Mathematical Analysis on Transmission of Nosocomial Infection Applying Combination Therapy

• Published in: Journal of applied mathematics Vol. 2025; no. 1
• Main Authors: Rokib, Saiful Islam, Hossain, Shahadat, Malek, Maria Binte, Ruhi, Fariha Akter, Mallick, Uzzwal Kumar
• Format: Journal Article
• Language: English
• Published: New York John Wiley & Sons, Inc 01.01.2025; Wiley
• Subjects: Antibiotics; Bacteria; Bacterial infections; Care and treatment; Combination therapy; Differential equations; Disease; Drug resistance; Drug resistance in microorganisms; Epidemics; Epidemiology; Health aspects; Health care; Hospital patients; Hospitalization; Hospitals; Infection; Mathematical analysis; Mathematical models; Medical care, Cost of; Medical personnel; Nosocomial infections; Numerical analysis; Ordinary differential equations; Pathogens; Plasmids; Public health; Surgery; China
• ISSN: 1110-757X; 1687-0042
• DOI: 10.1155/jama/3002490

Nosocomial infections, such as those caused by carbapenem‐resistant Klebsiella pneumoniae (CRKP) transmitted into hospitals, worsen patient outcomes, strain healthcare infrastructure, increase treatment costs, prolong hospital stays, and complicate medical treatment due to their high level of antibiotic resistance. Taking into account these detrimental aspects, this study deals with a dynamic system of nonlinear differential equations with maintenance preventive strategies, and treatment applying combination therapy has been considered to prevent CRKP transmission and reduce antibiotic resistance while accounting for two hospital populations. The analytical analysis includes positivity, boundedness, existence of a unique solution, stability at equilibrium points, reproduction number ( R 0 ), sensitivity, and convergence of state variables. And, the numerical simulations were performed using the fourth‐order Runge–Kutta method. We find that the proper implementation of hygiene practices among hospitalized patients and the consistent use of personal protective equipment (PPE) by healthcare workers play an important role in preventing CRKP transmission in hospitals. Additionally, applying combination therapy as a treatment approach for CRKP reduces antibiotic resistance. Consequently, this improves hospital safety and ensures a healthier environment by minimizing the spread of infectious agents and reducing the risks of nosocomial infections.