Effect of adaptive rewiring delay in an SIS network epidemic model

In the real world, in order to avoid the infection risk, people tend to cut off the links with their infected neighbors, then look for other susceptible individuals to rewire. However, the rewiring process does not occur immediately, but takes some time. We therefore establish a delayed SIS network model with adaptive rewiring mechanism and analyze the long-term steady states for the system with and without the rewiring delay. We find that with the rewiring time, there are infinite equilibria lie on a line in a high-dimensional state space, which is quite different from normal delayed model. The numerical simulation results show that the system approaches to different steady state on the line under the same initial values and different rewiring delays, and the stable limit cycle can appear with the increase of rewiring delay. These surprising results may provide new insights into the study of delayed network epidemic model.