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Title: Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks

Abstract

We present and analyze a discrete-time susceptible-infected epidemic network model which represents each host as a separate entity and allows heterogeneous hosts and contacts. We establish a necessary and sufficient condition for global stability of the disease-free equilibrium of the system (defined as epidemic controllability) which defines the epidemic reproduction number of the network. When this condition is not fulfilled, we show that the system has a unique, locally stable equilibrium. As a result, we further derive sufficient conditions for epidemic controllability in terms of the epidemic rates and the network topology.

Authors:
 [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1343012
Report Number(s):
LLNL-JRNL-404031
Journal ID: ISSN 1023-6198
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Difference Equations and Applications
Additional Journal Information:
Journal Volume: 15; Journal Issue: 4; Journal ID: ISSN 1023-6198
Publisher:
Taylor & Francis
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; 99 GENERAL AND MISCELLANEOUS; epidemic network; network dynamics; connectivity; epidemic control; dynamical system; reproduction number

Citation Formats

Kostova, Tanya. Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks. United States: N. p., 2010. Web. doi:10.1080/10236190902766835.
Kostova, Tanya. Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks. United States. doi:10.1080/10236190902766835.
Kostova, Tanya. Fri . "Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks". United States. doi:10.1080/10236190902766835. https://www.osti.gov/servlets/purl/1343012.
@article{osti_1343012,
title = {Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks},
author = {Kostova, Tanya},
abstractNote = {We present and analyze a discrete-time susceptible-infected epidemic network model which represents each host as a separate entity and allows heterogeneous hosts and contacts. We establish a necessary and sufficient condition for global stability of the disease-free equilibrium of the system (defined as epidemic controllability) which defines the epidemic reproduction number of the network. When this condition is not fulfilled, we show that the system has a unique, locally stable equilibrium. As a result, we further derive sufficient conditions for epidemic controllability in terms of the epidemic rates and the network topology.},
doi = {10.1080/10236190902766835},
journal = {Journal of Difference Equations and Applications},
number = 4,
volume = 15,
place = {United States},
year = {2010},
month = {7}
}

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