### Abstract or Additional Information

We consider a model for epidemic networks, which is a nonlocal SIS-type system giving the time evolution of Susceptibles and Infected. The topology of the network is given by the degree distribution of its nodes, so that the degree plays here the role of a spatial variable. We analyze the system assuming density-dependent or frequency-dependent transmission. We prove global existence results. We establish the existence of an endemic equilibrium above a threshold value, which is optimal under specific assumptions. We investigate the stability of this endemic equilibrium and study the asymptotic behaviour of the solution for large times. We compare our results to the ones obtained for the discrete system from which this model is derived.

The seminar will be held in Thackeray 427.