Transmission Dynamics of Resistant Bacteria in a Predator-Prey System

This paper discusses the impact on human health caused by the addition of antibiotics in the feed of food animals. We use the established transmission rule of resistant bacteria and combine it with a predator-prey system to determine a differential equations model. The equations have three steady equilibrium points corresponding to three population dynamics states under the influence of resistant bacteria. In order to quantitatively analyze the stability of the equilibrium points, we focused on the basic reproduction numbers. Then, both the local and global stability of the equilibrium points were quantitatively analyzed by using essential mathematical methods. Numerical results are provided to relate our model properties to some interesting biological cases. Finally, we discuss the effect of the two main parameters of the model, the proportion of antibiotics added to feed and the predation rate, and estimate the human health impacts related to the amount of feed antibiotics used. We further propose an approach for the prevention of the large-scale spread of resistant bacteria and illustrate the necessity of controlling the amount of in-feed antibiotics used.

[1]  E. Venturino.  The effects of diseases on competing species. , 2001, Mathematical biosciences.

[2]  Lansun Chen,et al.  Modeling and analysis of a predator-prey model with disease in the prey. , 2001, Mathematical biosciences.

[3]  Bob W. Kooi,et al.  Stabilization and complex dynamics in a predator-prey model with predator suffering from an infectious disease , 2011 .

[4]  Y. Hsieh,et al.  Predator–prey model with disease infection in both populations , 2008, Mathematical medicine and biology : a journal of the IMA.

[5]  Yibin Kang,et al.  A predator–prey model with diseases in both prey and predator , 2013 .

[6]  Samrat Chatterjee,et al.  Disease in prey population and body size of intermediate predator reduce the prevalence of chaos-conclusion drawn from Hastings-Powell model , 2009 .

[7]  R. Holt,et al.  Infectious Disease and Species Coexistence: A Model of Lotka-Volterra Form , 1985, The American Naturalist.

[8]  H. Hethcote,et al.  Modeling HIV Transmission and AIDS in the United States , 1992 .

[9]  Ezio Venturino,et al.  Epidemics spreading in predator–prey systems , 2012, Int. J. Comput. Math..

[10]  R. Anderson,et al.  Vancomycin-resistant enterococci in intensive-care hospital settings: transmission dynamics, persistence, and the impact of infection control programs. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Joydip Dhar,et al.  Modelling a predator–prey system with infected prey in polluted environment , 2010 .

[12]  M. Haque,et al.  A predator–prey model with disease in the predator species only , 2010 .

[13]  E. Stobberingh,et al.  Antibiotic resistance of faecal Escherichia coli in poultry, poultry farmers and poultry slaughterers. , 2001, The Journal of antimicrobial chemotherapy.

[14]  Franziska Schwarz,et al.  Antibiotic resistance spread in food , 1997, Nature.

[15]  N. French,et al.  Excretion of Vancomycin-Resistant Enterococci by Wild Mammals , 2002, Emerging infectious diseases.

[16]  Roy M. Anderson,et al.  The Population Dynamics of Microparasites and Their Invertebrate Hosts , 1981 .

[17]  Santabrata Chakravarty,et al.  A predator-prey model with disease in prey , 2013 .

[18]  Lansun Chen,et al.  A ratio-dependent predator-prey model with disease in the prey , 2002, Appl. Math. Comput..

[19]  T. O. Carroll,et al.  Modeling the role of viral disease in recurrent phytoplankton blooms , 1994 .

[20]  A. Suárez,et al.  Analysis of an age-structured predator–prey model with disease in the prey☆ , 2006 .

[21]  Herbert W. Hethcote,et al.  Four predator prey models with infectious diseases , 2001 .

[22]  Kusumika Kundu,et al.  A predator–prey mathematical model with both the populations affected by diseases , 2011 .

[23]  H. Gaskins,et al.  ANTIBIOTICS AS GROWTH PROMOTANTS:MODE OF ACTION , 2002, Animal biotechnology.

[24]  R. Anderson,et al.  Studies of antibiotic resistance within the patient, hospitals and the community using simple mathematical models. , 1999, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[25]  Carl T. Bergstrom,et al.  Ecological theory suggests that antimicrobial cycling will not reduce antimicrobial resistance in hospitals. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[26]  Shigui Ruan,et al.  Qualitative analysis of models with different treatment protocols to prevent antibiotic resistance. , 2010, Mathematical biosciences.

[27]  T. Jukes,et al.  The multiple nature of the animal protein factor. , 1949 .

