Global stability of a multi-group model with vaccination age, distributed delay and random perturbation

Jinhu  Xu; Yicang  Zhou

doi:10.3934/mbe.2015.12.1083

Article Contents

2015, Volume 12, Issue 5: 1083-1106. Doi: 10.3934/mbe.2015.12.1083

This issue Previous Article Heteroclinic bifurcation for a general predator-prey model with Allee effect and state feedback impulsive control strategy Next Article Cilium height difference between strokes is more effective in driving fluid transport in mucociliary clearance: A numerical study

Global stability of a multi-group model with vaccination age, distributed delay and random perturbation

Jinhu Xu^1, and
Yicang Zhou^1,

1.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049

Received: August 31, 2014

Revised: December 31, 2014

Published: May 2015

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Abstract

A multi-group epidemic model with distributed delay and vaccination age has been formulated and studied. Mathematical analysis shows that the global dynamics of the model is determined by the basic reproduction number $\mathcal{R}_0$: the disease-free equilibrium is globally asymptotically stable if $\mathcal{R}_0\leq1$, and the endemic equilibrium is globally asymptotically stable if $\mathcal{R}_0>1$. Lyapunov functionals are constructed by the non-negative matrix theory and a novel grouping technique to establish the global stability. The stochastic perturbation of the model is studied and it is proved that the endemic equilibrium of the stochastic model is stochastically asymptotically stable in the large under certain conditions.

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Mathematics Subject Classification: 34E10, 37H10, 92D25, 93D20.

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