Delayed information induced self-protection leads to oscillations in an epidemic model

In this study, an SEIR epidemic model is considered and studied that incorporates the effect of delay in information dependent self-protection along with the effect of screening and saturated treatment. The proposed model is analysed and stability of equilibria is established. The local asymptotic stability of the disease free equilibrium is ensured for R₀ < 1 and it is unstable otherwise. Whereas, for R₀ > 1, the proposed model has the unique endemic equilibrium point. In addition, under some parametric conditions, the model has also two endemic equilibria for the case R₀ < 1. For all delay values, the local asymptotic stability of the unique endemic equilibrium is established under some parametric constraints. Further, the occurrence of the periodic oscillations is also observed when the delay crosses a threshold value via Hopf bifurcation.