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A Data-Driven Approach to Quantifying Immune States in Sepsis

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¹Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências da Universidade de Lisboa, P-1649-003 Lisboa Codex, Portugal.

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Summary

This summary is machine-generated.

This study analyzes stochastic epidemic models on random graphs using pair and triplet approximations. We derive analytical power spectra for fluctuations, improving accuracy where simpler models fail.

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Area of Science:

Epidemiology
Statistical Physics
Network Science

Background:

Stochastic epidemic models on complex networks are crucial for understanding disease spread.
The pair approximation is a common method but has limitations in accuracy.

Purpose of the Study:

To analyze fluctuations in stochastic epidemic models on random graphs.
To develop and validate improved approximation methods beyond the pair approximation.

Main Methods:

Derivation of a master equation for the stochastic process.
System size expansion to obtain the power spectrum of fluctuations.
Development of an uncorrelated triplet approximation.

Main Results:

The pair approximation accurately predicts fluctuation spectra when its deterministic equations are valid.
The triplet approximation improves accuracy in parameter regimes where the pair approximation fails.
Analytical power spectra from the master equation match simulation results.

Conclusions:

The choice of approximation method (pair vs. triplet) is critical for accurate fluctuation analysis in epidemic models.
Advanced approximations like the triplet method are necessary for capturing complex system dynamics.
Analytical methods provide valuable tools for predicting epidemic behavior and fluctuations.