Core Concepts
Understanding metastable behavior in the SIS process on Erdös-Rényi graphs requires accounting for correlations and neighbor interactions.
Abstract
The article delves into the challenges of characterizing metastable behavior in the SIS process on graphs, proposing improved methods to address inaccuracies caused by ignoring correlations. It explores predictions for infected fractions based on graph characteristics and degree distributions, highlighting the impact of size bias and neighbor correlations on estimation accuracy.
Directory:
- Abstract
- Challenges in characterizing metastable behavior.
- Proposed methods to address inaccuracies.
- Introduction
- Historical context of Covid-19 outbreak.
- Mathematical Models for Infectious Diseases
- Focus on SIS process models.
- Review of Models for Infected Fraction
- Challenges in exact analysis due to exponential state space.
- Annealed and Quenched Predictions
- Comparison of annealed and quenched methods for predicting infected fraction.
- Model Definitions
- Detailed model definitions for predicting quasi-stationary behavior.
- Improved Heuristics for Infected Fraction
- Utilizing degrees to design more accurate prediction methods.
- Systematic Errors I: Size Bias and Infection Paradox
- Addressing underestimation issues due to size bias.
- Systematic Errors II: Neighbor Correlation
- Exploring errors from neglecting neighbor correlations.
Stats
Existing mean-field methods overestimate metastable infected fraction in sparse graphs.
The effective infection rate is crucial in predicting quasi-stationary behavior accurately.