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Optimizing Hospital Infection Control: The Role of Mathematical Modeling

  • Tan N. Doan (a1), David C. M. Kong (a1), Carl M. J. Kirkpatrick (a1) and Emma S. McBryde (a2)

Multidrug-resistant bacteria are major causes of nosocomial infections and are associated with considerable morbidity, mortality, and healthcare costs. Preventive strategies have therefore become increasingly important. Mathematical modeling has been widely used to understand the transmission dynamics of nosocomial infections and the quantitative effects of infection control measures. This review will explore the principles of mathematical modeling used in nosocomial infections and discuss the effectiveness of infection control measures investigated using mathematical modeling.

Infect Control Hosp Epidemiol 2014;35(12):1521–1530

Corresponding author
Victorian Infectious Diseases Service, Royal Melbourne Hospital, Peter Doherty Institute for Infection and Immunity, Level 4, 792 Elizabeth Street, Melbourne, Victoria 3000, Australia (; or, David C. M. Kong, PhD, Centre for Medicine Use and Safety, Faculty of Pharmacy and Pharmaceutical Sciences, Monash University, 381 Royal Parade, Melbourne, Victoria 3052, Australia (
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1.De Angelis G, Murthy A, Beyersmann J, Harbarth S. Estimating the impact of healthcare-associated infections on length of stay and costs. Clin Microbiol Infect 2010;16:17291735.
2.Hawkey PM, Jones AM. The changing epidemiology of resistance. J Antimicrob Chemother 2009;64:i3i10.
3.Alanis AJ. Resistance to antibiotics: are we in the post-antibiotic era? Arch Med Res 2005;36:697705.
4.Grundmann H, Hellriegel B. Mathematical modelling: a tool for hospital infection control. Lancet Infect Dis 2006;6:3945.
5.Stangl DK. Bridging the gap between statistical analysis and decision making in public health research. Stat Med 2005;24:503511.
6.van Kleef E, Robotham JV, Jit M, Deeny SR, Edmunds WJ. Modelling the transmission of healthcare associated infections: a systematic review. BMC Infect Dis 2013;13:113.
7.Vynnycky E, White RG. An Introduction to Infectious Disease Modelling. New York: Oxford University Press, 2010.
8.Bailey N. The Biomathematics of Malaria. London: Charles Griffin, 1975.
9.Cooper BS, Medley GF, Scott GM. Preliminary analysis of the transmission dynamics of nosocomial infections: stochastic and management effects. J Hosp Infect 1999;43:131147.
10.Pelupessy I, Bonten MJ, Diekmann O. How to assess the relative importance of different colonization routes of pathogens within hospital settings. Proc Natl Acad Sci USA 2002;99:56015605.
11.McBryde ES, Pettitt AN, McElwain DL. A stochastic mathematical model of methicillin resistant Staphylococcus aureus transmission in an intensive care unit: predicting the impact of interventions. J Theor Biol 2007;245:470481.
12.McBryde ES, Pettitt AN, Cooper BS, McElwain DL. Characterizing an outbreak of vancomycin-resistant enterococci using hidden Markov models. J R Soc Interface 2007;4:745754.
13.Cooper B, Lipsitch M. The analysis of hospital infection data using hidden Markov models. Biostatistics 2004;5:223237.
14.Mishra S, Fisman DN, Boily MC. The ABC of terms used in mathematical models of infectious diseases. J Epidemiol Community Health 2011;65:8794.
15.Keeling MJ, Danon L. Mathematical modelling of infectious diseases. Br Med Bull 2009;92:3342.
16.Chamchod F, Ruan S. Modeling methicillin-resistant Staphylococcus aureus in hospitals: transmission dynamics, antibiotic usage and its history. Theor Biol Med Model 2012;9:114.
17.Austin DJ, Bonten MJ, Weinstein RA, Slaughter S, Anderson RM. Vancomycin-resistant enterococci in intensive-care hospital settings: transmission dynamics, persistence, and the impact of infection control programs. Proc Natl Acad Sci USA 1999;96:69086913.
18.Bonten MJ, Austin DJ, Lipsitch M. Understanding the spread of antibiotic resistant pathogens in hospitals: mathematical models as tools for control. Clin Infect Dis 2001;33:17391746.
19.Raboud J, Saskin R, Simor A, et al. Modeling transmission of methicillin-resistant Staphylococcus aureus among patients admitted to a hospital. Infect Control Hosp Epidemiol 2005;26:607615.
