Contact processes and moment closure on adaptive networks

TL;DR

This paper reviews the use of contact processes and moment-closure approximations to model adaptive networks, highlighting their applications in understanding dynamic phenomena like epidemics and opinion formation.

Contribution

It provides a comprehensive overview of the moment-closure technique applied to adaptive networks, including methodological details and recent developments.

Findings

Effective low-dimensional ODE models for adaptive networks

Insights into epidemic and opinion dynamics on evolving networks

Tutorial and review of recent advances in the field

Abstract

Contact processes describe the transmission of distinct properties of nodes via the links of a network. They provide a simple framework for many phenomena, such as epidemic spreading and opinion formation. Combining contact processes with rules for topological evolution yields an adaptive network in which the states of the nodes can interact dynamically with the topological degrees of freedom. By moment-closure approximation it is possible to derive low-dimensional systems of ordinary differential equations that describe the dynamics of the adaptive network on a coarse-grained level. In this chapter we discuss the approximation technique itself as well as its applications to adaptive networks. Thus, it can serve both as a tutorial as well as a review of recent results.