EPIDEMIC SPREADING ON THREE-LAYER INTERDEPENDENT NETWORKS

Abstract

Many epidemic diseases spread among three different populations with different contact patterns and infection rates. In response to such diseases, we propose two new types of three-layer interdependent networks — string-coupled networks and circular-coupled networks. We investigate an epidemic spreading on the two types of interdependent networks, propose two mathematical models through heterogeneous mean field approach and prove global stability of the disease-free and endemic equilibria. Through theoretical and numerical analysis, we find the following: the increase of each infection rate affects effectively only its own subnetwork and neighbors; in a string-coupled network, the middle subnetwork has bigger impact on the basic reproduction number than the end subnetworks with the growth of network size or infection rates; the basic reproduction number on a circular-coupled network is larger than that on a string-coupled network for a fixed network size; but the change of the basic reproduction number (or the average infection densities) is almost the same on both string-coupled and circular-coupled networks with the increasing of certain infection rate.