Journal of Applied Mathematics

An Epidemic Model for Tick-Borne Disease with Two Delays

Dan Li, Wanbiao Ma, and Zhichao Jiang

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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 0, which is a threshold quantity for stability of equilibria, is calculated. If 01, then the infection-free equilibrium is globally asymptotically stable, and this is the only equilibrium. On the contrary, if 0>1, 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 0>1.

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J. Appl. Math., Volume 2013 (2013), Article ID 427621, 11 pages.

First available in Project Euclid: 14 March 2014

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Li, Dan; Ma, Wanbiao; Jiang, Zhichao. An Epidemic Model for Tick-Borne Disease with Two Delays. J. Appl. Math. 2013 (2013), Article ID 427621, 11 pages. doi:10.1155/2013/427621.

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