer-order approaches. Analytical investigations establish the positivity, boundedness, and existence of unique solutions, alongside the derivation of the effective reproduction number R e . Local stability analysis of the disease-free equilibrium and Hyers–Ulam stability of the system are rigorously proven. Numerical simulations, employing an Adams–Bashforth–Moulton predictor–corrector scheme, demonstrate that fractional-order dynamics significantly influence outbreak trajectories and intervention efficacy. Sensitivity analysis identifies environmental transmission rate, vaccine efficacy, and viral shedding as key drivers of disease spread. The findings underscore the importance of integrated control strategies, particularly high-efficacy vaccination and environmental decontamination, for effective FMD management in endemic regions. • A Caputo fractional-order SVEIQRB model is developed for Foot-and-Mouth Disease dynamics. • Direct animal-to-animal and indirect environmental transmission pathways are jointly modeled. • Positivity, boundedness, stability, and Hyers–Ulam stability of the model are established. • Fractional-order dynamics significantly affect outbreak size and intervention performance. • Vaccination efficacy and environmental decontamination are key drivers of FMD control.