A model of drug resistance with infection by health care workers

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2010, 7(4): 779-792. doi: 10.3934/mbe.2010.7.779

A model of drug resistance with infection by health care workers

Avner Friedman ^1, , Najat Ziyadi ^2, and Khalid Boushaba ^3,

1.	The Ohio State University, Department of Mathematics, Columbus, OH 43210, United States
2.	The Ohio State University, Mathematical Biosciences Institute, Columbus, OH 43210, United States
3.	Iowa State University, Department of Mathematics, 482 Carver Hall Ames, IA 50011

Received March 2010 Revised July 2010 Published October 2010

Abstract
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Antibiotic resistant organisms (ARO) pose an increasing serious threat in hospitals. One of the most life threatening ARO is methicillin-resistant staphylococcus aureus (MRSA). In this paper, we introduced a new mathematical model which focuses on the evolution of two bacterial strains, drug-resistant and non-drug resistant, residing within the population of patients and health care workers in a hospital. The model predicts that as soon as drug is administered, the average load of the non-resistant bacteria will decrease and eventually (after 6 weeks of the model's simulation) reach a very low level. However, the average load of drug-resistant bacteria will initially decrease, after treatment, but will later bounce back and remain at a high level. This level can be made lower if larger amount of drug is given or if the contact between health care workers and patients is reduced.

Keywords: infection in hospital, Drug resistant bacteria, health care workers..

Mathematics Subject Classification: Primary: 92C60; Secondary: 34B60, 35L6.

Citation: Avner Friedman, Najat Ziyadi, Khalid Boushaba. A model of drug resistance with infection by health care workers. Mathematical Biosciences & Engineering, 2010, 7 (4) : 779-792. doi: 10.3934/mbe.2010.7.779

References:

