The Laplace Adomian Decomposition Method Approach to Analyze the Fractional Order Model for Transmission of Antibiotic Resistance from Animals to Humans

Abstract

Antimicrobial resistance (AMR) has emerged as one of the most critical global health 
challenges, threatening the sustainability of modern medicine and food security. It affects 
not only humans but also animals, plants, and the broader environment through interconnected 
ecological pathways. Animals, in particular, can act as reservoirs for multidrug-resistant 
(MDR) microorganisms, facilitating the transfer of resistant strains to humans through direct 
contact, environmental contamination, or the consumption of contaminated animal products. 
Understanding this complex transmission cycle is essential for developing effective control 
strategies. This study presents a mathematical investigation into the dynamics of 
antimicrobial resistance transmission between animals and humans using a fractional-order 
modeling approach. The model employs the Laplace Adomian Decomposition Method (LADM) 
to obtain an analytical approximation of the nonlinear fractional differential equations (FDEs) 
formulated with the Caputo fractional derivative. The fractional framework captures the 
memory and hereditary characteristics inherent in biological systems, offering a more 
realistic representation of infection dynamics compared to traditional integer-order models. 
The study establishes the existence, uniqueness, and stability of the proposed model’s 
solution, confirming its reliability for theoretical and numerical analysis. Furthermore, the 
model maintains dimensional consistency and reflects realistic transmission parameters that 
align with epidemiological observations. Numerical simulations and graphical illustrations are 
presented to elucidate the influence of fractional orders and key parameters on the spread 
of resistance. Finally, the outcomes derived from the LADM approach are compared with 
those obtained using the Differential Transform Method (DTM), demonstrating strong 
agreement and validating the accuracy and computational efficiency of the proposed 
technique. Overall, this study contributes a robust analytical tool for understanding and 
predicting the dynamics of antimicrobial resistance, thereby supporting the development of 
effective public health and veterinary interventions within the One Health framework.