2012, 9(3): 601-625. doi: 10.3934/mbe.2012.9.601

Modeling the effects of introducing a new antibiotic in a hospital setting: A case study

1. 

Department of Mathematics & Statistics and Institute for Quantitative Biology, East Tennessee State University, Johnson City, TN, 37659, United States

2. 

Department of Mathematics and Computer Science, Meredith College, Raleigh, NC, 27607, United States

3. 

Department of Mathematics & Statistics and Institute for Quantitative Biology, East Tennessee State University, Johnson City, TN, United States

Received  August 2011 Revised  March 2012 Published  July 2012

The increase in antibiotic resistance continues to pose a public health risk as very few new antibiotics are being produced, and bacteria resistant to currently prescribed antibiotics is growing. Within a typical hospital setting, one may find patients colonized with bacteria resistant to a single antibiotic, or, of a more emergent threat, patients may be colonized with bacteria resistant to multiple antibiotics. Precautions have been implemented to try to prevent the growth and spread of antimicrobial resistance such as a reduction in the distribution of antibiotics and increased hand washing and barrier preventions; however, the rise of this resistance is still evident. As a result, there is a new movement to try to re-examine the need for the development of new antibiotics. In this paper, we use mathematical models to study the possible benefits of implementing a new antibiotic in this setting; through these models, we examine the use of a new antibiotic that is distributed in various ways and how this could reduce total resistance in the hospital. We compare several different models in which patients colonized with both single and dual-resistant bacteria are present, including a model with no additional treatment protocols for the population colonized with dual-resistant bacteria as well as models including isolation and/or treatment with a new antibiotic. We examine the benefits and limitations of each scenario in the simulations presented.
Citation: Michele L. Joyner, Cammey C. Manning, Brandi N. Canter. Modeling the effects of introducing a new antibiotic in a hospital setting: A case study. Mathematical Biosciences & Engineering, 2012, 9 (3) : 601-625. doi: 10.3934/mbe.2012.9.601
References:
[1]

Alberto Sandiumenge, Emili Diaz, Alejandro Rodriguez, Loreto Vidaur, Laura Canadell, Montserrat Olona, Montserrat Rue and Jordi Rello, Impact of diversity of antibiotic use on the development of antimicrobial resistance, Journal of Antimicrobial Chemotherapy, 57 (2006), 1197-1204. doi: 10.1093/jac/dkl097.

[2]

Alfonso J. Alanis, Resistance to antibiotics: Are we in the post-antibiotic era?, Archives of Medical Research, 36 (2005), 697-705. doi: 10.1016/j.arcmed.2005.06.009.

[3]

Bruce R. Levin and Klas I. Udekwu, Population dynamics of antibiotic treatment: A mathematical model and hypotheses for time-kill and continuous-culture experiments, Antimicrobial Agents and Chemotherapy, 54 (2010), 3414-3426. doi: 10.1128/AAC.00381-10.

[4]

B. R. Levin, M. Lipsitch, V. Perrot, S. Schrag, R. Antia, L. Simonsen and N. Moore, The population genetics of antibiotic resistance, Clinical Infectious Diseases, 24 (1997), S9-S16. doi: 10.1093/clinids/24.Supplement_1.S9.

[5]

Carl T. Bergstrom, Monique Lo and Marc Lipsitch, Ecological theory suggests that antimicrobial cycling will not reduce antimicrobial resistance in hospitals, PNAS, 101 (2004), 13285-13290. doi: 10.1073/pnas.0402298101.

[6]

Christophe Fraser, Steven Riley, Roy M. Anderson and Neil M. Ferguson, Factors that make an infectious disease outbreak controllable, PNAS, 101 (2004), 6146-6151. doi: 10.1073/pnas.0307506101.

[7]

Csaba Pal, Maria D. Macia, Antonio Oliver, Ira Schachar and Angus Buckling, Coevolution with viruses drives the evolution of bacterial mutation rates, Nature, 450 (2007), 1079-1081. doi: 10.1038/nature06350.

[8]

D. M. Hamby, A review of techniques for parameter sensitivity analysis of environmental models, Environmental Monitoring and Assessment, 32 (1994), 135-154. doi: 10.1007/BF00547132.

