Centrality-based epidemic control in complex social networks

Abstract

Recent progress in the areas of network science and control has shown a significant promise in understanding and analyzing epidemic processes. A well-known model to study epidemics processes used by both control and epidemiological research communities is the susceptible–infected–susceptible (SIS) dynamics to model the spread of disease/viruses over contact networks of infected and susceptible individuals. The SIS model has two metastable equilibria: one is called the endemic equilibrium and the other is known as the disease-free or healthy-state equilibrium. Control theory provides the tools to design control actions (allocating curing or vaccination resources) in order to achieve and stabilize the disease-free equilibrium. However, the control actions are often designed for the entire community. Based on the ideas developed in graph-theoretic control, this paper aims to study allocating curing resources to a target group instead of the entire community. This target group is selected based on centrality rank in different types of random networks. Our results show that specific graph properties are involved in the epidemic control. In particular, we show that (1) the clustering-coefficient and (2) the degree distribution of the network are effective in the selection of these target groups for epidemic control.