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Journal of Applied Mathematics
Volume 2013, Article ID 427621, 11 pages
Research Article

An Epidemic Model for Tick-Borne Disease with Two Delays

Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

Received 23 September 2013; Accepted 18 November 2013

Academic Editor: Hui-Shen Shen

Copyright © 2013 Dan Li 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.


We have considered an epidemic model of a tick-borne infection which has nonviraemic transmission in addition to the viremic transmission. The basic reproduction number , which is a threshold quantity for stability of equilibria, is calculated. If , then the infection-free equilibrium is globally asymptotically stable, and this is the only equilibrium. On the contrary, if , then an infection equilibrium appears which is globally asymptotically stable, when one time delay is absent. By applying a permanence theorem for infinite dimensional systems, we obtain that the disease is always present when .