icon: Fast Simulation of Epidemics on Coevolving Networks

TL;DR

This work extends the classical SIS model by incorporating stochastic rules that allow for the association of susceptible nodes and the dissociation of infected nodes, and outperforms standard baselines in terms of computational efficiency while revealing new emergent patterns in epidemic spread.

Abstract

We introduce a fast simulation technique for modeling epidemics on adaptive networks. Our rejection-based algorithm efficiently simulates the co-evolution of the network structure and the epidemic dynamics. We extend the classical SIS model by incorporating stochastic rules that allow for the association of susceptible nodes and the dissociation of infected nodes. The method outperforms standard baselines in terms of computational efficiency while revealing new emergent patterns in epidemic spread. Code is made available at github.com/GerritGr/icon.

Figures (4)

• Figure 1: Schematic illustration of our continuous-time coevolving spreading model inspired by wang2019adaptive. Similar to the standard SIS model, infected (red) nodes can 1) transmit their infection to neighboring susceptible (blue) nodes and can 2) recover (become susceptible again). Additionally, two connected infected nodes can dissociate (removing their edge), and two unconnected susceptible nodes can associate (creating an edge between them).
• Figure 2: Evolution of prevalence (left) and average degree (right) for three example trajectories on a Erdős–Rényi graph model with 1000 nodes.
• Figure 3: [Lower is better.] Mean CPU time of our rejection-based method (icon) compared to two baselines using three graph models based on five runs (see also Appendix \ref{['sec:detailed-runtime-results']}).
• Figure 4: Some results for different parameter combinations for random graphs with 1000 nodes.