1. Analysis of an epidemic model with awareness decay on regular random networks
- Author
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Istvan Z. Kiss, David Juher, Joan Saldaña, Ministerio de Ciencia e Innovación (Espanya), and Generalitat de Catalunya. Agència de Gestió d'Ajuts Universitaris i de Recerca
- Subjects
Statistics and Probability ,Health Knowledge, Attitudes, Practice ,Time Factors ,Epidemics -- Mathematical models ,FOS: Physical sciences ,Dynamical Systems (math.DS) ,Communicable Diseases ,Models, Biological ,Quantitative Biology - Quantitative Methods ,General Biochemistry, Genetics and Molecular Biology ,Epidemic thresholds ,Stochastic processes ,Network epidemic models ,Epidèmies -- Models matemàtics ,FOS: Mathematics ,Humans ,Statistical physics ,Mathematics - Dynamical Systems ,Epidemics ,Quantitative Biology - Populations and Evolution ,Quantitative Methods (q-bio.QM) ,Bifurcation ,Mathematics ,General Immunology and Microbiology ,Continuum (measurement) ,Stochastic process ,Processos de ramificació ,Applied Mathematics ,Preventive behavioural responses ,Populations and Evolution (q-bio.PE) ,Processos estocàstics ,General Medicine ,Nonlinear Sciences - Adaptation and Self-Organizing Systems ,Constant rate ,Branching processes ,Bifurcation analysis ,FOS: Biological sciences ,Modeling and Simulation ,Disease Susceptibility ,General Agricultural and Biological Sciences ,Epidemic model ,Adaptation and Self-Organizing Systems (nlin.AO) ,Mathematical economics - 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.)
- Published
- 2021