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Computational and Mathematical Methods in Medicine
Volume 2015, Article ID 638074, 12 pages
http://dx.doi.org/10.1155/2015/638074
Research Article

Transmission Dynamics of Resistant Bacteria in a Predator-Prey System

1School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
2City institute, Dalian University of Technology, Dalian 116600, China
3School of Innovation Experiment, Dalian University of Technology, Dalian 116024, China

Received 8 October 2014; Revised 7 January 2015; Accepted 7 January 2015

Academic Editor: Maria N. D. S. Cordeiro

Copyright © 2015 Xubin Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. L. Stokstad and T. H. Jukes, “The multiple nature of the animal protein factor,” The Journal of Biological Chemistry, vol. 180, no. 2, pp. 647–654, 1949. View at Google Scholar · View at Scopus
  2. R. L. Preston, “The role of animal drugs in food animal production,” 1988.
  3. T. G. Nagaraja and M. M. Chengappa, “Liver abscesses in feedlot cattle: a review,” Journal of Animal Science, vol. 76, no. 1, pp. 287–298, 1998. View at Google Scholar · View at Scopus
  4. H. R. Gaskins, C. T. Collier, and D. B. Anderson, “Antibiotics as growth promotants: mode of action,” Animal Biotechnology, vol. 13, no. 1, pp. 29–42, 2002. View at Publisher · View at Google Scholar · View at Scopus
  5. D. McClary and G. Vogel, “Effect of timing of tilmicosin metaphylaxis on control of bovine respiratory disease and performance in feeder cattle,” The Bovine Practitioner, no. 33, pp. 155–161, 1999. View at Google Scholar
  6. B. Flemming, E. Hanne-Dorthe, L. Monnet Dominique et al., DANMAP 2000: Consumption of Antimicrobial Agents and Occurence of Antimicrobial Resistance in Bacteria from Food Animals, Foods and Humans in Denmark, Danish Veterinary Institute, 2001.
  7. B. Flemming, H.-D. Emborg, A. Sigrid et al., “DANMAP 97: consumption of antimicrobial agents and occurrence of antimicrobial resistance in bacteria from food animals, food and humans in Danmark,” 1998.
  8. F. Bager, DANMAP 98-Consumption of antimicrobial agents and occurrence of antimicrobial in bacteria from food animals, food and humans in Denmark, 1999.
  9. F. Bager, DANMAP 99-Consumption of Antimicrobial Agents and Occurrence of Antimicrobial Resistance in Bacteria from Food Animals, Food and Humans in Denmark, Statens Serum Institut, Danish Veterinary and Food Administration, Danish Medicines Agency, Danish Veterinary Laboratory, Copenhagen, Denmark, 2000.
  10. F. Bager, H. D. Emborg, F. M. Aarestrup et al., “The Danish experience following the ban of antimicrobial growth promoters: trends in microbial resistance and antimicrobial use,” in Proceedings of Alltech's 18th Annual Symposium: From Niche Markets to Mainstream, Lexington, Ky, USA, 2002.
