Disease dynamics and mean field models for clustered networks
María Del Valle Rafo1, Juan Pablo Di Mauro2, Juan Pablo Aparicio3
1Instituto de Investigaciones en Energía no Convencional (INENCO), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Universidad Nacional de Salta, Av. Bolivia 5100, 4400 Salta, Argentina.
Journal of Theoretical Biology
|May 3, 2021
Summary
This study models disease spread in clustered social networks, like households and workplaces. A new mean field model accurately captures disease dynamics and can be adapted for vector-borne diseases.
Area of Science:
- Epidemiology
- Network Science
- Mathematical Biology
Background:
- Social networks exhibit clustered structures with short mean path lengths.
- Analyzing disease dynamics in such networks is crucial for public health.
Purpose of the Study:
- To analyze disease dynamics in small-world networks comprising households and workplaces.
- To develop a mean field model for predicting disease spread in these networks.
Main Methods:
- Numerical computation of basic reproduction numbers (R0).
- Development of a mean field model using a derived exponent (p).
- Analysis of susceptible proportion at endemic equilibrium.
Main Results:
- The average susceptible proportion (
) differs from R0^-1 at endemic equilibrium. - An exponent 'p' was identified such that
^p = R0^-1. - The developed mean field model accurately captures disease dynamics.
Conclusions:
- A novel mean field model effectively describes disease spread in clustered social networks.
- The model provides a framework for understanding disease transmission in household and workplace settings.
- The approach can be extended to model vector-borne diseases within social networks.
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