Stability and Hopf bifurcation for an epidemic disease model with time delay

摘要

The conditions for stability and Hopf bifurcation of a SIR disease model with survival probability and time delay are analysed. Firstly, the conditions of the existence and local stability of disease-free and endemic equilibrium are investigated. Secondly, we found that there are stability switches, and Hopf bifurcation occur for endemic equilibrium when the time delay τ passed through a sequence of critical values. Finally, we verify the analytic results by module Simulink in Matlab.