  11. V. Perreten, F. Schwarz, L. Cresta, M. Boeglin, G. Dasen, and M. Teuber, “Antibiotic resistance spread in food,” Nature, vol. 389, no. 6653, pp. 801–802, 1997. View at Google Scholar · View at Scopus
  12. M. Teuber, “Spread of antibiotic resistance with food-borne pathogens,” Cellular and Molecular Life Sciences, vol. 56, no. 9-10, pp. 755–763, 1999. View at Publisher · View at Google Scholar · View at Scopus
  13. V. J. Harwood, M. Brownell, W. Perusek, and J. E. Whitlock, “Vancomycin-resistant Enterococcus spp. Isolated from Wastewater and chicken feces in the United States,” Applied and Environmental Microbiology, vol. 67, no. 10, pp. 4930–4933, 2001. View at Publisher · View at Google Scholar · View at Scopus
  14. L. A. Devriese, M. Ieven, H. Goossens et al., “Presence of vancomycin-resistant enterococci in farm and pet animals,” Antimicrobial Agents and Chemotherapy, vol. 40, no. 10, pp. 2285–2287, 1996. View at Google Scholar · View at Scopus
  15. D. J. P. Mallon, J. E. Corkill, S. M. Hazel et al., “Excretion of vancomycin-resistant enterococci by wild mammals,” Emerging Infectious Diseases, vol. 8, no. 6, pp. 636–638, 2002. View at Publisher · View at Google Scholar · View at Scopus
  16. A. E. van den Bogaard, N. London, C. Driessen, and E. E. Stobberingh, “Antibiotic resistance of faecal Escherichia coli in poultry, poultry farmers and poultry slaughterers,” Journal of Antimicrobial Chemotherapy, vol. 47, no. 6, pp. 763–771, 2001. View at Publisher · View at Google Scholar · View at Scopus
  17. S. M. Donabedian, L. A. Thal, E. Hershberger et al., “Molecular characterization of gentamicin-resistant Enterococci in the United States: Evidence of spread from animals to humans through food,” Journal of Clinical Microbiology, vol. 41, no. 3, pp. 1109–1113, 2003. View at Publisher · View at Google Scholar · View at Scopus
  18. A. D. Anderson, J. M. Nelson, S. Rossiter, and F. J. Angulo, “Public health consequences of use of antimicrobial agents in food animals in the United States,” Microbial Drug Resistance, vol. 9, no. 4, pp. 373–379, 2003. View at Publisher · View at Google Scholar · View at Scopus
  19. I. Phillips, M. Casewell, T. Cox et al., “Does the use of antibiotics in food animals pose a risk to human health? A critical review of published data,” Journal of Antimicrobial Chemotherapy, vol. 53, no. 1, pp. 28–52, 2004. View at Publisher · View at Google Scholar · View at Scopus
  20. L. Tollefson and M. A. Miller, “Antibiotic use in food animals: controlling the human health impact,” Journal of AOAC International, vol. 83, no. 2, pp. 245–254, 2000. View at Google Scholar · View at Scopus
  21. C. T. Bergstrom, M. Lo, and M. Lipsitch, “Ecological theory suggests that antimicrobial cycling will not reduce antimicrobial resistance in hospitals,” Proceedings of the National Academy of Sciences of the United States of America, vol. 101, no. 36, pp. 13285–13290, 2004. View at Publisher · View at Google Scholar · View at Scopus
  22. S. Bonhoeffer, M. Lipsitch, and B. R. Levin, “Evaluating treatment protocols to prevent antibiotic resistance,” Proceedings of the National Academy of Sciences of the United States of America, vol. 94, no. 22, pp. 12106–12111, 1997. View at Publisher · View at Google Scholar · View at Scopus
  23. R. D. Kouyos, P. A. zur Wiesch, and S. Bonhoeffer, “On being the right size: the impact of population size and stochastic effects on the evolution of drug resistance in hospitals and the community,” PLoS Pathogens, vol. 7, no. 4, Article ID e1001334, 2011. View at Publisher · View at Google Scholar · View at Scopus
  24. G. F. Webb, E. M. C. D'Agata, P. Magal, and S. Ruan, “A model of antibiotic-resistant bacterial epidemics in hospitals,” Proceedings of the National Academy of Sciences of the United States of America, vol. 102, no. 37, pp. 13343–13348, 2005. View at Publisher · View at Google Scholar · View at Scopus
  25. H. R. Sun, X. Lu, and S. Ruan, “Qualitative analysis of models with different treatment protocols to prevent antibiotic resistance,” Mathematical Biosciences, vol. 227, no. 1, pp. 56–67, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. D. J. Austin and R. M. Anderson, “Studies of antibiotic resistance within the patient, hospitals and the community using simple mathematical models,” Philosophical Transactions of the Royal Society B: Biological Sciences, vol. 354, no. 1384, pp. 721–738, 1999. View at Publisher · View at Google Scholar · View at Scopus
