### Mathematical Biosciences and Engineering

2020, Issue 4: 4127-4146. doi: 10.3934/mbe.2020229
Research article Special Issues

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

• 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.

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

### Related Papers:

• 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.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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