[9]

Dale N. Gerding, Tom A. Larson, Rita A. Hughes, Mary Weiler, Carol Shanholtzer and Lance R. Peterson, Aminoglycoside resistance and aminoglycoside usage: Ten years of experience in one hospital, Antimicrobial Agents and Chemotherapy, (1991), 1284-1290.

[10]

Dan I. Andersson and Bruce R. Levin, The biological cost of antibiotic resistance, Current Opinion in Microbiology, 2 (1999), 489-493.

[11]

David M. Shlaes, Dale N. Gerding, Joseph F. John Jr., William A. Craig, Donald L. Bornstein, Robert A. Duncan, Mark R. Eckman, William E. Farrer, William H. Greene, Victor Lorian, Stuart Levy, John E. McGowan Jr., Sindy M. Paul, Joel Ruskin, Fred C. Tenover and Chatrchai Watanakunakorn, Society for healthcare epidemiology of America joint committee on the prevention of antimicrobial resistance: Guidelines for prevention of antimicrobial resistance in hospitals, Clinical Infectious Diseases, 25 (1997), 584-599. doi: 10.1086/513766.

[12]

D. J. Austin and K. G. Kristinsson and R. M. Anderson, The relationship between the volume of antimicrobial consumption in human communities and the frequency of resistance, PNAS, 96 (1999), 1152-1156. doi: 10.1073/pnas.96.3.1152.

[13]

D. J. Austin, M. Kakehashi and R. M. Anderson, The transmission dynamics of antibiotic-resistant bacteria: The relationship between resistance in commensal organisms and antibiotic consumption, Proceedings: Biological Sciences, 264 (1997), 1629-1638. doi: 10.1098/rspb.1997.0227.

[14]

Eduardo Massad, Marcelo N. Burattini and Francisco A. B. Coutinho, An optimization model for antibiotic use, Applied Mathematics and Computation, 201 (2008), 161-167. doi: 10.1016/j.amc.2007.12.007.

[15]

Elaine S. Walker and Foster Levy, Genetic trends in population evolving antibiotic resistance, Evolution, 55 (2001), 1110-1122.

[16]

Erika M. C. D'Agata, Pierre Magal, Damien Olivier, Shigui Ruan and Glenn F. Webb, Modeling antibiotic resistance in hospitals: The impact of minimizing duration treatment, Journal of Theoretical Biology, 249 (2007), 487-499. doi: 10.1016/j.jtbi.2007.08.011.

[17]

F. D. Pien and W. K. K. Lau and N. Sur, Antibiotic use in a small community hospital, West J. Med., 130 (1979), 498-502.

[18]

Glenn F. Webb, Erika M. C. D'Agata, Pierre Magal and Shigui Ruan, A model of antibiotic-resistant bacterial epidemics, PNAS, 102 (2005), 13343-13348. doi: 10.1073/pnas.0504053102.

[19]

Harald J. van Loon, Menno R. Vriens, Ad C. Fluit, Annet Troelstra, Christiaan van der Werken, Jan Verhoef and Marc J. M. Bonten, Antibiotic rotation and development of gram-negative antibiotic resistance, American Journal Respiratory Critical Care Medicine, 171 (2005), 480-487. doi: 10.1164/rccm.200401-070OC.

[20]

Inti Pelupessy, Mac J. M. Bonten and Odo Diekmann, How to assess the relative importance of different colonization routes of pathogens within hospital settings, PNAS, 99 (2002), 5601-5605. doi: 10.1073/pnas.082412899.

[21]

Jesus Silva, Mechanisms of antibiotic resistance, Current Therapeutic Research, 57 (1996), 30-35. doi: 10.1016/S0011-393X(96)80095-6.

[22]

Jesus Blazquez, Antonio Oliver and Jose-Maria Gomez-Gomez, Mutation and evolution of antibiotic resistance: Antibiotics as promoters of antibiotic resistance?, Current Drug Targets, 3 (2002), 345-349.

[23]

J. L. Martinez and F. Baquero, Mutation frequencies and antibiotic resistance, Antimicrobial Agents and Chemotherapy, 44 (2000), 1771-1777. doi: 10.1128/AAC.44.7.1771-1777.2000.