  27. G. L. French, “The continuing crisis in antibiotic resistance,” International Journal of Antimicrobial Agents, vol. 36, no. 3, pp. S3–S7, 2010. View at Publisher · View at Google Scholar · View at Scopus
  28. R. A. Weinstein, M. J. M. Bonten, D. J. Austin, and M. Lipsitch, “Understanding the spread of antibiotic resistant pathogens in hospitals: mathematical models as tools for control,” Clinical Infectious Diseases, vol. 33, no. 10, pp. 1739–1746, 2001. View at Publisher · View at Google Scholar · View at Scopus
  29. 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,” Proceedings of the National Academy of Sciences of the United States of America, vol. 96, no. 12, pp. 6908–6913, 1999. View at Publisher · View at Google Scholar · View at Scopus
  30. A. J. Lotka, “Analytical note on certain rhythmic relations in organic systems,” Proceedings of the National Academy of Sciences of the United States of America, vol. 6, no. 7, pp. 410–415, 1920. View at Publisher · View at Google Scholar
  31. K. P. Hadeler and H. I. Freedman, “Predator-prey populations with parasitic infection,” Journal of Mathematical Biology, vol. 27, no. 6, pp. 609–631, 1989. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. E. Venturino, “The influence of diseases on Lotka-Volterra systems,” The Rocky Mountain Journal of Mathematics, vol. 24, no. 1, pp. 381–402, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. B. Edward and T. O. Carroll, “Modeling the role of viral disease in recurrent phytoplankton blooms,” Journal of Mathematical Biology, vol. 32, no. 8, pp. 857–863, 1994. View at Publisher · View at Google Scholar
  34. E. Venturino, “The effects of diseases on competing species,” Mathematical Biosciences, vol. 174, no. 2, pp. 111–131, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  35. J. Chattopadhyay, S. Pal, and A. El Abdllaoui, “Classical predator-prey system with infection of prey population? A mathematical model,” Mathematical Methods in the Applied Sciences, vol. 26, no. 14, pp. 1211–1222, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  36. H. W. Hethcote, W. Wang, L. Han, and Z. Ma, “A predator—prey model with infected prey,” Theoretical Population Biology, vol. 66, no. 3, pp. 259–268, 2004. View at Publisher · View at Google Scholar · View at Scopus
  37. L. Han, Z. Ma, and H. W. Hethcote, “Four predator prey models with infectious diseases,” Mathematical and Computer Modelling, vol. 34, no. 7-8, pp. 849–858, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  38. J. Chattopadhyay, R. R. Sarkar, and G. Ghosal, “Removal of infected prey prevent limit cycle oscillations in an infected prey-predator system—a mathematical study,” Ecological Modelling, vol. 156, no. 2-3, pp. 113–121, 2002. View at Publisher · View at Google Scholar · View at Scopus
  39. K. P. Das, S. Chatterjee, and J. Chattopadhyay, “Disease in prey population and body size of intermediate predator reduce the prevalence of chaos-conclusion drawn from Hastings-Powell model,” Ecological Complexity, vol. 6, no. 3, pp. 363–374, 2009. View at Publisher · View at Google Scholar · View at Scopus
  40. B. W. Kooi, G. A. K. van Voorn, and K. P. Das, “Stabilization and complex dynamics in a predator-prey model with predator suffering from an infectious disease,” Ecological Complexity, vol. 8, no. 1, pp. 113–122, 2011. View at Publisher · View at Google Scholar · View at Scopus
  41. M. Delgado, M. Molina-Becerra, and A. Suárez, “Analysis of an age-structured predator-prey model with disease in the prey,” Nonlinear Analysis: Real World Applications, vol. 7, no. 4, pp. 853–871, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  42. R. M. Anderson and R. M. May, “The population dynamics of microparasites and their invertebrate hosts,” Philosophical Transactions of the Royal Society B: Biological Sciences, vol. 291, no. 1054, pp. 451–524, 1981. View at Publisher · View at Google Scholar
  43. J. Chattopadhyay and O. Arino, “A predator-prey model with disease in the prey,” Nonlinear Analysis: Theory, Methods & Applications, vol. 36, pp. 747–766, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  44. R. M. Anderson and R. M. May, “The invasion, persistence and spread of infectious diseases within animal and plant communities.,” Philosophical transactions of the Royal Society of London. Series B: Biological sciences, vol. 314, no. 1167, pp. 533–570, 1986. View at Publisher · View at Google Scholar · View at Scopus
