New approaches to epidemic modeling on networks

Area of Science:

• Epidemiology
• Network Science
• Mathematical Modeling

Background:

• Traditional epidemic models often assume uniform transmission probabilities.
• Modeling disease spread in complex networks requires accounting for varying contact infectiousness.

Purpose of the Study:

• To introduce two novel, independent mathematical models for simulating epidemic spread in networks.
• To incorporate variable transmission probabilities between contacts.
• To analyze these models using mean-field approximations.

Main Methods:

• Development of two distinct epidemic spread models for networks.
• Application of mean-field approximations for analytical tractability.
• Introduction and analysis of a generalized [Formula: see text]-matrix.

Main Results:

• The first model computes infection probability based on contact number and transmissibility, similar to percolation theory.
• The second model, a dynamic approach, is simplified via mean-field approximation, reducing system dimensionality.
• Both models link epidemic outbreak characteristics to the properties of the novel [Formula: see text]-matrix.

Conclusions:

• The [Formula: see text]-matrix serves as a generalized metric for predicting epidemic outbreaks.
• This matrix offers a more precise characterization of infection pathways than traditional measures.
• The developed models provide new tools for understanding epidemic dynamics in heterogeneous contact networks.