Hopf bifurcation in an SIR epidemic model with psychological effect and distributed time delay

In this chapter, we are concerned with an SIR epidemic model with psychological effect and distributed time delay, which would be realistic to consider people's behavior change during the epidemic period due to nonpharmaceutical interventions such as lockdown. For general distribution functions, by using the theory of center manifold and Poincaré normal form, we obtain the characteristic values that determine the property of the Hopf bifurcation: the direction, stability, and period of the bifurcated periodic solution. Specifically, we consider the case of the truncated exponential distribution and show that the stable periodic solution can arise through the Hopf bifurcation.