American Institute of Mathematical Sciences

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

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

Cameron Browne 1, and  Glenn F. Webb 1,

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.
Keywords: antibiotic resistance, Bacterial infection, next generation matrix., local stability, Lyapunov functional.
Mathematics Subject Classification: Primary: 92C60; Secondary: 34D2.
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. Google Scholar

[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. Google Scholar

[3]

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

[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. Google Scholar

[5]

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

[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. Google Scholar

[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. Google Scholar

[8]

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

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[13]

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

[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. Google Scholar

[15]

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

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

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. Google Scholar

[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. Google Scholar

[3]

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

[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. Google Scholar

[5]

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

[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. Google Scholar

[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. Google Scholar

[8]

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

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[13]

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

[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. Google Scholar

[15]

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

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

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