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Stability analysis for the spread of health care-associated infection (HCAI) with and without self infection and control

Author Affiliations

  • 1Mathematics Department, Faculty of Mathematics and Sciences, Halu Oleo University, Kendari, Indonesia

Res. J. Mathematical & Statistical Sci., Volume 5, Issue (5), Pages 1-8, May,12 (2017)

Abstract

Patients during the course of their medical treatment in a hospital often contract healthcare-associated infections (HCAI) or hospital-acquired infections (HAI). Such infection has seriously become concerned in hospital management since many nosocomial infections have caused health care expenses increasing due to lengthened hospital stay and morbidity. In this study, we develop a mathematical model describing the spread of HCAI and discuss the dynamic behaviour of its solution. There are four type models developed; i.e., with cross infection only and self-cross infection, both are studied under with and without control. All models have a disease-free equilbrium and a positive endemic equilibrium.We derive a threshold condition for each model in which above the threshold the presence of a HCAI is able to spread in the unit care, otherwise, if below the threshold condition the infection is died out.The threshold condition is defined as the basic reproductive number. Numerical experiments show how the dynamics of HCAI is changing as several model parameters below and above threshold condition for each model.

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