Modeling Antibiotic-Resistant Infections at Fractional Order

Antibiotic resistance is a serious public health problem because it causes increased human morbidity and mortality from resistant diseases. The goal of this study is to better understand the complicated links between antibiotic use and the formation of resistant bacterial strains. A four-state model for community-acquired antibiotic resistance is constructed, which includes both forward and backward mutation processes, as well as an additional compartment for antibiotic supply modified by usage. The model is examined using the context of the hybrid fractional-order derivative. The study analyzes the well-posedness aspects of the hybrid fractional-order model, as well as stability results, with a focus on the use of Volterra-type Lyapunov functions for equilibrium states. The Lipschitz condition guarantees uniqueness, and computational simulations with the Laplace–Adomian decomposition technique investigate the fractional operator’s influence. The model’s behavior is investigated using sensitivity and chaos analysis of the solution in a bounded domain. Simulation results with a constant proportional Caputo operator demon-strate the impact of different fractional-order values. The study aims to improve understanding of bacterial illnesses by comparing the results with the Caputo fractional operator, supporting observations related to health phenomena. The incorporation of fractional calculus enhances the reliability of the proposed model for improving public health interventions and policies.