[24]

Jose-Antonio Martinez, Josep-Maria Nicolas, Francesc Marco, Juan-Pablo Horcajada, Gloria Garcia-Segarra, Antoni Trilla, Carles Codina, Antoni Torres and Josep Mensa, Comparison of antimicrobial cycling and mixing strategies in two medical intensive care units, Critical Care Medicine, 34 (2006), 329-335. doi: 10.1097/01.CCM.0000195010.63855.45.

[25]

Karen Chow, Xiaohong Wang, R. Curtiss III and Carlos Castillo-Chavez, Evaluating the efficacy of antimicrobial cycling programmes and patient isolation on dual resistance in hospitals, Journal of Biological Dynamics, 5 (2010), 27-43.

[26]

Marc Lipsitch, Carl T. Bergstrom and Bruce R. Levin, The epidemiology of antibiotic resistance in hospitals: Paradoxes and prescriptions, PNAS, 97 (2000), 1938-1943. doi: 10.1073/pnas.97.4.1938.

[27]

Marc Lipsitch and Matthew H. Samore, Antimicrobial use and antimicrobial resistance: A population perspective, Emerging Infectious Diseases, 8 (2002), 347-354.

[28]

Michael Haber, Bruce R. Levin and Piotr Kramarz, Antibiotic control of antibiotic resistance in hospitals: A simulation study, BMC Infectious Diseases, 10 (2010). doi: 10.1186/1471-2334-10-254.

[29]

Michael B. Rothberg, Penelope S. Pekow, Maureen Lahti, Oren Brody, Daniel J. Skiest and Peter K. Lindenauer, Antibiotic therapy and treatment failure in patients hospitalized for acute exacerbations of chronic obstructive pulmonary disease, JAMA, 303 (2010), 2035-2042. doi: 10.1001/jama.2010.672.

[30]

P. van den Driessche and James 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.

[31]

Richard E. Lenski, Bacterial evolution and the cost of antibiotic resistance, International Microbiology, 1 (1998), 265-270.

[32]

Robert F. Betts, William M. Valenti, Stanley W. Chapman, Tasnee Chonmaitree, Gail Mowrer, Patricia Pincus, Marjorie Messner and Richard Robertson, Five-year surveillance of aminoglycoside usage in a university hospital, Antimicrobial Agents and Chemotherapy, 100 (1984), 219-222.

[33]

Sebastian Bonhoeffer, Marc Lipsitch and Bruce R. Levin, Evaluating treatment protocols to prevent antibiotic resistance, PNAS, 94 (1997), 12106-12111. doi: 10.1073/pnas.94.22.12106.

[34]

William J. Moss, M. Claire Beers, Elizabeth Johnson, David G. Nichols, Trish M. Perl, James D. Dick, Michael A. Veltri and Rodney E. Willoughby Jr., Pilot study of antibiotic cycling in a pediatric intensive care unit, Critical Care Medicine, 30 (2002), 1877-1882. doi: 10.1097/00003246-200208000-00034.

[35]

Y. Claire Wang and Marc Lipsitch, Upgrading antibiotic use within a class: Tradeoff between resistance and treatment success, PNAS, 103 (2006), 9655-9660. doi: 10.1073/pnas.0600636103.

show all references

References:
[1]

Alberto Sandiumenge, Emili Diaz, Alejandro Rodriguez, Loreto Vidaur, Laura Canadell, Montserrat Olona, Montserrat Rue and Jordi Rello, Impact of diversity of antibiotic use on the development of antimicrobial resistance, Journal of Antimicrobial Chemotherapy, 57 (2006), 1197-1204. doi: 10.1093/jac/dkl097.

[2]

Alfonso J. Alanis, Resistance to antibiotics: Are we in the post-antibiotic era?, Archives of Medical Research, 36 (2005), 697-705. doi: 10.1016/j.arcmed.2005.06.009.

[3]

Bruce R. Levin and Klas I. Udekwu, Population dynamics of antibiotic treatment: A mathematical model and hypotheses for time-kill and continuous-culture experiments, Antimicrobial Agents and Chemotherapy, 54 (2010), 3414-3426. doi: 10.1128/AAC.00381-10.

[4]

B. R. Levin, M. Lipsitch, V. Perrot, S. Schrag, R. Antia, L. Simonsen and N. Moore, The population genetics of antibiotic resistance, Clinical Infectious Diseases, 24 (1997), S9-S16. doi: 10.1093/clinids/24.Supplement_1.S9.

