A fractional–order MRSA transmission model: theoretical analysis and screening strategy comparison

Hospital outbreaks of methicillin-resistant Staphylococcus aureus (MRSA) remain difficult to contain because both patients and healthcare workers can carry and transmit the bacterium, often without symptoms. A Caputo fractional-order model is developed to capture this transmission process at hospital admission and discharge, partitioning the hospital population into uncolonized, colonized, and infected patients, uncontaminated and contaminated healthcare workers, and screened community members classified as flagged or unflagged. The framework is used to compare admission-based against discharge-based screening across several coverage levels. Before any simulation is attempted, the underlying mathematics is examined in detail: recasting the system as an equivalent Volterra integral equation shows that the total hospital census is conserved, that nonnegative initial data produce nonnegative and bounded trajectories, and that a unique solution exists for every admissible initial condition. This solution is shown to depend continuously on both the initial data and the model parameters, the Picard iteration used in its construction converges geometrically, and the system possesses at least one equilibrium state. Having established this analytical foundation, the model is integrated numerically by means of the fractional Adams–Bashforth–Moulton predictor–corrector scheme. The resulting simulations indicate that consistent hygiene and isolation practices progressively suppress transmission: colonized and infected patient numbers decline, contamination among healthcare workers peaks early before receding under sustained protocols, and isolation-unit occupancy falls as fewer patients require it. Once adopted consistently, screening at either admission or discharge stabilizes the flagged-patient population, underscoring the value of the fractional-order framework for anticipating hospital infection trends.