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A nosocomial epidemic model with infection of patients due to contaminated rooms
| 1. | Mathematics Department, Vanderbilt University, Nashville, TN 37240, United States, United States |
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Under a Creative Commons license
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), 923-940. |
| [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), 583-600.
doi: 10.1007/BF02218848. |
| [3] |
D. T. Gillespie, Exact stochastic simulation of coupled chemical reactions, The journal of physical chemistry, 81 (1977), 2340-2361.
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), 1473-1474.
doi: 10.1086/503439. |
| [5] |
M. McKenna, Clean sweep, Scientific American, 307 (2012), 30-31.
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), 1045-1051.
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), 1201-1208.
doi: 10.1111/j.1469-0691.2010.03420.x. |
| [8] |
W. H. Organization et al., Antimicrobial Resistance: Global Report on Surveillance 2014. geneva, switzerland: Who, 2014, 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), 1265-1272.
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), p595.
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), 1067-1082.
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), 1513-1532.
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), 1005-1007. |
| [15] |
PBS, PBS frontline: Hunting the nightmare bacteria, 2013, URL http://www.pbs.org/wgbh/pages/frontline/health-science-technology/hunting-the-nightmare-bacteria/a-superbug-outbreak-at-nih/l. |
| [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), 29-48.
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), 161-173.
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), 115-124.
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), 3-11. |
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), 923-940. |
| [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), 583-600.
doi: 10.1007/BF02218848. |
| [3] |
D. T. Gillespie, Exact stochastic simulation of coupled chemical reactions, The journal of physical chemistry, 81 (1977), 2340-2361.
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), 1473-1474.
doi: 10.1086/503439. |
| [5] |
M. McKenna, Clean sweep, Scientific American, 307 (2012), 30-31.
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), 1045-1051.
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), 1201-1208.
doi: 10.1111/j.1469-0691.2010.03420.x. |
| [8] |
W. H. Organization et al., Antimicrobial Resistance: Global Report on Surveillance 2014. geneva, switzerland: Who, 2014, 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), 1265-1272.
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), p595.
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), 1067-1082.
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), 1513-1532.
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), 1005-1007. |
| [15] |
PBS, PBS frontline: Hunting the nightmare bacteria, 2013, URL http://www.pbs.org/wgbh/pages/frontline/health-science-technology/hunting-the-nightmare-bacteria/a-superbug-outbreak-at-nih/l. |
| [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), 29-48.
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), 161-173.
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), 115-124.
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), 3-11. |
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