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Backward bifurcation for some general recovery functions
Author(s) -
Villavicencio Pulido Geiser,
Barradas Ignacio,
Luna Beatriz
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4074
Subject(s) - monotone polygon , mathematics , bifurcation , nonlinear system , recovery rate , simple (philosophy) , function (biology) , mathematical economics , biology , geometry , physics , epistemology , chromatography , quantum mechanics , evolutionary biology , philosophy , chemistry
We consider an epidemic model for the dynamics of an infectious disease that incorporates a nonlinear function h ( I ), which describes the recovery rate of infectious individuals. We show that in spite of the simple structure of the model, a backward bifurcation may occur if the recovery rate h ( I ) decreases and the velocity of the recovery ratedh ( 0 ) dIis below a threshold value in the beginning of the epidemic. These functions would represent a weak reaction or slow treatment measures because, for instance, of limited allocation of resources o sparsely distributed populations. This includes commonly used functionals, as the monotone saturating Michaelis–Menten, and non monotone recovery rates, used to represent a recovery rate limited by the increasing number of infected individuals. We are especially interested in control policies that can lead to recovery functions that avoid backward bifurcation. Copyright © 2016 John Wiley & Sons, Ltd.