Fractional-Order Mathematical Modeling of Methicillin- Resistant Staphylococcus aureus Transmission in Hospitals

This article investigates the environmental contamination and antibiotic exposure effect on the transmission dynamics of the Methicillin-Resistant Staphylococcus aureus (MRSA) model in hospitals using the fractional Adams–Bashforth–Moulton Method (ABMM). This epidemic model simulates the dynamics of patient populations, bacterial contamination, and healthcare worker safety under varying conditions. This model provides critical insights into the interactions between hospital practices, environmental factors, and infection dynamics, demonstrating the importance of symmetry in balancing hospital admission and discharge rates to manage infection spread effectively. The analysis extends to the impact of environmental bacterial density and hospital admission rates on patient colonization. Increasing admission rates introduce more susceptible patients, exacerbating infection spread when bacterial density is high. Conversely, lower admission rates and bacterial density result in a more controlled infection environment. The model further investigates how varying discharge rates influence colonization dynamics, highlighting that effective discharge practices can mitigate infection spread, especially in high-bacterial density scenarios. It must be noted that this model is studied fractionally for the first time. Overall, this model provides critical insights into the interactions between hospital practices, environmental factors, and infection dynamics, offering valuable guidance for infection control strategies and hospital policy formulation. By adjusting fractional order constant (σ) values and analyzing different scenarios, this research aids in understanding and managing bacterial infections in healthcare settings. The proposed method is able to provide the results presented in the figures within this study considering the influence of many factors.