A fractional-order model for nosocomial infection caused by Pseudomonas aeruginosa in Northern Cyprus.

Pseudomonas aeruginosa, a resilient gram-negative bacterium, poses a persistent threat as a leading cause of nosocomial infections, particularly in resource-constrained regions. Despite existing treatment and control measures, the bacterium continues to challenge healthcare systems, especially in developing nations. This paper introduces a fractional-order model to elucidate the dynamic behavior of nosocomial infections caused by P. aeruginosa and to compare the efficacy of carbapenems and aminoglycosides in treatment. The model's existence and uniqueness are established, and both global and local stability are confirmed. The effective reproduction number is computed, revealing an epidemic potential with a value of 1.02 in Northern Cyprus. Utilizing real-life data from a university hospital and employing numerical simulations, our results indicate that patients exhibit higher sensitivity and lower resistance to aminoglycoside treatment compared to carbapenems. Aminoglycosides consistently outperform carbapenems across key metrics, including the reduction of susceptible population, infection numbers, treatment efficacy, total infected population, hospital occupancy, and effective reproduction number. The fractional-order approach emerges as a suitable and insightful tool for studying the transmission dynamics of the disease and assessing treatment effectiveness. This research provides a robust foundation for refining treatment strategies against P. aeruginosa infections, contributing valuable insights for healthcare practitioners and policymakers alike.