International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

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.

References

  1. Austin D.J. and Anderson R.M. (1999)., Studies of antibiotic resistance within the patient, hospitals and the community using simple mathematical models., Philos. Trans. R Soc. Lond. B Biol. Sci., 354 (1384), 721-738.
  2. D’Agata E.M., Webb G. and Horn M. (2005)., A mathematical model quantifying the impact of antibiotic exposure and other interventions on the endemic prevalence of vancomycin-resistant enterococci., J. Infect. Dis. 192(11), 2004-2011.
  3. Capasso V. (2008)., Lecture Notes in Biomathematics: Mathematical Structures of Epydemic Systems., Milan : Springer.
  4. CDC, Centers for Disease Control and Prevention. (2012). Healthcare-associ¬ated Infections (HAIs). Available from: http://www.cdc. gov/HAI/surveillance., undefined, undefined
  5. CDC, Centers for Disease Control and Prevention. (2015). Healthcare-associ¬ated Infections (HAIs). Available from: http://www.cdc. gov/HAI/surveillance., undefined, undefined
  6. Choi B. and Pak A. (2003)., A simple approximate mathematical model to predict the number of severe acute respiratory syndrome cases and deaths., J. Epi. Comm. Health, 57(10), 831-835.
  7. Ducel G. (2002)., Prevention of Hospital-Acquired Infections, A practical guide., Second edition.World Health Organization.Department of Communicable Disease, Surveillance and Response. Geneva.
  8. McBryde Emma (2006)., Mathematical and Statistical Modelling of Infectious Diseases in Hospitals., PhD Thesis, QUT, Australia.
  9. Grundmann H. and Hellriegel B. (2006)., Mathematical Modelling: a Tool for Hospital Infection Control., The Lancet Infectious Disease, 6(1), 39-45
  10. van Kleef E., Robotham J.V., Jit M., Deeny S.R. and Edmunds W.J. (2013)., Modelling the transmission of healthcare associated infections: a systematic review., BMC Infectious Diseases, 13(1), 294-307.
  11. Klevens R.M, Edwards J.R. Richards C.L. Jr, Horan T. C., Gaynes R.P., Pollock D.A. and Cardo D. M. (2007)., Estimating health care-associated infections and deaths in U.S. hospitals., Public Health Rep., 122(2), 160-166.
  12. LaSalle J.P. (1976)., The Stability of Dynamical Systems., SIAM, Philadelphia, USA.
  13. Light R.W. (2001)., Infectious Disease, Nosocomial Infection, Harrison’s Principle of Internal Medicine, 15 Edition., CD Room.
  14. Lowy F.D. (2003)., Antimicrobial resistance: the example of Staphylococcus aureus., J. Clin. Invest., 111(9), 1265-1273.
  15. McBryde E.S., Bradley L.C., Whitby M. and McElwain D.L.S. (2004)., An investigation of contract transmision of methicillin resistant Staphylococcus aures., The Journal of Hospital Infection, 58(2), 104-108.
  16. McBryde E.S., Pettitt A.N. and McElwain D.L.S. (2007)., A stochastic mathematical model of methicillin resistant Staphylococcus aureus transmission in an intensive care unit: Predicting the impact of interventions., Journal of Theoretical Biology, 245(3), 470-481.
  17. Murray J.D. (2002). Mathematical Biology: I. An Introduction, Third Edition. Washington, Springer., undefined, undefined
  18. Synder E.H. (2013)., A Mathematical Model for Antibiotic Resistance in a Hospital Setting with a Varying Population., East Tenesse State University.
  19. Vincent J.L., Rello J., Marshall J., Silva E., Anzueto A, Martin C. D., Moreno R., Lipman J., Gomersall C., Sakr Y. and Reinhart K. (2009)., International study of the prevalence and outcomes of infection in intensive care units., JAMA, 302(21), 2323-2329.
  20. Waaler H., Geser A. and Anderson S. (1962)., The use of mathematical models in the study of epidemiology of tuberculosis., Am. J. Public Health, 52(6), 1002-1013.
  21. WHO. (2002)., Prevention of Hospital-Acquired Infections: Practical Guide., 2nd Edition. Malta: WHO/CDS/CSR/EPH
  22. WHO.(2009)., WHO guidelines on hand hygiene in health care. Geneva., World Health Organization.
  23. WHO.(2012)., WHO guidelines on hand hygiene in health care. Geneva.,