Geodesic
Dynamical Analysis of a Stage-Structured Model for Lyme Disease with Two Delays
Canadian mathematical bulletin, Tome 59 (2016) no. 2, pp. 363-380

Voir la notice de l'article provenant de la source Cambridge

DOI

In this paper, a nonlinear stage-structured model for Lyme disease is considered. The model is a system of diòerential equations with two time delays. We derive the basic reproductive rate ${{R}_{0}}\left( {{\tau }_{1}},\,{{\tau }_{2}} \right)$ . If ${{R}_{0}}\left( {{\tau }_{1}},\,{{\tau }_{2}} \right)\,<\,1$ , then the boundary equilibrium is globally asymptotically stable. If ${{R}_{0}}\left( {{\tau }_{1}},\,{{\tau }_{2}} \right)\,>\,1$ , then there exists a unique positive equilibrium whose local asymptotic stability and the existence of Hopf bifurcations are established by analyzing the distribution of the characteristic values. An explicit algorithm for determining the direction of Hopf bifurcations and the stability of the bifurcating periodic solutions is derived by using the normal form and the center manifold theory. Some numerical simulations are performed to confirm the correctness of theoretical analysis. Finally, some conclusions are given.
DOI : 10.4153/CMB-2015-063-x
Mots-clés : 34D20, disease, stage-structure, time delay, Lyapunov functional stability, Hopf bifurcation 
Li, Dan; Ma, Wanbiao. Dynamical Analysis of a Stage-Structured Model for Lyme Disease with Two Delays. Canadian mathematical bulletin, Tome 59 (2016) no. 2, pp. 363-380. doi: 10.4153/CMB-2015-063-x
@article{10_4153_CMB_2015_063_x,
     author = {Li, Dan and Ma, Wanbiao},
     title = {Dynamical {Analysis} of a {Stage-Structured} {Model} for {Lyme} {Disease} with {Two} {Delays}},
     journal = {Canadian mathematical bulletin},
     pages = {363--380},
     year = {2016},
     volume = {59},
     number = {2},
     doi = {10.4153/CMB-2015-063-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-063-x/}
}
TY  - JOUR
AU  - Li, Dan
AU  - Ma, Wanbiao
TI  - Dynamical Analysis of a Stage-Structured Model for Lyme Disease with Two Delays
JO  - Canadian mathematical bulletin
PY  - 2016
SP  - 363
EP  - 380
VL  - 59
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-063-x/
DO  - 10.4153/CMB-2015-063-x
ID  - 10_4153_CMB_2015_063_x
ER  - 
%0 Journal Article
%A Li, Dan
%A Ma, Wanbiao
%T Dynamical Analysis of a Stage-Structured Model for Lyme Disease with Two Delays
%J Canadian mathematical bulletin
%D 2016
%P 363-380
%V 59
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-063-x/
%R 10.4153/CMB-2015-063-x
%F 10_4153_CMB_2015_063_x

Cité par Sources :