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Analysis of an epidemic model with awareness decay on regular random networks

The existence of a die-out threshold (different from the classic disease-invasion one) defining a region of slow extinction of an epidemic has been proved elsewhere for susceptible-aware-infectious-susceptible models without awareness decay, through bifurcation analysis. By means of an equivalent mean-field model defined on regular random networks, we interpret the dynamics of the system in this region and prove that the existence of bifurcation for this second epidemic threshold crucially depends on the absence of awareness decay. We show that the continuum of equilibria that characterizes the slow die-out dynamics collapses into a unique equilibrium when a constant rate of awareness decay is assumed, no matter how small, and that the resulting bifurcation from the disease-free equilibrium is equivalent to that of standard epidemic models. We illustrate these findings with continuous-time stochastic simulations on regular random networks with different degrees. Finally, the behaviour of solutions with and without decay in awareness is compared around the second epidemic threshold for a small rate of awareness decay

This work has been partially supported by the Research Grant MTM2011-27739-C04-03 of the Spanish Government (D.J. and J.S.), the Project 2009-SGR-345 (J.S.) of the Generalitat de Catalunya, and IMA Collaborative Grant (SGS01/13), UK (I.K. and J.S.)

© Journal of Theoretical Biology, 2015, vol. 365, p. 457-468

Elsevier

Manager: Ministerio de Ciencia e Innovación (Espanya)
Generalitat de Catalunya. Agència de Gestió d’Ajuts Universitaris i de Recerca
Author: Juher, David
Kiss, Istvan Z.
Saldaña Meca, Joan
Date: 2015 January 21
Abstract: The existence of a die-out threshold (different from the classic disease-invasion one) defining a region of slow extinction of an epidemic has been proved elsewhere for susceptible-aware-infectious-susceptible models without awareness decay, through bifurcation analysis. By means of an equivalent mean-field model defined on regular random networks, we interpret the dynamics of the system in this region and prove that the existence of bifurcation for this second epidemic threshold crucially depends on the absence of awareness decay. We show that the continuum of equilibria that characterizes the slow die-out dynamics collapses into a unique equilibrium when a constant rate of awareness decay is assumed, no matter how small, and that the resulting bifurcation from the disease-free equilibrium is equivalent to that of standard epidemic models. We illustrate these findings with continuous-time stochastic simulations on regular random networks with different degrees. Finally, the behaviour of solutions with and without decay in awareness is compared around the second epidemic threshold for a small rate of awareness decay
This work has been partially supported by the Research Grant MTM2011-27739-C04-03 of the Spanish Government (D.J. and J.S.), the Project 2009-SGR-345 (J.S.) of the Generalitat de Catalunya, and IMA Collaborative Grant (SGS01/13), UK (I.K. and J.S.)
Format: application/pdf
Citation: 023568
ISSN: 0022-5193 (versió paper)
1095-8541 (versió electrònica)
Document access: http://hdl.handle.net/10256/11221
Language: eng
Publisher: Elsevier
Collection: MICINN/PN 2012-2015/MTM2011-27739-C04-03
AGAUR/2009-2013/2014 SGR-345
Versió preprint del document publicat a: http://dx.doi.org/10.1016/j.jtbi.2014.10.013
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Is part of: © Journal of Theoretical Biology, 2015, vol. 365, p. 457-468
Rights: Tots els drets reservats
Subject: Epidèmies -- Models matemàtics
Epidemics -- Mathematical models
Processos estocàstics
Stochastic processes
Processos de ramificació
Branching processes
Title: Analysis of an epidemic model with awareness decay on regular random networks
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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