American Institute of Mathematical Sciences

Advanced
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

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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[17]

R. J. LeVeque, "Numerical Methods for Conservation Laws," Second edition, Lectures in Mamathematics, ETH Zürich, Birkhäuser Verlag, Basel, 1992.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[17]

R. J. LeVeque, "Numerical Methods for Conservation Laws," Second edition, Lectures in Mamathematics, ETH Zürich, Birkhäuser Verlag, Basel, 1992.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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