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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 252718, 14 pages
http://dx.doi.org/10.1155/2014/252718
Research Article

Dynamics and Biocontrol: The Indirect Effects of a Predator Population on a Host-Vector Disease Model

1Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China
2Department of Mathematics, Shaoxing University, Shaoxing, Zhejiang 312000, China
3School of Finance and Economics, Jiangsu University, Zhenjiang, Jiangsu 212013, China

Received 11 July 2013; Revised 29 November 2013; Accepted 10 December 2013; Published 27 January 2014

Academic Editor: Yanni Xiao

Copyright © 2014 Fengyan Zhou and Hongxing Yao. 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.

Abstract

A model of the interactions among a host population, an insect-vector population, which transmits virus from hosts to hosts, and a vector predator population is proposed based on virus-host, host-vector, and prey (vector)-enemy theories. The model is investigated to explore the indirect effect of natural enemies on host-virus dynamics by reducing the vector densities, which shows the basic reproduction numbers (without predators) and (with predators) that provide threshold conditions on determining the uniform persistence and extinction of the disease in a host population. When the model is absent from predator, the disease is persistent if ; in such a case, by introducing predators of a vector, then the insect-transmitted disease will be controlled if . From the point of biological control, these results show that an additional predator population of the vector may suppress the spread of vector-borne diseases. In addition, there exist limit cycles with persistence of the disease or without disease in presence of predators. Finally, numerical simulations are conducted to support analytical results.