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Asymptotic and transient dynamics of SEIR epidemic models on weighted networks

Part of: Parabolic equations and systems Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  26 April 2022

CANRONG TIAN ,
ZUHAN LIU  and
SHIGUI RUAN Open the ORCID record for SHIGUI RUAN [Opens in a new window]
CANRONG TIAN
Affiliation:
School of Mathematics and Physics, Yancheng Institute of Technology, Yancheng, Jiangsu 224003, China emails: tiancanrong@163.com; zhliu@yzu.edu.cn
ZUHAN LIU
Affiliation:
School of Mathematics and Physics, Yancheng Institute of Technology, Yancheng, Jiangsu 224003, China emails: tiancanrong@163.com; zhliu@yzu.edu.cn
SHIGUI RUAN
Affiliation:
Department of Mathematics, University of Miami, Coral Gables, FL 33146, USA email: ruan@math.miami.edu
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Abstract

We study the effect of population mobility on the transmission dynamics of infectious diseases by considering a susceptible-exposed-infectious-recovered (SEIR) epidemic model with graph Laplacian diffusion, that is, on a weighted network. First, we establish the existence and uniqueness of solutions to the SEIR model defined on a weighed graph. Then by constructing Liapunov functions, we show that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity and the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than unity. Finally, we apply our generalized weighed graph to Watts–Strogatz network and carry out numerical simulations, which demonstrate that degrees of nodes determine peak numbers of the infectious population as well as the time to reach these peaks. It also indicates that the network has an impact on the transient dynamical behaviour of the epidemic transmission.

Keywords

Asymptotic and transient dynamicsgraph Laplacian operatorLiapunov functionnetworkSEIR model

MSC classification

Primary: 35R02: Partial differential equations on graphs and networks (ramified or polygonal spaces) 35K57: Reaction-diffusion equations
Secondary: 92D30: Epidemiology
Type
Papers
Information
European Journal of Applied Mathematics , Volume 34 , Issue 2 , April 2023 , pp. 238 - 261
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Footnotes

†

This work was partially supported by NSFC grants (61877052 and 11871065), Jiangsu Province 333 Talent Project, Jiangsu Province Qinglan Project, and NSF grant (DMS-1853622).

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