Global stability of a multi-group model with generalized nonlinear incidence and vaccination age

Jinhu  Xu; Yicang  Zhou

doi:10.3934/dcdsb.2016.21.977

Article Contents

2016, Volume 21, Issue 3: 977-996. Doi: 10.3934/dcdsb.2016.21.977

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Global stability of a multi-group model with generalized nonlinear incidence and vaccination age

Jinhu Xu^1, and
Yicang Zhou^1,

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

Received: May 31, 2014

Revised: April 30, 2015

Published: April 2016

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Abstract

A multi-group epidemic model with general nonlinear incidence and vaccination age structure has been formulated and studied. Mathematical analysis shows that the global stability of disease-free equilibrium and endemic equilibrium of the model are determined by the basic reproduction number $\mathcal{R}_0$: the disease-free equilibrium is globally asymptotically stable if $\mathcal{R}_0<1$, the endemic equilibrium is globally asymptotically stable if $\mathcal{R}_0>1$. The Lyapunov functionals for the global dynamics of the multi-group model are constructed by applying the theory of non-negative matrices and a novel grouping technique in estimating the derivative.

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Mathematics Subject Classification: Primary: 92D25, 92D30; Secondary: 35B35, 37B25.

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