Thermodynamic efficiency of contagions: A statistical mechanical analysis of the SIS epidemic model

TL;DR

This paper models SIS epidemic dynamics on networks using thermodynamic principles, deriving analytical solutions and identifying critical phases through statistical mechanics, providing new insights into epidemic behavior.

Contribution

It introduces a thermodynamic framework for SIS epidemics, applying the Maximum Entropy principle to derive steady state distributions and interpret epidemic variables.

Findings

Closed-form solutions for certain cases

Identification of criticality and phases in epidemic processes

Validation of analytical results with numerical simulations

Abstract

We present a novel approach to the study of epidemics on networks as thermodynamic phenomena, considering the thermodynamic efficiency of contagions, considered as distributed computational processes. Modelling SIS dynamics on a contact network statistical-mechanically, we follow the Maximum Entropy principle to obtain steady state distributions and derive, under certain assumptions, relevant thermodynamic quantities both analytically and numerically. In particular, we obtain closed form solutions for some cases, while interpreting key epidemic variables, such as the reproductive ratio $R_0$ of a SIS model, in a statistical mechanical setting. On the other hand, we consider configuration and free entropy, as well as the Fisher Information, in the epidemiological context. This allowed us to identify criticality and distinct phases of epidemic processes. For each of the considered thermodynamic quantities, we compare the analytical solutions informed by the Maximum Entropy principle with the numerical estimates for SIS epidemics simulated on Watts-Strogatz random graphs.