Mean-field models for non-Markovian epidemics on networks

Area of Science:

• Epidemiology
• Network Science
• Mathematical Modeling

Background:

• Epidemic modeling uses various network approaches.
• Edge-based compartmental models are one such method.
• Previous models often assumed specific transmission/recovery distributions.

Purpose of the Study:

• To extend edge-based compartmental models for general probability distributions.
• To rigorously prove the equivalence between edge-based compartmental and message passing models.
• To establish a framework for deriving known pairwise models.

Main Methods:

• Developed a novel extension of the edge-based compartmental model.
• Employed rigorous mathematical proofs to establish model equivalence.
• Analyzed the implications for large-scale network ensembles.

Main Results:

• Demonstrated the equivalence of edge-based compartmental and message passing models for general independent processes.
• Proved the new model's exactness on infinite-sized configuration model networks.
• Showcased derivation of known pairwise models from the generalized framework.

Conclusions:

• The extended model provides a unified and exact approach to epidemic modeling on networks.
• This work bridges compartmental and message passing frameworks.
• Offers a foundation for analyzing diverse epidemic dynamics with greater precision.