[5]

Carl T. Bergstrom, Monique Lo and Marc Lipsitch, Ecological theory suggests that antimicrobial cycling will not reduce antimicrobial resistance in hospitals, PNAS, 101 (2004), 13285-13290. doi: 10.1073/pnas.0402298101.

[6]

Christophe Fraser, Steven Riley, Roy M. Anderson and Neil M. Ferguson, Factors that make an infectious disease outbreak controllable, PNAS, 101 (2004), 6146-6151. doi: 10.1073/pnas.0307506101.

[7]

Csaba Pal, Maria D. Macia, Antonio Oliver, Ira Schachar and Angus Buckling, Coevolution with viruses drives the evolution of bacterial mutation rates, Nature, 450 (2007), 1079-1081. doi: 10.1038/nature06350.

[8]

D. M. Hamby, A review of techniques for parameter sensitivity analysis of environmental models, Environmental Monitoring and Assessment, 32 (1994), 135-154. doi: 10.1007/BF00547132.

[9]

Dale N. Gerding, Tom A. Larson, Rita A. Hughes, Mary Weiler, Carol Shanholtzer and Lance R. Peterson, Aminoglycoside resistance and aminoglycoside usage: Ten years of experience in one hospital, Antimicrobial Agents and Chemotherapy, (1991), 1284-1290.

[10]

Dan I. Andersson and Bruce R. Levin, The biological cost of antibiotic resistance, Current Opinion in Microbiology, 2 (1999), 489-493.

[11]

David M. Shlaes, Dale N. Gerding, Joseph F. John Jr., William A. Craig, Donald L. Bornstein, Robert A. Duncan, Mark R. Eckman, William E. Farrer, William H. Greene, Victor Lorian, Stuart Levy, John E. McGowan Jr., Sindy M. Paul, Joel Ruskin, Fred C. Tenover and Chatrchai Watanakunakorn, Society for healthcare epidemiology of America joint committee on the prevention of antimicrobial resistance: Guidelines for prevention of antimicrobial resistance in hospitals, Clinical Infectious Diseases, 25 (1997), 584-599. doi: 10.1086/513766.

[12]

D. J. Austin and K. G. Kristinsson and R. M. Anderson, The relationship between the volume of antimicrobial consumption in human communities and the frequency of resistance, PNAS, 96 (1999), 1152-1156. doi: 10.1073/pnas.96.3.1152.

[13]

D. J. Austin, M. Kakehashi and R. M. Anderson, The transmission dynamics of antibiotic-resistant bacteria: The relationship between resistance in commensal organisms and antibiotic consumption, Proceedings: Biological Sciences, 264 (1997), 1629-1638. doi: 10.1098/rspb.1997.0227.

[14]

Eduardo Massad, Marcelo N. Burattini and Francisco A. B. Coutinho, An optimization model for antibiotic use, Applied Mathematics and Computation, 201 (2008), 161-167. doi: 10.1016/j.amc.2007.12.007.

[15]

Elaine S. Walker and Foster Levy, Genetic trends in population evolving antibiotic resistance, Evolution, 55 (2001), 1110-1122.

[16]

Erika M. C. D'Agata, Pierre Magal, Damien Olivier, Shigui Ruan and Glenn F. Webb, Modeling antibiotic resistance in hospitals: The impact of minimizing duration treatment, Journal of Theoretical Biology, 249 (2007), 487-499. doi: 10.1016/j.jtbi.2007.08.011.

[17]

F. D. Pien and W. K. K. Lau and N. Sur, Antibiotic use in a small community hospital, West J. Med., 130 (1979), 498-502.

[18]

Glenn F. Webb, Erika M. C. D'Agata, Pierre Magal and Shigui Ruan, A model of antibiotic-resistant bacterial epidemics, PNAS, 102 (2005), 13343-13348. doi: 10.1073/pnas.0504053102.

[19]

Harald J. van Loon, Menno R. Vriens, Ad C. Fluit, Annet Troelstra, Christiaan van der Werken, Jan Verhoef and Marc J. M. Bonten, Antibiotic rotation and development of gram-negative antibiotic resistance, American Journal Respiratory Critical Care Medicine, 171 (2005), 480-487. doi: 10.1164/rccm.200401-070OC.

