About: Bifurcation analysis of an SIRS epidemic model with a generalized nonmonotone and saturated incidence rate

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About: Bifurcation analysis of an SIRS epidemic model with a generalized nonmonotone and saturated incidence rate Goto Sponge NotDistinct Permalink

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
has title	Bifurcation analysis of an SIRS epidemic model with a generalized nonmonotone and saturated incidence rate
Creator	Lu, Min Ruan, Shigui Huang, Jicai Yu, Pei Ruan, S Yu, (
Source	Elsevier; Medline; PMC
abstract	Abstract In this paper, we study a susceptible-infectious-recovered (SIRS) epidemic model with a generalized nonmonotone and saturated incidence rate k I 2 S 1 + β I + α I 2 , in which the infection function first increases to a maximum when a new infectious disease emerges, then decreases due to psychological effect, and eventually tends to a saturation level due to crowding effect. It is shown that there are a weak focus of multiplicity at most two and a cusp of codimension at most two for various parameter values, and the model undergoes saddle-node bifurcation, Bogdanov-Takens bifurcation of codimension two, Hopf bifurcation, and degenerate Hopf bifurcation of codimension two as the parameters vary. It is shown that there exists a critical value α = α 0 for the psychological effect, and two critical values k = k 0 , k 1 ( k 0 < k 1 ) for the infection rate such that: (i) when α > α 0 , or α ≤ α 0 and k ≤ k 0 , the disease will die out for all positive initial populations; (ii) when α = α 0 and k 0 < k ≤ k 1 , the disease will die out for almost all positive initial populations; (iii) when α = α 0 and k > k 1 , the disease will persist in the form of a positive coexistent steady state for some positive initial populations; and (iv) when α < α 0 and k > k 0 , the disease will persist in the form of multiple positive periodic coexistent oscillations and coexistent steady states for some positive initial populations. Numerical simulations, including the existence of one or two limit cycles and data-fitting of the influenza data in Mainland China, are presented to illustrate the theoretical results.
has issue date	2019-07-15(xsd:dateTime)
bibo:doi	10.1016/j.jde.2019.03.005
bibo:pmid	32226129
has license	els-covid
sha1sum (hex)	96bbfb4e9db97a3c63b247ef0898122f10d099dc
schema:url	https://doi.org/10.1016/j.jde.2019.03.005
resource representing a document's title	Bifurcation analysis of an SIRS epidemic model with a generalized nonmonotone and saturated incidence rate
has PubMed Central identifier	PMC7094459
has PubMed identifier	32226129
schema:publication	Journal of Differential Equations
resource representing a document's body	covid:96bbfb4e9db97a3c63b247ef0898122f10d099dc#body_text
is schema:about of	named entity 'EPIDEMIC MODEL' named entity 'GENERALIZED' named entity 'INCREASES' named entity 'DEGENERATE HOPF BIFURCATION' named entity 'INITIAL' named entity 'FORM' named entity 'EPIDEMIC MODEL' named entity 'STUDY' named entity 'LEVEL' named entity 'FOCUS' named entity 'LIMIT' named entity 'INCIDENCE RATE' named entity 'CRITICAL' named entity 'FUNCTION' named entity 'DIE' named entity 'CROWDING EFFECT' named entity 'THEORETICAL' named entity 'SADDLE-NODE BIFURCATION' named entity 'INFECTION' named entity 'POSITIVE' named entity 'DISEASE' named entity 'ANALYSIS' named entity 'SATURATED' named entity '28I' named entity 'PRESENTED' named entity 'SUSCEPTIBLE' named entity 'NEW' named entity 'PAPER' named entity 'BIFURCATION' named entity 'DUE TO' named entity 'STEADY STATE' named entity 'NUMERICAL SIMULATIONS' named entity 'DATA' named entity 'MODEL' named entity 'SATURATED' named entity 'SIRS' named entity 'MAXIMUM' named entity 'POPULATIONS' named entity 'MULTIPLICITY' named entity 'INFECTIOUS DISEASE' named entity 'MULTIPLE' named entity 'OSCILLATIONS' named entity 'WEAK' named entity 'STEADY' named entity 'INCIDENCE RATE' named entity 'BIFURCATION' named entity 'INCLUDING' named entity 'RESULTS' named entity 'FITTING' named entity 'CUSP' named entity 'SATURATION' named entity 'STATES' named entity 'INFECTION RATE' named entity 'PARAMETERS' named entity 'PSYCHOLOGICAL EFFECT' named entity 'HOPF BIFURCATION' named entity 'GENERALIZED' named entity 'VALUE' named entity 'ALMOST ALL' named entity 'PARAMETER' named entity 'VALUES' named entity 'INFLUENZA' named entity 'INFECTIOUS' named entity 'DECREASES' named entity 'VARIOUS' named entity 'PERIODIC' named entity 'RECOVERED' named entity 'MAINLAND CHINA' named entity 'incidence rate' named entity 'epidemic model' named entity 'saturation level' named entity 'infection' named entity 'Numerical simulations' named entity 'steady state' named entity '3.14' named entity '1/3'

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