Behavioral change delay drives the long-term epidemic oscillations

There is an evidence that the human behavioral change plays a central role in determining the spread of infectious diseases. This study introduces a response delay of the human behavioral change for self-protection into a dynamic system combining the transmission dynamics of infectious diseases with the behavior evolution dynamics. We initially study the existence and stability of equilibria of the coupled system without delay, and discuss the forward and backward bifurcations. We further prove that the coupled system with delay can undergo the Hopf bifurcation by choosing the delay as the bifurcation parameter, while there is no Hopf bifurcation of the proposed model in the absence of the delay effect. All the theoretical results are further verified through numerical simulations. As a result, we verify that the response delay is a key to drive the epidemic oscillations through inducing the Hopf bifurcation. Thus, it is crucial for the media to effectively report the development of emerging infectious diseases in real time, and for the general public to pay enough attention to the risk of infection.