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Journal of Applied Mathematics
Volume 2014, Article ID 245650, 10 pages
http://dx.doi.org/10.1155/2014/245650
Research Article

Global Dynamics of a Host-Vector-Predator Mathematical Model

1Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China
2Department of Mathematics, Shaoxing University, Shaoxing, Zhejiang 31200, China
3School of Finance and Economics, Jiangsu University, Zhenjiang, Jiangsu 212013, China

Received 18 April 2014; Accepted 2 July 2014; Published 22 July 2014

Academic Editor: Peter G L Leach

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 mathematical model which links predator-vector(prey) and host-vector theory is proposed to examine the indirect effect of predators on vector-host dynamics. The equilibria and the basic reproduction number R0 are obtained. By constructing Lyapunov functional and using LaSalle’s invariance principle, global stability of both the disease-free and disease equilibria are obtained. Analytical results show that R0 provides threshold conditions on determining the uniform persistence and extinction of the disease, and predator density at any time should keep larger or equal to its equilibrium level for successful disease eradication. Finally, taking the predation rate as parameter, we provide numerical simulations for the impact of predators on vector-host disease control. It is illustrated that predators have a considerable influence on disease suppression by reducing the density of the vector population.