[1]	D. J. Austin, M. J. M. Bonten, R. A. Weinstein, S. Slaughter and R. M. Anderson, Vancomycin-resistant enterococci in intensive-care hospital settings: Transmission dynamics, persistence, and the impact of infection control programs, PNAS, 96 (1999), 6908-6913. doi: doi:10.1073/pnas.96.12.6908.
[2]	M. C. J. Bootsma, O. Diekmann and M. J. M. Bonten, Controlling methicillin-resistant staphylococcus aureus: Quantifying the effects of interventions and rapid diagnostic testing, PNAS, 103 (2006), 5620-5625. doi: doi:10.1073/pnas.0510077103.
[3]	M. J. M. Bonten, R. Willems and R. A. Weinstein, Vancomycin-resistant enterococci: Why are they here, and where do they come from?, The Lancet Infectious Diseases, 1 (2001), 314-325. doi: doi:10.1016/S1473-3099(01)00145-1.
[4]	D. S. Burgess, Pharmacodynamic principles of antimicrobial therapy in the prevention of resistance, Chest, 115 (1999), 19S-23S. doi: doi:10.1378/chest.115.suppl_1.19S.
[5]	B. S. Cooper, G. F. Medley and G. M. Scott, Preliminary analysis of the transmission dynamics of nosocomial infections: Stochastic and management effects, The Journal of Hospital Infection, 43 (1999), 131-147. doi: doi:10.1053/jhin.1998.0647.
[6]	E. M. C. D'Agata, M. Dupont-Rouzeyrol, P. Magal, D. Olivier and S. Ruan, The impact of different antibiotic regimens on the emergence of antimicrobial-resistant bacteria, PLoS ONE, 3 (2008), e4036+. doi: doi:10.1371/journal.pone.0004036.
[7]	E. M. C. D'Agata, M. A. Horn and G. F. Webb, The impact of persistent gastrointestinal colonization on the transmission dynamics of vancomycin-resistant enterococci, The Journal of Infectious Diseases, 185 (2002), 766-773. doi: doi:10.1086/339293.
[8]	E. M. C. D'Agata, P. Magal, D. Olivier, S. Ruan and G. F. Webb, Modeling antibiotic resistance in hospitals: The impact of minimizing treatment duration, J. Theor. Biol., 249 (2007), 487-499. doi: doi:10.1016/j.jtbi.2007.08.011.
[9]	E. M. C. D'Agata, G. F. Webb and M. A. Horn, A mathematical model quantifying the impact of antibiotic exposure and other interventions on the endemic prevalence of vancomycin-resistant enterococci, The Journal of Infectious Diseases, 192 (2005), 2004-2011. doi: doi:10.1086/498041.
[10]	E. M. C. D'Agata, G. F. Webb, M. A. Horn, R. C. Moellering and S. Ruan, Modeling the invasion of community-acquired methicillin-resistant staphylococcus aureus into hospitals, Clinical Infectious Diseases, 48 (2009), 274-284. doi: doi:10.1086/595844.
[11]	B. M. Farr, C. D. Salgado, T. B. Karchmer and R. J. Sherertz, Can antibiotic-resistant nosocomial infections be controlled? The Lancet Infectious Diseases, 1 (2001), 38-45. doi: doi:10.1016/S1473-3099(01)00020-2.
[12]	H. Grundmann, M. Aires-de-Sousa, J. Boyce and E. Tiemersma, Emergence and resurgence of meticillin-resistant staphylococcus aureus as a public-health threat, The Lancet Infectious Diseases, 368 (2006), 874-885.
[13]	H. Grundmann and B. Hellriegel, Mathematical modelling: A tool for hospital infection control, The Lancet Infectious Diseases, 6 (2006), 39-45. doi: doi:10.1016/S1473-3099(05)70325-X.
[14]	K. Hiramatsu, Vancomycin-resistant staphylococcus aureus: A new model of antibiotic resistance, The Lancet Infectious Diseases, 1 (2001), 147-155. doi: doi:10.1016/S1473-3099(01)00091-3.
[15]	A. Handel, E. Margolis and B. R. Levin, Exploring the role of the immune response in preventing antibiotic resistance, Journal of Theoretical Biology, 256 (2009), 655-662. doi: doi:10.1016/j.jtbi.2008.10.025.
[16]	M. Lipsitch, C. T. Bergstrom and B. R. Levin, The epidemiology of antibiotic resistance in hospitals: Paradoxes and prescriptions, PNAS, 97 (2000), 1938-43. doi: doi:10.1073/pnas.97.4.1938.
[17]	R. J. LeVeque, "Numerical Methods for Conservation Laws," Second edition, Lectures in Mamathematics, ETH Zürich, Birkhäuser Verlag, Basel, 1992.
[18]	R. J. LeVeque, "Finite Volume Methods for Hyperbolic Problems," Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2002. doi: doi:10.1017/CBO9780511791253.
[19]	L. R. Peterson, Squeezing the antibiotic balloon: The impact of antimicrobial classes on emerging resistance, Clin. Microbiol. Infect. 11 Suppl., 5 (2005), 4-16.
[20]	D. L. Smith, J. Dushoff, E. N. Perencevich, A. D. Harris and S. A. Levin, Persistent colonization and the spread of antibiotic resistance in nosocomial pathogens: Resistance is a regional problem, PNAS, 101 (2004), 3709-3714. doi: doi:10.1073/pnas.0400456101.
[21]	L. Temime, P. Y. Boëlle, P. Courvalin and D. Guillemot, Bacterial resistance to penicillin g by decreased affinity of penicillin-binding proteins: A mathematical model, Emerging Infect. Dis., 9 (2003), 411-417.
[22]	G. F. Webb, E. M. C. D'Agata, P. Magal and S. Ruan, A model of antibiotic-resistant bacterial epidemics in hospitals, PNAS, 102 (2005), 13343-13348. doi: doi:10.1073/pnas.0504053102.
[23]	G. F. Webb, M. A. Horn, E. M. C. D'Agata, R. C. Moellering and S. Ruan, Competition of hospital-acquired and community-acquired methicillin-resistant Staphylococcus aureus strains in hospitals, J. Biol. Dyn., 4 (2010), 115-129. doi: doi:10.1080/17513750903026411.

show all references

References:

