Analysis of an epidemic model with awareness decay on regular random networks
Juher, David (Universitat de Girona. Departament d'Informàtica, Matemàtica Aplicada i Estadística)
Kiss, Istvan Z. (University of Sussex. Department of Mathematics)
Saldaña, Joan (Universitat de Girona. Departament d'Informàtica, Matemàtica Aplicada i Estadística)

Date:	2015
Abstract:	The existence of a die-out threshold (di erent 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 of 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.
Grants:	Ministerio de Economía y Competitividad MTM2011-27739-C04-03 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-345
Note:	Agraïments: IMA Collaborative Grant (SGS01/13), UK (I.K. and J.S.)
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Epidemic thresholds ; Network epidemic models ; Preventive behavioural responses
Published in:	Journal of Theoretical Biology, Vol. 365 (2015) , p. 457-468, ISSN 0022-5193

DOI: 10.1016/j.jtbi.2014.10.013

Postprint 27 p, 745.9 KB

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