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Computational and Mathematical Methods in Medicine
Volume 2015 (2015), Article ID 638074, 12 pages
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.


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.