Stability analysis and Hopf bifurcation in a diffusive epidemic model with two delays

Huan Dai; Yuying Liu; Junjie Wei; Huan Dai; Yuying Liu; Junjie Wei

doi:10.3934/mbe.2020229

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 4: 4127-4146. doi: 10.3934/mbe.2020229

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Stability analysis and Hopf bifurcation in a diffusive epidemic model with two delays

1.
School of Science, Harbin Institute of Technology (Weihai), Weihai 264209, China
2.
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received: 31 March 2020 Accepted: 01 June 2020 Published: 09 June 2020

A diffusive epidemic model with two delays subjecting to Neumann boundary conditions is considered. First we obtain the existence and the stability of the positive constant steady state. Then we investigate the existence of Hopf bifurcations by analyzing the distribution of the eigenvalues. Furthermore, we derive the normal form on the center manifold near the Hopf bifurcation singularity. Finally, some numerical simulations are carried out to illustrate the theoretical results.
- epidemic,
- two delays,
- Hopf bifurcation,
- normal form
Citation: Huan Dai, Yuying Liu, Junjie Wei. Stability analysis and Hopf bifurcation in a diffusive epidemic model with two delays[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 4127-4146. doi: 10.3934/mbe.2020229

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Abstract

A diffusive epidemic model with two delays subjecting to Neumann boundary conditions is considered. First we obtain the existence and the stability of the positive constant steady state. Then we investigate the existence of Hopf bifurcations by analyzing the distribution of the eigenvalues. Furthermore, we derive the normal form on the center manifold near the Hopf bifurcation singularity. Finally, some numerical simulations are carried out to illustrate the theoretical results.

References

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