Bifurcation analysis in an epidemic model on adaptive networks

In this paper, we study a delayed adaptive network epidemic model in which the local spatial connections of susceptible and susceptible individuals have time-delay effects on the rate of demographic change of local spatial connections of susceptible and susceptible individuals. We prove that the Hopf bifurcation occurs at the critical value t 0 with delay t as the bifurcation parameter. Then, by using the normal form method and the central manifold theory, the criteria for the bifurcation direction and stability are derived. Finally, numerical simulations are presented to show the feasibility of our results.

Automated summary

In this paper, we study a delayed adaptive network epidemic model where the rate of demographic change of susceptible and infected individuals is affected by the time-delay effects of local spatial connections. We prove the Hopf bifurcation occurs at the critical value t 0 with delay t as the bifurcation parameter. The criteria for the bifurcation direction and stability are derived using the normal form method and central manifold theory. Numerical simulations are provided to demonstrate the feasibility of the results.