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STABILITY AND PERSISTENCE IN A MODEL FOR BLUETONGUE DYNAMICS

Gourley, SA, Thieme, HR and van den Driessche, P (2011) STABILITY AND PERSISTENCE IN A MODEL FOR BLUETONGUE DYNAMICS SIAM J APPL MATH, 71 (4). 1280 - 1306. ISSN 0036-1399

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Abstract

A model for the time evolution of bluetongue, a viral disease in sheep and cattle that is spread by midges as vectors, is formulated as a delay di erential equation system of six equations. Midges are assumed to have a pre-adult stage of constant duration, and a general incubation period for bluetongue. A linear stability analysis leads to identi cation of a basic reproduction number that determines if the disease introduced at a low level dies out, or is uniformly weakly persistent in the midges. Stronger conditions su cient for global stability of the disease free equilibrium are derived. The control reproduction numbers, which guide control strategies for midges, cattle or sheep, are determined in the special case in which the incubation period for midges is exponentially distributed. The possibility of backward bifurcation is briefly discussed as is an equilibrium situation in which the disease wipes out sheep populations that are introduced in small numbers.

Item Type: Article
Additional Information: Copyright 2011 Society for Industrial and Applied Mathematics
Uncontrolled Keywords: bluetongue, delay, stability, disease persistence, type reproduction number, WEST-NILE-VIRUS, REPRODUCTION NUMBER, INFECTIOUS-DISEASE, TRANSMISSION, BIFURCATION, EQUATIONS, CATTLE
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Symplectic Elements
Date Deposited: 19 Mar 2012 12:10
Last Modified: 23 Sep 2013 19:18
URI: http://epubs.surrey.ac.uk/id/eprint/294659

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