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.
The transmission dynamics of COVID-19 is investigated through the prism of the Atangana-Baleanu fractional model with acquired immunity. Harmonic incidence mean-type aims to drive exposed and infected populations towards extinction in a finite time frame. The reproduction number is calculated based on the next-generation matrix. A disease-free equilibrium point can be achieved globally using the Castillo-Chavez approach. Using the additive compound matrix approach, the global stability of endemic equilibrium can be demonstrated. Utilizing Pontryagin’s maximum principle, we introduce three control variables to obtain the optimal control strategies. Laplace transform allows simulating the fractional-order derivatives analytically. Analysis of the graphical results led to a better understanding of the transmission dynamics.
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