2015, 12(4): 761-787. doi: 10.3934/mbe.2015.12.761

A nosocomial epidemic model with infection of patients due to contaminated rooms

1. 

Mathematics Department, Vanderbilt University, Nashville, TN 37240, United States, United States

Received  May 2014 Revised  January 2015 Published  April 2015

A model of epidemic bacterial infections in hospitals is developed. The model incorporates the infection of patients and the contamination of healthcare workers due to environmental causes. The model is analyzed with respect to the asymptotic behavior of solutions. The model is interpreted to provide insight for controlling these nosocomial epidemics.
Citation: Cameron Browne, Glenn F. Webb. A nosocomial epidemic model with infection of patients due to contaminated rooms. Mathematical Biosciences & Engineering, 2015, 12 (4) : 761-787. doi: 10.3934/mbe.2015.12.761
References:
[1]

M. Bani-Yaghoub, R. Gautam, Z. Shuai, P. van den Driessche and R. Ivanek, Reproduction numbers for infections with free-living pathogens growing in the environment,, Journal of biological dynamics, 6 (2012), 923.

[2]

H. Freedman, S. Ruan and M. Tang, Uniform persistence and flows near a closed positively invariant set,, Journal of Dynamics and Differential Equations, 6 (1994), 583. doi: 10.1007/BF02218848.

[3]

D. T. Gillespie, Exact stochastic simulation of coupled chemical reactions,, The journal of physical chemistry, 81 (1977), 2340. doi: 10.1021/j100540a008.

[4]

E. S. McBryde and D. L. McElwain, A mathematical model investigating the impact of an environmental reservoir on the prevalence and control of vancomycin-resistant enterococci,, Journal of Infectious Diseases, 193 (2006), 1473. doi: 10.1086/503439.

[5]

M. McKenna, Clean sweep,, Scientific American, 307 (2012), 30. doi: 10.1038/scientificamerican0912-30.

[6]

D. J. Morgan, E. Rogawski, K. A. Thom, J. K. Johnson, E. N. Perencevich, M. Shardell, S. Leekha and A. D. Harris, Transfer of multidrug-resistant bacteria to healthcare workers? gloves and gowns after patient contact increases with environmental contamination,, Critical care medicine, 40 (2012), 1045. doi: 10.1097/CCM.0b013e31823bc7c8.

[7]

S. Nseir, C. Blazejewski, R. Lubret, F. Wallet, R. Courcol and A. Durocher, Risk of acquiring multidrug-resistant gram-negative bacilli from prior room occupants in the intensive care unit,, Clinical Microbiology and Infection, 17 (2011), 1201. doi: 10.1111/j.1469-0691.2010.03420.x.

[8]

W. H. Organization et al., Antimicrobial Resistance: Global Report on Surveillance 2014., geneva, (2014).

[9]

S. Petti, G. A. Messano, A. Polimeni and S. J. Dancer, Effect of cleaning and disinfection on naturally contaminated clinical contact surfaces,, Acta stomatologica Naissi, 29 (2013), 1265. doi: 10.5937/asn1367265P.

[10]

N. Plipat, I. H. Spicknall, J. S. Koopman and J. N. Eisenberg, The dynamics of methicillin-resistant staphylococcus aureus exposure in a hospital model and the potential for environmental intervention,, BMC infectious diseases, 13 (2013). doi: 10.1186/1471-2334-13-595.

[11]

Z. Shuai, J. Heesterbeek and P. van den Driessche, Extending the type reproduction number to infectious disease control targeting contacts between types,, Journal of mathematical biology, 67 (2013), 1067. doi: 10.1007/s00285-012-0579-9.

[12]

Z. Shuai and P. van den Driessche, Global stability of infectious disease models using lyapunov functions,, SIAM Journal on Applied Mathematics, 73 (2013), 1513. doi: 10.1137/120876642.

[13]

H. L. Smith, The Theory of the Chemostat: Dynamics of Microbial Competition, vol. 13,, Cambridge university press, (1995). doi: 10.1017/CBO9780511530043.

[14]

P. Strassle, K. A. Thom, J. K. Johnsonm, S. Leekha, M. Lissauer, J. Zhu and A. D. Harris, The effect of terminal cleaning on environmental contamination rates of multidrug-resistant< i> acinetobacter baumannii< /i>,, American journal of infection control, 40 (2012), 1005.

[15]

PBS, PBS frontline: Hunting the nightmare bacteria, 2013,, URL , ().

[16]

P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Mathematical biosciences, 180 (2002), 29. doi: 10.1016/S0025-5564(02)00108-6.

[17]

X. Wang, Y. Xiao, J. Wang and X. Lu, A mathematical model of effects of environmental contamination and presence of volunteers on hospital infections in china,, Journal of theoretical biology, 293 (2012), 161. doi: 10.1016/j.jtbi.2011.10.009.

[18]

X. Wang, Y. Xiao, J. Wang and X. Lu, Stochastic disease dynamics of a hospital infection model,, Mathematical biosciences, 241 (2013), 115. doi: 10.1016/j.mbs.2012.10.002.

