An Epidemic Model for Tick‐Borne Disease with Two Delays

Dan Li, Wanbiao Ma and Zhichao Jiang

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

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 ℜ0, which is a threshold quantity for stability of equilibria, is calculated. If ℜ0 ≤ 1, then the infection‐free equilibrium is globally asymptotically stable, and this is the only equilibrium. On the contrary, if ℜ0 > 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 ℜ0 > 1.

Date: 2013
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https://doi.org/10.1155/2013/427621

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:427621

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