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On the Markovian Approach for Modeling the Dynamics of Nosocomial Infections

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Abstract

We analyze the dynamics of nosocomial infections in intensive care units (ICUs) by using a Markov chain model. Since population size in the ICU is small, in contrast to previous studies, we concentrate on the analytical solution rather than using simulation. We investigate how changes in the system parameters affect to some important behavioral indicators of the spread of the pathogen. We also present an exact measure of the number of secondary cases of infection produced by one colonized patient.

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References

  • Andersson H, Britton T (2000) Stochastic epidemic models and their statistical analysis. Lecture notes in biostatistics, vol 151. Springer, New York

  • Allen LJS (2008) An introduction to stochastic epidemic models. In: Lecture notes in mathematics, vol 1945. Springer, Berlin, pp 81–130

  • Allen LJS, van den Driessche P (2013) Relations between deterministic and stochastic thresholds for disease extinction in continuous- and discrete-time infectious disease models. Math Biosci 243:99–108

    Article  Google Scholar 

  • Artalejo JR, Economou A, Lopez-Herrero MJ (2010) On the number of recovered individuals in the SIS and SIR stochastic epidemic models. Math Biosci 228:45–55

    Article  Google Scholar 

  • Artalejo JR, Lopez-Herrero MJ (2010) Quasi-stationarity and ratio of expectations: a comparative study. J Theor Biol 266:264–274

    Article  Google Scholar 

  • Artalejo JR, Economou A, Lopez-Herrero MJ (2012) Stochastic epidemic models revisited: analysis of some continuous performance measures. J Biol Dyn 6:189–211

    Article  Google Scholar 

  • Artalejo JR, Lopez-Herrero MJ (2013) On the exact measure of disease spread in stochastic epidemic models. Bull Math Biol 75:1031–1050

    Google Scholar 

  • Artalejo JR, Economou A, Lopez-Herrero MJ (2013) Stochastic epidemic models with random environment: quasi-stationarity, extinction and final size. J Math Biol 67:799–831

    Google Scholar 

  • Bacaër N, Gomes MGM (2009) On the final size of epidemics with seasonality. Bull Math Biol 71:1954–1966

    Article  Google Scholar 

  • Chamchod F, Ruan S (2012) Modeling the spread of methicillin-resistant staphylococcus aureus in nursing homes for elderly. PloS One 7:e29757

    Google Scholar 

  • Ciarlet PG (1989) Introduction to numerical linear algebra and optimization. Cambridge University Press, Cambridge

    Google Scholar 

  • Cooper BS, Medley GF, Scott GM (1999) Preliminary analysis of the transmission dynamics of nosocomial infections: stochastic and management effects. J Hosp Infect 43:131–147

    Article  Google Scholar 

  • Daley DJ, Gani J (1999) Epidemic modelling: an introduction, cambridge studies in mathematical biology 15. Cambridge University Press, Cambridge

    Google Scholar 

  • Diekmann O, Heesterbeek JAP (2000) Mathematical epidemiology of infectious diseases: model building, analysis and interpretation. Wiley series in mathematical and computational biology. Wiley, Chichester

    Google Scholar 

  • Diekmann O, Heesterbeek H, Britton T (2013) Mathematical tools for understnading infectious disease dynamics. Princeton University Press, Princeton

    Google Scholar 

  • Hotta LK (2010) Bayesian melding estimation of a stochastic SEIR model. Math Popul Stud 17:101–111

    Article  Google Scholar 

  • Keeling MJ, Rohani P (2008) Modeling infectious diseases in humans and animals. Princeton University Press, Princeton

    Google Scholar 

  • Keeling MJ, Ross JV (2008) On methods for studying stochastic disease dynamics. J R Soc Interface 5:171–181

    Article  Google Scholar 

  • Kondakci S, Dincer C (2011) Internet epidemiology: healthy, susceptible, infected, quarantined, and recovered. Secur Commun Netw 4:216–238

    Article  Google Scholar 

  • Kouokam E, Auger P, Hassan H, Tchuente M (2008) Effect of the number of patches in a multi-path SIRS model with fast migration of the basic reproduction rate. Acta Biotheor 56:75–86

    Article  Google Scholar 

  • Li J, Blakeley D, Smith? RJ (2011) The failure of R0. Comput Math Methods Med 527610:17

    Google Scholar 

  • McBryde ES, Pettitt AN, McElwain DLS (2007) A stochastic mathematical model of methicillin resistant Staphylococcus aureus transmission in an intensive care unit: predicting the impact of interventions. J Theor Biol 245:470–481

    Article  Google Scholar 

  • Pinto A, Aguiar M, Martins J, Stollenwerk N (2010) Dynamics of epidemiological models. Acta Biotheor 58:381–389

    Article  Google Scholar 

  • Roberts MG (2007) The pluses and minuses of R0. J R Soc Interface 4:946–961

    Google Scholar 

  • Ross JV (2011) Invasion of infectious diseases in finite homogeneous populations. J Theor Biol 289:83–89

    Article  Google Scholar 

  • Stone P, Wilkinson-Herbots H, Isham V (2008) A stochastic model for head lice infections. J Math Biol 56:743–763

    Article  Google Scholar 

Download references

Acknowledgements

The author is grateful to the referees for their constructive comments which were certainly helpful to improve the paper. This work was supported by the Government of Spain (Department of Science and Innovation) and the European Commission through project MTM 2011-23864.

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  1. Faculty of Mathematics, Complutense University of Madrid, 28040, Madrid, Spain

    Jesus R. Artalejo

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  1. Jesus R. Artalejo
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Correspondence to Jesus R. Artalejo.

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Artalejo, J.R. On the Markovian Approach for Modeling the Dynamics of Nosocomial Infections. Acta Biotheor 62, 15–34 (2014). https://doi.org/10.1007/s10441-013-9204-6

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  • DOI: https://doi.org/10.1007/s10441-013-9204-6

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