[1]	D. J. Austin, M. J. M. Bonten, R. A. Weinstein, S. Slaughter and R. M. Anderson, Vancomycin-resistant enterococci in intensive-care hospital settings: Transmission dynamics, persistence, and the impact of infection control programs, PNAS, 96 (1999), 6908-6913. doi: doi:10.1073/pnas.96.12.6908.
[2]	M. C. J. Bootsma, O. Diekmann and M. J. M. Bonten, Controlling methicillin-resistant staphylococcus aureus: Quantifying the effects of interventions and rapid diagnostic testing, PNAS, 103 (2006), 5620-5625. doi: doi:10.1073/pnas.0510077103.
[3]	M. J. M. Bonten, R. Willems and R. A. Weinstein, Vancomycin-resistant enterococci: Why are they here, and where do they come from?, The Lancet Infectious Diseases, 1 (2001), 314-325. doi: doi:10.1016/S1473-3099(01)00145-1.
[4]	D. S. Burgess, Pharmacodynamic principles of antimicrobial therapy in the prevention of resistance, Chest, 115 (1999), 19S-23S. doi: doi:10.1378/chest.115.suppl_1.19S.
[5]	B. S. Cooper, G. F. Medley and G. M. Scott, Preliminary analysis of the transmission dynamics of nosocomial infections: Stochastic and management effects, The Journal of Hospital Infection, 43 (1999), 131-147. doi: doi:10.1053/jhin.1998.0647.
[6]	E. M. C. D'Agata, M. Dupont-Rouzeyrol, P. Magal, D. Olivier and S. Ruan, The impact of different antibiotic regimens on the emergence of antimicrobial-resistant bacteria, PLoS ONE, 3 (2008), e4036+. doi: doi:10.1371/journal.pone.0004036.
[7]	E. M. C. D'Agata, M. A. Horn and G. F. Webb, The impact of persistent gastrointestinal colonization on the transmission dynamics of vancomycin-resistant enterococci, The Journal of Infectious Diseases, 185 (2002), 766-773. doi: doi:10.1086/339293.
[8]	E. M. C. D'Agata, P. Magal, D. Olivier, S. Ruan and G. F. Webb, Modeling antibiotic resistance in hospitals: The impact of minimizing treatment duration, J. Theor. Biol., 249 (2007), 487-499. doi: doi:10.1016/j.jtbi.2007.08.011.
[9]	E. M. C. D'Agata, G. F. Webb and M. A. Horn, A mathematical model quantifying the impact of antibiotic exposure and other interventions on the endemic prevalence of vancomycin-resistant enterococci, The Journal of Infectious Diseases, 192 (2005), 2004-2011. doi: doi:10.1086/498041.
[10]	E. M. C. D'Agata, G. F. Webb, M. A. Horn, R. C. Moellering and S. Ruan, Modeling the invasion of community-acquired methicillin-resistant staphylococcus aureus into hospitals, Clinical Infectious Diseases, 48 (2009), 274-284. doi: doi:10.1086/595844.
[11]	B. M. Farr, C. D. Salgado, T. B. Karchmer and R. J. Sherertz, Can antibiotic-resistant nosocomial infections be controlled? The Lancet Infectious Diseases, 1 (2001), 38-45. doi: doi:10.1016/S1473-3099(01)00020-2.
[12]	H. Grundmann, M. Aires-de-Sousa, J. Boyce and E. Tiemersma, Emergence and resurgence of meticillin-resistant staphylococcus aureus as a public-health threat, The Lancet Infectious Diseases, 368 (2006), 874-885.
[13]	H. Grundmann and B. Hellriegel, Mathematical modelling: A tool for hospital infection control, The Lancet Infectious Diseases, 6 (2006), 39-45. doi: doi:10.1016/S1473-3099(05)70325-X.
[14]	K. Hiramatsu, Vancomycin-resistant staphylococcus aureus: A new model of antibiotic resistance, The Lancet Infectious Diseases, 1 (2001), 147-155. doi: doi:10.1016/S1473-3099(01)00091-3.
[15]	A. Handel, E. Margolis and B. R. Levin, Exploring the role of the immune response in preventing antibiotic resistance, Journal of Theoretical Biology, 256 (2009), 655-662. doi: doi:10.1016/j.jtbi.2008.10.025.
[16]	M. Lipsitch, C. T. Bergstrom and B. R. Levin, The epidemiology of antibiotic resistance in hospitals: Paradoxes and prescriptions, PNAS, 97 (2000), 1938-43. doi: doi:10.1073/pnas.97.4.1938.
[17]	R. J. LeVeque, "Numerical Methods for Conservation Laws," Second edition, Lectures in Mamathematics, ETH Zürich, Birkhäuser Verlag, Basel, 1992.
[18]	R. J. LeVeque, "Finite Volume Methods for Hyperbolic Problems," Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2002. doi: doi:10.1017/CBO9780511791253.
[19]	L. R. Peterson, Squeezing the antibiotic balloon: The impact of antimicrobial classes on emerging resistance, Clin. Microbiol. Infect. 11 Suppl., 5 (2005), 4-16.
[20]	D. L. Smith, J. Dushoff, E. N. Perencevich, A. D. Harris and S. A. Levin, Persistent colonization and the spread of antibiotic resistance in nosocomial pathogens: Resistance is a regional problem, PNAS, 101 (2004), 3709-3714. doi: doi:10.1073/pnas.0400456101.
[21]	L. Temime, P. Y. Boëlle, P. Courvalin and D. Guillemot, Bacterial resistance to penicillin g by decreased affinity of penicillin-binding proteins: A mathematical model, Emerging Infect. Dis., 9 (2003), 411-417.
[22]	G. F. Webb, E. M. C. D'Agata, P. Magal and S. Ruan, A model of antibiotic-resistant bacterial epidemics in hospitals, PNAS, 102 (2005), 13343-13348. doi: doi:10.1073/pnas.0504053102.
[23]	G. F. Webb, M. A. Horn, E. M. C. D'Agata, R. C. Moellering and S. Ruan, Competition of hospital-acquired and community-acquired methicillin-resistant Staphylococcus aureus strains in hospitals, J. Biol. Dyn., 4 (2010), 115-129. doi: doi:10.1080/17513750903026411.

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