Related Experiment Videos
Susceptible-infected-removed epidemic models with dynamic partnerships
1Division of Health Computer Sciences, University of Minnesota, Minneapolis 55455, USA.
Journal of Mathematical Biology
|January 1, 1995
Summary
This study introduces a dynamic network SIR model for disease transmission, analyzing dyad configurations to understand epidemic thresholds and growth rates. The findings offer explicit formulas for key epidemic quantities, applicable even with complex dynamics.
Area of Science:
- Epidemiology
- Mathematical Biology
- Network Science
Background:
- Classical Susceptible-Infected-Removed (SIR) models assume homogeneous mixing.
- Disease transmission dynamics are often influenced by complex social contact networks.
Purpose of the Study:
- To extend the SIR model to incorporate dynamic partnership networks.
- To develop a novel analytical method for understanding epidemic dynamics in these networks.
- To derive explicit formulas for epidemic threshold and growth rate.
Main Methods:
- Analysis of dyad configurations instead of individuals.
- Approximation using branching processes for large populations.
- Derivation of explicit formulas for homogeneous, Markovian models.
Main Results:
- Identified epidemic threshold (R0) and growth rate (lambda) using branching processes.
- Derived explicit formulas for R0, lambda, and the final epidemic size (omega).
- Demonstrated the relationship between omega and R0 remains consistent with simpler models.
Conclusions:
- The new dyad-based analysis provides a comprehensive understanding of epidemic dynamics in partnership networks.
- Explicit formulas allow quantification of errors from assuming instantaneous contacts.
- The model is generalizable to non-Markovian dynamics, heterogeneous contact rates, and variable infectivity.