  45. Y. Xiao and L. Chen, “Modeling and analysis of a predator-prey model with disease in the prey,” Mathematical Biosciences, vol. 171, no. 1, pp. 59–82, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  46. D. Greenhalgh and M. Haque, “A predator-prey model with disease in the prey species only,” Mathematical Methods in the Applied Sciences, vol. 30, no. 8, pp. 911–929, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  47. S. Sinha, O. P. Misra, and J. Dhar, “Modelling a predator-prey system with infected prey in polluted environment,” Applied Mathematical Modelling, vol. 34, no. 7, pp. 1861–1872, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  48. E. Venturino, “Mathematical population dynamics: analysis of heterogeneity, vol. one: theory of epidemics,” in Epidemics in Predator-Prey Models: Disease among the Prey, pp. 33–50, Wuertz Publishing, Winnipeg, Canada, 1995. View at Google Scholar
  49. M. Liu, Z. Jin, and M. Haque, “An impulsive predator-prey model with communicable disease in the prey species only,” Nonlinear Analysis: Real World Applications, vol. 10, no. 5, pp. 3098–3111, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  50. R. Bhattacharyya and B. Mukhopadhyay, “On an eco-epidemiological model with prey harvesting and predator switching: local and global perspectives,” Nonlinear Analysis. Real World Applications, vol. 11, no. 5, pp. 3824–3833, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  51. E. Venturino, “Epidemics in predator-prey models: disease in the predators,” IMA Journal of Mathematics Applied in Medicine and Biology, vol. 19, no. 3, pp. 185–205, 2002. View at Publisher · View at Google Scholar · View at Scopus
  52. Y. Xiao and L. Chen, “A ratio-dependent predator-prey model with disease in the prey,” Applied Mathematics and Computation, vol. 131, no. 2-3, pp. 397–414, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  53. M. Haque and E. Venturino, “An ecoepidemiological model with disease in predator: the ratio-dependent case,” Mathematical Methods in the Applied Sciences, vol. 30, no. 14, pp. 1791–1809, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  54. M. Haque, “A predator-prey model with disease in the predator species only,” Nonlinear Analysis. Real World Applications, vol. 11, no. 4, pp. 2224–2236, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  55. F. M. Hilker and K. Schmitz, “Disease-induced stabilization of predator-prey oscillations,” Journal of Theoretical Biology, vol. 255, no. 3, pp. 299–306, 2008. View at Publisher · View at Google Scholar · View at Scopus
  56. P. Auger, R. Mchich, T. Chowdhury, G. Sallet, M. Tchuente, and J. Chattopadhyay, “Effects of a disease affecting a predator on the dynamics of a predator-prey system,” Journal of Theoretical Biology, vol. 258, no. 3, pp. 344–351, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  57. Y.-H. Hsieh and C.-K. Hsiao, “Predator-prey model with disease infection in both populations,” Mathematical Medicine and Biology, vol. 25, no. 3, pp. 247–266, 2008. View at Publisher · View at Google Scholar · View at Scopus
  58. K. pada Das, K. Kundu, and J. Chattopadhyay, “A predator-prey mathematical model with both the populations affected by diseases,” Ecological Complexity, vol. 8, no. 1, pp. 68–80, 2011. View at Publisher · View at Google Scholar · View at Scopus
  59. X. Gao, Q. Pan, M. He, and Y. Kang, “A predator-prey model with diseases in both prey and predator,” Physica A. Statistical Mechanics and its Applications, vol. 392, no. 23, pp. 5898–5906, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  60. C. J. Briggs and M. F. Hoopes, “Stabilizing effects in spatial parasitoid-host and predator-prey models: a review,” Theoretical Population Biology, vol. 65, no. 3, pp. 299–315, 2004. View at Publisher · View at Google Scholar · View at Scopus
  61. S. Chaudhuri, A. Costamagna, and E. Venturino, “Epidemics spreading in predator-prey systems,” International Journal of Computer Mathematics, vol. 89, no. 4, pp. 561–584, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  62. H. W. Hethcote and J. W. van Ark, Modeling HIV Transmission and AIDS in the United States, Springer, New York, NY, USA, 1992.
  63. R. D. Holt and J. Pickering, “Infectious disease and species coexistence: a model of Lotka- Volterra form,” American Naturalist, vol. 126, no. 2, pp. 196–211, 1985. View at Publisher · View at Google Scholar · View at Scopus
  64. E. Venturino, “On epidemics crossing the species barrier in interacting population models,” Varahmihir Journal of Mathematical Sciences, vol. 6, no. 1, pp. 247–263, 2006. View at Google Scholar · View at MathSciNet