Replicating hypergraph disease dynamics with lower-order interactions

Area of Science:

• Epidemiology
• Network Science
• Computational Modeling

Background:

• Compartmental models like SIS/SIR are standard for epidemic and information diffusion studies.
• Network structures enhance realism by simulating pairwise interactions.
• Simplicial contagion models (SCM) use hypergraphs for higher-order interactions (groups > 2).

Purpose of the Study:

• To unify classical compartmental models with simplicial contagion models.
• To extend models to arbitrary-order hyperedge interactions.
• To investigate if higher-order interactions yield fundamentally different dynamics than pairwise interactions.

Main Methods:

• Developed an agent-based model unifying SIS/SIR and SCM.
• Extended the model for interactions on hyperedges of any order.
• Demonstrated replication of higher-order dynamics using scaled pairwise interactions.

Main Results:

• Steady-state dynamics of pairwise interactions can replicate higher-order simulations via scaled parameters.
• Dynamically varying disease parameters allow pairwise models to mimic transient and steady-state higher-order dynamics.
• The approximation is robust to model misspecification and applies to complex, heterogeneous hypergraphs.

Conclusions:

• Pairwise interaction models can approximate higher-order contagion dynamics through parameter scaling.
• Higher-order network topologies can be effectively represented by modified lower-order models.
• Hypergraph topology heterogeneities can impact the accuracy of pairwise approximations.