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Title: Dynamics of an epidemic model with delays and stage structure

Abstract

In this paper, dynamics of a stage-structured epidemic model with delays and nonlinear incidence rate is analyzed. Local stability and existence of Hopf bifurcation is discussed by choosing possible combination of the delays as the bifurcation parameter. It is proved that the unique endemic equilibrium is locally asymptotically stable when the delay is suitably small and a bifurcating periodic solution will be caused once the delay passes through the corresponding critical value of the delay. We make use of the normal form theory and center manifold theorem to obtain the explicit formulas for determining the properties of the Hopf bifurcation. Numerical simulations supporting our obtained findings are carried out in the end.

Authors:
 [1];  [2]
  1. Bengbu University, Department of Mathematics and Physics (China)
  2. School of Statistics and Applied Mathematics, Anhui University of Finance and Economics (China)
Publication Date:
OSTI Identifier:
22769312
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 2; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; BIFURCATION; COMPUTERIZED SIMULATION; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; STABILITY

Citation Formats

Liu, Juan, and Wang, Kai. Dynamics of an epidemic model with delays and stage structure. United States: N. p., 2018. Web. doi:10.1007/S40314-017-0452-Y.
Liu, Juan, & Wang, Kai. Dynamics of an epidemic model with delays and stage structure. United States. doi:10.1007/S40314-017-0452-Y.
Liu, Juan, and Wang, Kai. Tue . "Dynamics of an epidemic model with delays and stage structure". United States. doi:10.1007/S40314-017-0452-Y.
@article{osti_22769312,
title = {Dynamics of an epidemic model with delays and stage structure},
author = {Liu, Juan and Wang, Kai},
abstractNote = {In this paper, dynamics of a stage-structured epidemic model with delays and nonlinear incidence rate is analyzed. Local stability and existence of Hopf bifurcation is discussed by choosing possible combination of the delays as the bifurcation parameter. It is proved that the unique endemic equilibrium is locally asymptotically stable when the delay is suitably small and a bifurcating periodic solution will be caused once the delay passes through the corresponding critical value of the delay. We make use of the normal form theory and center manifold theorem to obtain the explicit formulas for determining the properties of the Hopf bifurcation. Numerical simulations supporting our obtained findings are carried out in the end.},
doi = {10.1007/S40314-017-0452-Y},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 2,
volume = 37,
place = {United States},
year = {2018},
month = {5}
}