[19]

M. Wolkewitz, M. Dettenkofer, H. Bertz, M. Schumacher and J. Huebner, Environmental contamination as an important route for the transmission of the hospital pathogen vre: modeling and prediction of classical interventions,, Infectious Diseases: Research and Treatment, 1 (2008), 3.

show all references

References:
[1]

M. Bani-Yaghoub, R. Gautam, Z. Shuai, P. van den Driessche and R. Ivanek, Reproduction numbers for infections with free-living pathogens growing in the environment,, Journal of biological dynamics, 6 (2012), 923.

[2]

H. Freedman, S. Ruan and M. Tang, Uniform persistence and flows near a closed positively invariant set,, Journal of Dynamics and Differential Equations, 6 (1994), 583. doi: 10.1007/BF02218848.

[3]

D. T. Gillespie, Exact stochastic simulation of coupled chemical reactions,, The journal of physical chemistry, 81 (1977), 2340. doi: 10.1021/j100540a008.

[4]

E. S. McBryde and D. L. McElwain, A mathematical model investigating the impact of an environmental reservoir on the prevalence and control of vancomycin-resistant enterococci,, Journal of Infectious Diseases, 193 (2006), 1473. doi: 10.1086/503439.

[5]

M. McKenna, Clean sweep,, Scientific American, 307 (2012), 30. doi: 10.1038/scientificamerican0912-30.

[6]

D. J. Morgan, E. Rogawski, K. A. Thom, J. K. Johnson, E. N. Perencevich, M. Shardell, S. Leekha and A. D. Harris, Transfer of multidrug-resistant bacteria to healthcare workers? gloves and gowns after patient contact increases with environmental contamination,, Critical care medicine, 40 (2012), 1045. doi: 10.1097/CCM.0b013e31823bc7c8.

[7]

S. Nseir, C. Blazejewski, R. Lubret, F. Wallet, R. Courcol and A. Durocher, Risk of acquiring multidrug-resistant gram-negative bacilli from prior room occupants in the intensive care unit,, Clinical Microbiology and Infection, 17 (2011), 1201. doi: 10.1111/j.1469-0691.2010.03420.x.

[8]

W. H. Organization et al., Antimicrobial Resistance: Global Report on Surveillance 2014., geneva, (2014).

[9]

S. Petti, G. A. Messano, A. Polimeni and S. J. Dancer, Effect of cleaning and disinfection on naturally contaminated clinical contact surfaces,, Acta stomatologica Naissi, 29 (2013), 1265. doi: 10.5937/asn1367265P.

[10]

N. Plipat, I. H. Spicknall, J. S. Koopman and J. N. Eisenberg, The dynamics of methicillin-resistant staphylococcus aureus exposure in a hospital model and the potential for environmental intervention,, BMC infectious diseases, 13 (2013). doi: 10.1186/1471-2334-13-595.

[11]

Z. Shuai, J. Heesterbeek and P. van den Driessche, Extending the type reproduction number to infectious disease control targeting contacts between types,, Journal of mathematical biology, 67 (2013), 1067. doi: 10.1007/s00285-012-0579-9.

[12]

Z. Shuai and P. van den Driessche, Global stability of infectious disease models using lyapunov functions,, SIAM Journal on Applied Mathematics, 73 (2013), 1513. doi: 10.1137/120876642.

[13]

H. L. Smith, The Theory of the Chemostat: Dynamics of Microbial Competition, vol. 13,, Cambridge university press, (1995). doi: 10.1017/CBO9780511530043.

[14]

P. Strassle, K. A. Thom, J. K. Johnsonm, S. Leekha, M. Lissauer, J. Zhu and A. D. Harris, The effect of terminal cleaning on environmental contamination rates of multidrug-resistant< i> acinetobacter baumannii< /i>,, American journal of infection control, 40 (2012), 1005.

[15]

PBS, PBS frontline: Hunting the nightmare bacteria, 2013,, URL , ().

[16]

P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Mathematical biosciences, 180 (2002), 29. doi: 10.1016/S0025-5564(02)00108-6.

[17]

X. Wang, Y. Xiao, J. Wang and X. Lu, A mathematical model of effects of environmental contamination and presence of volunteers on hospital infections in china,, Journal of theoretical biology, 293 (2012), 161. doi: 10.1016/j.jtbi.2011.10.009.

[18]

X. Wang, Y. Xiao, J. Wang and X. Lu, Stochastic disease dynamics of a hospital infection model,, Mathematical biosciences, 241 (2013), 115. doi: 10.1016/j.mbs.2012.10.002.

[19]

M. Wolkewitz, M. Dettenkofer, H. Bertz, M. Schumacher and J. Huebner, Environmental contamination as an important route for the transmission of the hospital pathogen vre: modeling and prediction of classical interventions,, Infectious Diseases: Research and Treatment, 1 (2008), 3.

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