Epidemiological modeling on complex networks

Abstract

The present chapter is devoted to review some literatures on the modeling infectious disease on complex networks. From the following several aspects we give a brief summary about solving the problem of the disease spread: Modeling approaches of epidemic dynamics on complex networks, Application of percolation theory in propagation dynamics, Epidemic models in complex network with demographics and Epidemic spreading on multilayer networks. In the first section, the Node-based and Edge-based mean-field modeling approaches on complex networks are reviewed and compared respectively, and the second section reviews the application of bond percolation in the single network (undirected graphs, directed graphs, bipartite graphs and clustered networks) and coupled networks (overlap networks and interconnected networks), then gives a review about the disease epidemics and site or bond percolation or both site and bond percolation in small-world networks. Following, we present an overview on some of recent studies on epidemic dynamics with demographics and epidemic processes on multilayer networks in the last two section, respectively.