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Author:

Zhang, Jiajia (Zhang, Jiajia.) | Qiao, Yuanhua (Qiao, Yuanhua.) (Scholars:乔元华)

Indexed by:

EI Scopus SCIE

Abstract:

In this paper, an SIR epidemic model considering hospital resources and vaccination is established and the rich dynamics and complex bifurcations are investigated. Firstly, the existence of disease-free equilibrium and endemic equilibria is explored. It is founded that when the vaccination rate is not high, the number of endemic equilibrium points changed easily with the number of hospital resources and vaccination, resulting in transcritical bifurcation and saddle???node bifurcations. Secondly, different types singularities such as degenerate saddle???node of codimension 1 at the disease-free equilibrium, and cusp or focus type Bogdanov???Takens singularities of codimension 3 at endemic equilibria are presented. Thirdly, bifurcation analysis at these equilibria is investigated, and it is found that the system undergoes a sequence of bifurcations, including Hopf, degenerate Hopf bifurcation, homoclinic bifurcation, the cusp type Bogdanov???Takens bifurcation of codimension 2, and the focus type Bogdanov???Takens bifurcation of codimension 3 which are the organizing centers for a series of bifurcations with lower codimension. And the system shows very rich dynamics such as the existence of multiple coexistent periodic orbits, homoclinic loops. Finally, numerical simulations are presented to verify the theoretical results. ?? 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Keyword:

Saddle-node bifurcation Transcritical bifurcation Bogdanov-Takens bifurcation SIR epidemic model Degenerate Hopf bifurcation

Author Community:

  • [ 1 ] [Zhang, Jiajia]Beijing Univ Technol, Fac Sci, Beijing 100124, Peoples R China
  • [ 2 ] [Qiao, Yuanhua]Beijing Univ Technol, Fac Sci, Beijing 100124, Peoples R China

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Source :

MATHEMATICS AND COMPUTERS IN SIMULATION

ISSN: 0378-4754

Year: 2023

Volume: 208

Page: 157-185

4 . 6 0 0

JCR@2022

ESI Discipline: ENGINEERING;

ESI HC Threshold:19

Cited Count:

WoS CC Cited Count:

SCOPUS Cited Count: 12

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 0

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