Global stability for multi-group SIR and SEIR epidemic models with age-dependent susceptibility

Jinliang Wang; Xianning Liu; Toshikazu Kuniya; Jingmei Pang

doi:10.3934/dcdsb.2017151

Article Contents

2017, Volume 22, Issue 7: 2795-2812. Doi: 10.3934/dcdsb.2017151

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Global stability for multi-group SIR and SEIR epidemic models with age-dependent susceptibility

1.
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
2.
China, School of Mathematical Science, Heilongjiang University, Harbin 150080, China
3.
Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe-shi, Hyogo 657-0067, Japan

Author Bio: jinliangwang@hlju.edu.cn (J. Wang); tkuniya@port.kobe-u.ac.jp (T. Kuniya); jingmeipang@aliyun.com (J. Pang)
corresponding author: liuxn@swu.edu.cn (X. Liu)
corresponding author: liuxn@swu.edu.cn (X. Liu)

Received: September 2013

Revised: March 2017

Published: October 2017

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Abstract

In this paper, we investigate the global asymptotic stability of multi-group SIR and SEIR age-structured models. These models allow the infectiousness and the death rate of susceptible individuals to vary and depend on the susceptibility, with which we can consider the heterogeneity of population. We establish global dynamics and demonstrate that the heterogeneity does not alter the dynamical structure of the basic SIR and SEIR with age-dependent susceptibility. Our results also demonstrate that, for age structured multi-group models considered, the graph-theoretic approach can be successfully applied by choosing an appropriate weighted matrix as well.

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Mathematics Subject Classification: Primary:92D30;Secondary:35F31, 34D23.

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