About: Global Dynamics of a Susceptible-Infectious-Recovered Epidemic Model with a Generalized Nonmonotone Incidence Rate

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An Entity of Type : schema:ScholarlyArticle, within Data Space : wasabi.inria.fr associated with source document(s)

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type	Academic Article research paper schema:ScholarlyArticle
isDefinedBy	Covid-on-the-Web dataset
title	Global Dynamics of a Susceptible-Infectious-Recovered Epidemic Model with a Generalized Nonmonotone Incidence Rate
Creator	Lu, Min Huang, Jicai Yu, Pei Yu, · Ruan, ·
source	Medline; PMC
abstract	A susceptible-infectious-recovered (SIRS) epidemic model with a generalized nonmonotone incidence rate [Formula: see text] ([Formula: see text] such that [Formula: see text] for all [Formula: see text] ) is considered in this paper. It is shown that the basic reproduction number [Formula: see text] does not act as a threshold value for the disease spread anymore, and there exists a sub-threshold value [Formula: see text] such that: (i) if [Formula: see text] , then the disease-free equilibrium is globally asymptotically stable; (ii) if [Formula: see text] , then there is a unique endemic equilibrium which is a nilpotent cusp of codimension at most three; (iii) if [Formula: see text] , then there are two endemic equilibria, one is a weak focus of multiplicity at least three, the other is a saddle; (iv) if [Formula: see text] , then there is again a unique endemic equilibrium which is a weak focus of multiplicity at least three. As parameters vary, the model undergoes saddle-node bifurcation, backward bifurcation, Bogdanov–Takens bifurcation of codimension three, Hopf bifurcation, and degenerate Hopf bifurcation of codimension three. Moreover, it is shown that there exists a critical value [Formula: see text] for the psychological effect [Formula: see text] , a critical value [Formula: see text] for the infection rate k, and two critical values [Formula: see text] for [Formula: see text] that will determine whether the disease dies out or persists in the form of positive periodic coexistent oscillations or coexistent steady states under different initial populations. Numerical simulations are given to demonstrate the existence of one, two or three limit cycles.
has issue date	2020-06-29(xsd:dateTime)
bibo:doi	10.1007/s10884-020-09862-3
bibo:pmid	32837121
has license	no-cc
sha1sum (hex)	4f2654234c7200107ad04c1f0ae5b4c3de19ebc4
schema:url	https://doi.org/10.1007/s10884-020-09862-3
resource representing a document's title	Global Dynamics of a Susceptible-Infectious-Recovered Epidemic Model with a Generalized Nonmonotone Incidence Rate
has PubMed Central identifier	PMC7322403
has PubMed identifier	32837121
schema:publication	J Dyn Differ Equ
resource representing a document's body	covid:4f2654234c7200107ad04c1f0ae5b4c3de19ebc4#body_text
is schema:about of	named entity 'STABLE' named entity 'HOPF BIFURCATION' named entity '28I' named entity 'EPIDEMIC MODEL' named entity 'ENDEMIC' named entity 'POPULATIONS' named entity 'FOCUS' named entity 'SIRS' named entity 'incidence rate' named entity 'globally asymptotically stable' named entity 'codimension' named entity 'Hopf bifurcation' named entity 'codimension' named entity 'Hopf bifurcation' named entity 'Epidemic Model' named entity 'cusp singularity' named entity '1.1' named entity '2.11' named entity '2.2' named entity 'codimension' named entity 'avian influenza' named entity 'Hopf bifurcation' named entity '2.2' named entity 'Hopf bifurcation' named entity 'infection' named entity 'limit cycle' named entity '1.1' named entity 'codimension' named entity 'index theory' named entity '2.2' named entity 'codimension' named entity 'saddle-node bifurcation' named entity 'endemic' named entity 'Hopf bifurcation' named entity 'codimension' named entity 'limit cycles' named entity '2.2' named entity 'infection rate' named entity 'saddle-node bifurcation' named entity 'infectious disease' named entity 'infectious diseases' named entity 'codimension' named entity 'codimension' named entity '1.1' named entity 'Hopf bifurcation' named entity 'limit cycles' named entity 'aggressive measures' named entity 'limit cycle' named entity 'endemic equilibrium' named entity 'Hopf bifurcation' named entity 'limit cycles' named entity 'China' named entity 'endemic equilibrium' named entity 'infection' named entity 'infection rate' named entity '2.2' named entity 'limit cycle' named entity 'measles' named entity 'MATLAB' named entity 'bifurcation diagram' named entity 'bifurcation diagram' named entity 'limit cycle' named entity 'Dumortier' named entity 'limit cycle' named entity 'basic reproduction number' named entity 'versal unfolding' named entity 'limit cycle' named entity 'periodic orbit' named entity 'attractor' named entity 'limit cycles' named entity 'globally asymptotically stable' named entity '2.2' named entity 'incidence rates' named entity 'versal unfolding' named entity 'basic reproduction number' named entity '1.1' named entity 'incidence rate'

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