Assessment of Brucellosis Dynamics Through Fractional-Order Models with Empirical Validation

Abstract

The study represents a comprehensive fractional-order modeling framework for the transmission dynamics of brucellosis, incorporating Caputo–Fabrizio (CF) and Atangana–Baleanu in Caputo (ABC) sense operators. The primary objective is to investigate how different fractional operators and derivative orders influence the temporal progression and long-term persistence of brucellosis. To achieve this, we estimate the model parameters using the least-squares method, calibrated against real epidemiological data from mainland China. We also provide a qualitative analysis establishing the existence and uniqueness of solutions under the CF and ABC formulations. For numerical simulations, we implement the Adams–Bashforth predictor–corrector method and employ it across a range of fractional orders to visualize the evolution of all model compartments. Through comparative analysis, we find that fractional models capture memory effects more effectively than the classical approach, with the ABC operator yielding the closest fit to observed data. These findings underscore the effectiveness of fractional operators in modeling the chronic and persistent behavior of brucellosis. © 2026 NSP.