STABILITY AND PERSISTENCE IN A MODEL FOR BLUETONGUE DYNAMICS

被引：10

作者：

Gourley, Stephen A. ^{[1
]}

Thieme, Horst R. ^{[2
]}

van den Driessche, P. ^{[3
]}

机构：

[1] Univ Surrey, Dept Math, Surrey GU2 7XH, England

[2] Arizona State Univ, Sch Math & Stat Sci, Tempe, AZ 85287 USA

[3] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2011年 / 71卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

bluetongue; delay; stability; disease persistence; type reproduction number; WEST-NILE VIRUS; DISEASE; BIFURCATION; EQUATIONS;

D O I：

10.1137/090775014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 differential equation system of six equations. Midges are assumed to have a preadult stage of constant duration and a general incubation period for bluetongue. A linear stability analysis leads to identification 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 sufficient 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.

引用

页码：1280 / 1306

页数：27