Title of article :
Stability and Hopf Bifurcation Analysis of an Epidemic Model with Time Delay
Author/Authors :
Zhang, Yue Harbin Engineering University - Harbin, China , Li, Xue School of Computer Science and Technology - Harbin Institute of Technology - Harbin, China , Zhang, Xianghua Heilongjiang University of Science and Technology, China , Yin, Guisheng Harbin Engineering University - Harbin, China
Abstract :
Epidemic models are normally used to describe the spread of infectious diseases. In this paper, we will discuss an epidemic model
with time delay. Firstly, the existence of the positive fixed point is proven; and then, the stability and Hopf bifurcation are
investigated by analyzing the distribution of the roots of the associated characteristic equations. Thirdly, the theory of normal
form and manifold is used to drive an explicit algorithm for determining the direction of Hopf bifurcation and the stability of
the bifurcation periodic solutions. Finally, some simulation results are carried out to validate our theoretic analysis.
Keywords :
Epidemic , Hopf , Analysis
Journal title :
Computational and Mathematical Methods in Medicine
