An Epidemic Model for Tick-Borne Disease with Two Delays | Zendy

Dan Li | Zendy; Wanbiao Ma | Zendy; Zhichao Jiang | Zendy

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An Epidemic Model for Tick-Borne Disease with Two Delays

Author(s) -

Dan Li,

Wanbiao Ma,

Zhichao Jiang

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/427621

Subject(s) - transmission (telecommunications) , path (computing) , mathematics , physics , algorithm , combinatorics , computer science , telecommunications , programming language

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 0 ≤1,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.©2013 Dan Li et al.

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