[20]

Inti Pelupessy, Mac J. M. Bonten and Odo Diekmann, How to assess the relative importance of different colonization routes of pathogens within hospital settings, PNAS, 99 (2002), 5601-5605. doi: 10.1073/pnas.082412899.

[21]

Jesus Silva, Mechanisms of antibiotic resistance, Current Therapeutic Research, 57 (1996), 30-35. doi: 10.1016/S0011-393X(96)80095-6.

[22]

Jesus Blazquez, Antonio Oliver and Jose-Maria Gomez-Gomez, Mutation and evolution of antibiotic resistance: Antibiotics as promoters of antibiotic resistance?, Current Drug Targets, 3 (2002), 345-349.

[23]

J. L. Martinez and F. Baquero, Mutation frequencies and antibiotic resistance, Antimicrobial Agents and Chemotherapy, 44 (2000), 1771-1777. doi: 10.1128/AAC.44.7.1771-1777.2000.

[24]

Jose-Antonio Martinez, Josep-Maria Nicolas, Francesc Marco, Juan-Pablo Horcajada, Gloria Garcia-Segarra, Antoni Trilla, Carles Codina, Antoni Torres and Josep Mensa, Comparison of antimicrobial cycling and mixing strategies in two medical intensive care units, Critical Care Medicine, 34 (2006), 329-335. doi: 10.1097/01.CCM.0000195010.63855.45.

[25]

Karen Chow, Xiaohong Wang, R. Curtiss III and Carlos Castillo-Chavez, Evaluating the efficacy of antimicrobial cycling programmes and patient isolation on dual resistance in hospitals, Journal of Biological Dynamics, 5 (2010), 27-43.

[26]

Marc Lipsitch, Carl T. Bergstrom and Bruce R. Levin, The epidemiology of antibiotic resistance in hospitals: Paradoxes and prescriptions, PNAS, 97 (2000), 1938-1943. doi: 10.1073/pnas.97.4.1938.

[27]

Marc Lipsitch and Matthew H. Samore, Antimicrobial use and antimicrobial resistance: A population perspective, Emerging Infectious Diseases, 8 (2002), 347-354.

[28]

Michael Haber, Bruce R. Levin and Piotr Kramarz, Antibiotic control of antibiotic resistance in hospitals: A simulation study, BMC Infectious Diseases, 10 (2010). doi: 10.1186/1471-2334-10-254.

[29]

Michael B. Rothberg, Penelope S. Pekow, Maureen Lahti, Oren Brody, Daniel J. Skiest and Peter K. Lindenauer, Antibiotic therapy and treatment failure in patients hospitalized for acute exacerbations of chronic obstructive pulmonary disease, JAMA, 303 (2010), 2035-2042. doi: 10.1001/jama.2010.672.

[30]

P. van den Driessche and James 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.

[31]

Richard E. Lenski, Bacterial evolution and the cost of antibiotic resistance, International Microbiology, 1 (1998), 265-270.

[32]

Robert F. Betts, William M. Valenti, Stanley W. Chapman, Tasnee Chonmaitree, Gail Mowrer, Patricia Pincus, Marjorie Messner and Richard Robertson, Five-year surveillance of aminoglycoside usage in a university hospital, Antimicrobial Agents and Chemotherapy, 100 (1984), 219-222.

[33]

Sebastian Bonhoeffer, Marc Lipsitch and Bruce R. Levin, Evaluating treatment protocols to prevent antibiotic resistance, PNAS, 94 (1997), 12106-12111. doi: 10.1073/pnas.94.22.12106.

[34]

William J. Moss, M. Claire Beers, Elizabeth Johnson, David G. Nichols, Trish M. Perl, James D. Dick, Michael A. Veltri and Rodney E. Willoughby Jr., Pilot study of antibiotic cycling in a pediatric intensive care unit, Critical Care Medicine, 30 (2002), 1877-1882. doi: 10.1097/00003246-200208000-00034.

[35]

Y. Claire Wang and Marc Lipsitch, Upgrading antibiotic use within a class: Tradeoff between resistance and treatment success, PNAS, 103 (2006), 9655-9660. doi: 10.1073/pnas.0600636103.

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