Journal of Applied Mathematics

An Epidemic Model for Tick-Borne Disease with Two Delays

Dan Li, Wanbiao Ma, and Zhichao Jiang

Full-text: Open access

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808275

Digital Object Identifier
doi:10.1155/2013/427621

Mathematical Reviews number (MathSciNet)
MR3138974

Zentralblatt MATH identifier
06950670

Citation

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. https://projecteuclid.org/euclid.jam/1394808275


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