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

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posted on 2023-06-08, 23:33 authored by David Juher, Istvan Kiss, Joan Saldaña
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.

Funding

IMA Collaborative Grant; SGS01/13

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Journal of Theoretical Biology

ISSN

0022-5193

Publisher

Elsevier

Volume

365

Page range

457-468

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2015-12-15

First Open Access (FOA) Date

2015-12-15

First Compliant Deposit (FCD) Date

2015-12-15

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