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

Juher, David, Kiss, Istvan Z and Saldaña, Joan (2015) Analysis of an epidemic model with awareness decay on regular random networks. Journal of Theoretical Biology, 365. pp. 457-468. ISSN 0022-5193

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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 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.

Item Type: Article
Keywords: Network epidemic models; Preventive behavioural responses; Epidemic thresholds
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Sinead Rance
Date Deposited: 15 Dec 2015 13:51
Last Modified: 25 Jun 2017 15:35
URI: http://sro.sussex.ac.uk/id/eprint/58486

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