Dynamical Analysis of a Stage-Structured Model for Lyme Disease with Two Delays

Canadian mathematical bulletin

Wanbiao Ma¹  Dan Li¹ 

[1] Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, P.R. China

关键词: Lyme disease;    stage-structure;    time delay;    Lyapunov functional stability Hopf bifurcation.;   

DOI  :  10.4153/CMB-2015-063-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this paper, anonlinear stage-structured model for Lyme disease is considered. The model is a system of differential equations with two time delays. The basic reproductive rate, $R_0(au_1,au_2)$, isderived. If $R_0(au_1,au_2)lt 1$, then the boundary equilibriumis globally asymptotically stable. If $R_0(au_1,au_2)gt 1$,then there existsa unique positive equilibrium whose local asymptotical stabilityand the existence ofHopf bifurcations are established by analyzing the distributionof the characteristic values.An explicit algorithm for determining the direction of Hopf bifurcationsand thestability of the bifurcating periodic solutions is derived byusing the normal form andthe center manifold theory. Some numerical simulations are performedto confirm the correctnessof theoretical analysis. At last, some conclusions are given.

【 授权许可】

Unknown