20.Wang J, Wang L, Magal P, et al. Modelling the transmission dynamics of meticillin-resistant Staphylococcus aureus in Beijing Tongren hospital. J Hosp Infect 2011;79:302308.
21.Wang X, Xiao Y, Wang J, Lu X. A mathematical model of effects of environmental contamination and presence of volunteers on hospital infections in China. J Theor Biol 2012;293:161173.
22.Pressley J, D’Agata EM, Webb GF. The effect of co-colonization with community-acquired and hospital-acquired methicillin-resistant Staphylococcus aureus strains on competitive exclusion. J Theor Biol 2010;264:645656.
23.D’Agata EM, Horn MA, Webb GF. The impact of persistent gastrointestinal colonization on the transmission dynamics of vancomycin-resistant enterococci. J Infect Dis 2002;185:766773.
24.D’Agata EM, Webb G, Horn M. A mathematical model quantifying the impact of antibiotic exposure and other interventions on the endemic prevalence of vancomycin-resistant enterococci. J Infect Dis 2005;192:20042011.
25.Perencevich EN, Fisman DN, Lipsitch M, Harris AD, Morris JG Jr, Smith DL. Projected benefits of active surveillance for vancomycin-resistant enterococci in intensive care units. Clin Infect Dis 2004;38:11081115.
26.Grima DT, Webb GF, D’Agata EM. Mathematical model of the impact of a nonantibiotic treatment for Clostridium difficile on the endemic prevalence of vancomycin-resistant enterococci in a hospital setting. Comput Math Methods Med 2012;2012:605861.
27.Chamchod F, Ruan S. Modeling the spread of methicillin-resistant Staphylococcus aureus in nursing homes for elderly. PLoS ONE 2012;7:19.
28.D’Agata EM, Magal P, Olivier D, Ruan S, Webb GF. Modeling antibiotic resistance in hospitals: the impact of minimizing treatment duration. J Theor Biol 2007;249:487499.
29.McBryde ES, McElwain DL. A mathematical model investigating the impact of an environmental reservoir on the prevalence and control of vancomycin-resistant enterococci. J Infect Dis 2006;193:14731474.
30.Pittet D, Allegranzi B, Sax H, et al. Evidence-based model for hand transmission during patient care and the role of improved practices. Lancet Infect Dis 2006;6:641652.
31.Marra AR, Camargo TZ, Cardoso VJ, et al. Hand hygiene compliance in the critical care setting: a comparative study of 2 different alcohol handrub formulations. Am J Infect Control 2013;41:136139.
32.Martin-Madrazo C, Soto-Diaz S, Canada-Dorado A, et al. Cluster randomized trial to evaluate the effect of a multimodal hand hygiene improvement strategy in primary care. Infect Control Hosp Epidemiol 2012;33:681688.
33.Dos Santos RP, Konkewicz LR, Nagel FM, et al. Changes in hand hygiene compliance after a multimodal intervention and seasonality variation. Am J Infect Control 2013;41:10121016.
34.Kaier K, Mutters NT, Frank U. Bed occupancy rates and hospital-acquired infections—should beds be kept empty? Clin Microbiol Infect 2012;18:941945.
35.Patel M, Weinheimer JD, Waites KB, Baddley JW. Active surveillance to determine the impact of methicillin-resistant Staphylococcus aureus colonization on patients in intensive care units of a Veterans Affairs medical center. Infect Control Hosp Epidemiol 2008;29:503509.
36.Willing BP, Russell SL, Finlay BB. Shifting the balance: antibiotic effects on host-microbiota mutualism. Nat Rev Microbiol 2011;9:233243.
37.Gonzales R, Anderer T, McCulloch CE, et al. A cluster randomized trial of decision support strategies for reducing antibiotic use in acute bronchitis. JAMA Intern Med 2013;173:267273.
38.Boyce JM. Environmental contamination makes an important contribution to hospital infection. J Hosp Infect 2007;2:5054.
39.Jit M, Brisson M. Modelling the epidemiology of infectious diseases for decision analysis: a primer. Pharmacoeconomics 2011;29:371386.
40.Hollingsworth TD. Controlling infectious disease outbreaks: lessons from mathematical modelling. J Public Health Policy 2009;30:328341.
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Infection Control & Hospital Epidemiology
  • ISSN: 0899-823X
  • EISSN: 1559-6834
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