[28]  Ezio Venturino,et al.  Epidemics in predator-prey models: disease in the predators. , 2002, IMA journal of mathematics applied in medicine and biology.

[29]  F. Angulo,et al.  Public health consequences of use of antimicrobial agents in food animals in the United States. , 2003, Microbial drug resistance.

[30]  David Greenhalgh,et al.  A predator–prey model with disease in the prey species only , 2007 .

[31]  G. Webb,et al.  A model of antibiotic-resistant bacterial epidemics in hospitals. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[32]  H. I. Freedman,et al.  Predator-prey populations with parasitic infection , 1989, Journal of mathematical biology.

[33]  T. Nagaraja,et al.  Liver abscesses in feedlot cattle: a review. , 1998, Journal of animal science.

[34]  R M May,et al.  The invasion, persistence and spread of infectious diseases within animal and plant communities. , 1986, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[35]  J. R. Johnson,et al.  Molecular Characterization of Gentamicin-Resistant Enterococci in the United States: Evidence of Spread from Animals to Humans through Food , 2003, Journal of Clinical Microbiology.

[36]  A. J. Lotka.  Analytical Note on Certain Rhythmic Relations in Organic Systems , 1920, Proceedings of the National Academy of Sciences.

[37]  Zhen Jin,et al.  An impulsive predator–prey model with communicable disease in the prey species only , 2009 .

[38]  S Bonhoeffer,et al.  Evaluating treatment protocols to prevent antibiotic resistance. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[39]  Ezio Venturino,et al.  The Influence of Diseases on Lotka-Volterra Systems , 1993 .

[40]  F. Hilker,et al.  Disease-induced stabilization of predator-prey oscillations. , 2008, Journal of theoretical biology.

[41]  S. Bonhoeffer,et al.  On Being the Right Size: The Impact of Population Size and Stochastic Effects on the Evolution of Drug Resistance in Hospitals and the Community , 2011, PLoS Pathogens.

[42]  F. Aarestrup,et al.  DANMAP 99-Consumption of antimicrobial agents and occurrence of antimicrobial resistance in bacteria from food animals , food and humans in Denmark Statens Serum , 2000 .

[43]  M. Miller,et al.  Antibiotic use in food animals: controlling the human health impact. , 2000, Journal of AOAC International.

[44]  H. Goossens,et al.  Presence of vancomycin-resistant enterococci in farm and pet animals , 1996, Antimicrobial agents and chemotherapy.

[45]  M. Lipsitch,et al.  Understanding the spread of antibiotic resistant pathogens in hospitals: mathematical models as tools for control. , 2001, Clinical infectious diseases : an official publication of the Infectious Diseases Society of America.

[46]  S. M. Breedlove,et al.  Sex on the brain , 1997, Nature.

[47]  J. Chattopadhyay,et al.  Classical predator–prey system with infection of prey population—a mathematical model , 2003 .

[48]  M. Hoopes,et al.  Stabilizing effects in spatial parasitoid-host and predator-prey models: a review. , 2004, Theoretical population biology.

[49]  E. Venturino.  On epidemics crossing the species barrier in interacting population models , 2006 .

[50]  Ezio Venturino,et al.  An ecoepidemiological model with disease in predator: the ratio‐dependent case , 2007 .

[51]  M. Teuber.  Spread of antibiotic resistance with food-borne pathogens , 1999, Cellular and Molecular Life Sciences CMLS.

[52]  V. Harwood,et al.  Vancomycin-Resistant Enterococcus spp. Isolated from Wastewater and Chicken Feces in the United States , 2001, Applied and Environmental Microbiology.

[53]  Ron Jones,et al.  Does the use of antibiotics in food animals pose a risk to human health? A critical review of published data. , 2003, The Journal of antimicrobial chemotherapy.

[54]  Zhien Ma,et al.  A predator-prey model with infected prey. , 2004, Theoretical population biology.

[55]  R. Sarkar,et al.  Removal of infected prey prevent limit cycle oscillations in an infected prey–predator system—a mathematical study , 2002 .

[56]  Maurice Tchuente,et al.  Effects of a disease affecting a predator on the dynamics of a predator-prey system. , 2009, Journal of theoretical biology.

[57]  G L French,et al.  The continuing crisis in antibiotic resistance. , 2010, International journal of antimicrobial agents.

[58]  B. Mukhopadhyay,et al.  On an eco-epidemiological model with prey harvesting and predator switching: Local and global perspectives , 2010 .

[59]  HighWire Press.  Philosophical Transactions of the Royal Society of London , 1781, The London Medical Journal.