Optimal control analysis for a Candida auris nosocomial infection model with environmental transmission

In this paper, we propose a mathematical model to investigate the role of environmental reservoirs in the transmission dynamics of the rising Candida auris infections in nosocomial settings. The ability of the pathogen to resist commonly used hospital disinfectants ensures its persistent contamination of hospital surfaces and medical equipment readily leading to patient colonization. Colonized patients shed the pathogen into their surroundings thereby increasing the fungal concentration in the hospital environment. We analyze the model for its basic mathematical properties, perform sensitivity analysis, and formulate an optimal problem to determine the efficiency of control interventions, namely, standard transmission precautions, proper laboratory identification, and isolation of patients identified with colonization in reducing the contamination and transmission of C. auris infections. We characterize the optimal controls using Pontryagin's Minimum Principle and further prove the uniqueness of the optimality system. Numerical simulations are performed to substantiate the theoretical analysis, and the results are illustrated graphically.