Hopf bifurcation analysis for a delayed nonlinear-SEIR epidemic model on networks

Using graph Laplacian diffusion, a delayed Susceptible-Exposed-Infected-Removed (SEIR) epidemic model with a non-linear incidence rate has been considered. This model incorporates a diffusion term that captures population mobility through a network. The local stability analysis for each steady state is demonstrated. Furthermore, we have explored the existence of Hopf bifurcation at the endemic equilibrium and addressed its direction using the Normal Form Theory and Center of Manifold Theorem. To visually illustrate our theoretical findings, we have performed computational experiments on a small-world Watts-Strogatz graph.