Unification of theoretical approaches for epidemic spreading on complex networks

TL;DR

This paper reviews and unifies various theoretical models of epidemic spreading on complex networks, highlighting their connections and aiming to improve the accuracy of predictions by considering network topology and correlations.

Contribution

It unifies the main theoretical approaches for epidemic spreading on complex networks, establishing connections to enhance understanding and development of more accurate models.

Findings

Links between different theoretical approaches are established.

Provides insights for developing improved epidemic models.

Highlights the importance of network topology and correlations.

Abstract

Models of epidemic spreading on complex networks have attracted great attention among researchers in physics, mathematics, and epidemiology due to their success in predicting and controlling scenarios of epidemic spreading in real-world scenarios. To understand the interplay between epidemic spreading and the topology of a contact network, several outstanding theoretical approaches have been developed. An accurate theoretical approach describing the spreading dynamics must take both the network topology and dynamical correlations into consideration at the expense of increasing the complexity of the equations. In this short survey we unify the most widely used theoretical approaches for epidemic spreading on complex networks in terms of increasing complexity, including the mean-field, the heterogeneous mean-field, the quench mean-field, dynamical message-passing, link percolation, and pairwise approximation. We build connections among these approaches to provide new insights into developing an accurate theoretical approach to spreading dynamics on complex networks.