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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Individual based models and differential equations models of nosocomial epidemics in hospital intensive care units

Pages: 1145 - 1166, Volume 22, Issue 3, May 2017      doi:10.3934/dcdsb.2017056

 
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Glenn F. Webb - Mathematics Department, Vanderbilt University, Nashville, TN 37240, United States (email)

Abstract: Mathematical models of antibiotic resistant infection epidemics in hospital intensive care units are developed with two modeling methods, individual based models and differential equations based models. Both models dynamically track uninfected patients, patients infected with a nonresistant bacterial strain not on antibiotics, patients infected with a nonresistant bacterial strain on antibiotics, and patients infected with a resistant bacterial strain. The outputs of the two modeling methods are shown to be complementary with respect to a common parameterization, which justifies the differential equations modeling approach for very small patient populations present in an intensive care unit. The model outputs are classified with respect to parameters to distinguish the extinction or endemicity of the bacterial strains. The role of stewardship of antibiotic use is analyzed for mitigation of these nosocomial epidemics.

Keywords:  Epidemic model, antibiotic resistance, asymptotic stability, Lyapunov functional, invariance principal.
Mathematics Subject Classification:  Primary: 92C50, 92C60; Secondary: 34D20.

Received: September 2015;      Revised: December 2016;      Available Online: January 2017.

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