Open AccessStability analysis and Hopf bifurcation in a diffusive epidemic model with two delays
Author(s) -
Huan Dai,
Yu Ying Liu,
Jun Wei
Publication year - 2020
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2020229
Subject(s) - center manifold , hopf bifurcation , mathematics , eigenvalues and eigenvectors , stability (learning theory) , constant (computer programming) , neumann boundary condition , pitchfork bifurcation , mathematical analysis , bifurcation , manifold (fluid mechanics) , singularity , epidemic model , boundary (topology) , physics , nonlinear system , mechanical engineering , population , demography , quantum mechanics , machine learning , sociology , computer science , engineering , programming language
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.