An Epidemic Model for Tick-Borne Disease with Two Delays

Dan Li, Wanbiao Ma and Zhichao Jiang

Journal of Applied Mathematics, 2013, vol. 2013, 1-11

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 , 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 .

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:427621

DOI: 10.1155/2013/427621

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