Epidemic spread in interconnected directed networks

TL;DR

This paper develops a comprehensive epidemic model on interconnected directed networks, analyzing how network structure influences disease spread and identifying key thresholds for epidemic outbreaks.

Contribution

It introduces a generalized epidemic model on interconnected directed networks and provides theoretical analysis of stability and epidemic thresholds.

Findings

Basic reproduction number derived for interconnected directed networks

Global stability conditions for disease-free and endemic states established

Node degree independence reduces impact of network topology on spread

Abstract

In the real world, many complex systems interact with other systems. In addition, the intra- or inter-systems for the spread of information about infectious diseases and the transmission of infectious diseases are often not random, but with direction. Hence, in this paper, we build epidemic model based on an interconnected directed network, which can be considered as the generalization of undirected networks and bipartite networks. By using the mean-field approach, we establish the Susceptible-Infectious-Susceptible model on this network. We theoretically analyze the model, and obtain the basic reproduction number, which is also the generalization of the critical number corresponding to undirected or bipartite networks. And we prove the global stability of disease-free and endemic equilibria via the basic reproduction number as a forward bifurcation parameter. We also give a condition for epidemic prevalence only on a single subnetwork. Furthermore, we carry out numerical simulations, and find that the independence between each node's in- and out-degrees greatly reduce the impact of the network's topological structure on disease spread.