A Dissipativity Approach to Analyzing Composite Spreading Networks

TL;DR

This paper introduces a dissipativity-based framework for analyzing composite spreading networks, providing conditions for disease eradication and demonstrating its application through influenza outbreak simulations.

Contribution

It develops a novel dissipativity approach for analyzing interconnected spreading networks and derives conditions for their convergence to disease-free states.

Findings

Composite networks can be stabilized to disease-free states using dissipativity conditions.

Reducing interaction times below 79% can prevent influenza outbreaks in a school setting.

The method applies control theory to epidemiological network analysis.

Abstract

The study of spreading processes often analyzes networks at different resolutions, e.g., at the level of individuals or countries, but it is not always clear how properties at one resolution can carry over to another. Accordingly, in this work we use dissipativity theory from control system analysis to characterize composite spreading networks that are comprised by many interacting subnetworks. We first develop a method to represent spreading networks that have inputs and outputs. Then we define a composition operation for composing multiple spreading networks into a larger composite spreading network. Next, we develop storage and supply rate functions that can be used to demonstrate that spreading dynamics are dissipative. We then derive conditions under which a composite spreading network will converge to a disease-free equilibrium as long as its constituent spreading networks are dissipative with respect to those storage and supply rate functions. To illustrate these results, we use simulations of an influenza outbreak in a primary school, and we show that an outbreak can be prevented by decreasing the average interaction time between any pair of classes to less than 79% of the original interaction time.