Criticality and Information Dynamics in Epidemiological Models

E Erten,Mahendra Piraveenan,Joseph Lizier,Mikhail Prokopenko

doi:10.3390/e19050194

Abstract

Understanding epidemic dynamics has always been a challenge. As witnessed from the ongoing Zika or the seasonal Influenza epidemics, we still need to improve our analytical methods to better understand and control epidemics. While the emergence of complex sciences in the turn of the millennium have resulted in their implementation in modelling epidemics, there is still a need for improving our understanding of critical dynamics in epidemics. In this study, using agent-based modelling, we simulate a Susceptible-Infected-Susceptible (SIS) epidemic on a homogeneous network. We use transfer entropy and active information storage from information dynamics framework to characterise the critical transition in epidemiological models. Our study shows that both (bias-corrected) transfer entropy and active information storage maximise after the critical threshold ( R 0 = 1). This is the first step toward an information dynamics approach to epidemics. Understanding the dynamics around the criticality in epidemiological models can provide us insights about emergent diseases and disease control.

Highlights

The mathematical modelling of epidemics dates back to mid-18th century [1], while it was Kermack and McKendrick [2] who studied Susceptible-Infected-Recovered (SIR) model, being the first to use the formal models of epidemics, known generally as compartmental mean-field models [3].In these models, the population is categorised into distinct groups, depending on their infection status: susceptible individuals are the ones who has never had the infection and can have it upon contact with infected individuals, infected individuals have the infection and can transmit it to the susceptible individuals, and recovered individuals are those have recovered from the infection and are immune since
As the dynamics become supercritical, the target neighbour becomes more strongly bound to all of its neighbours collectively, and it becomes more difficult to predict its dynamics based on a single source neighbour alone; as such, the transfer entropy begins to decrease
We argue that the transfer entropy captures the extent of the distributed communications of the network-wide computation underlying the epidemic spread, while the active information storage corresponds to its distributed memory

Summary

Introduction

The mathematical modelling of epidemics dates back to mid-18th century [1], while it was Kermack and McKendrick [2] who studied Susceptible-Infected-Recovered (SIR) model, being the first to use the formal models of epidemics, known generally as compartmental mean-field models [3] In these models, the population is categorised into distinct groups, depending on their infection status: susceptible individuals are the ones who has never had the infection and can have it upon contact with infected individuals, infected individuals have the infection and can transmit it to the susceptible individuals, and recovered individuals are those have recovered from the infection and are immune since . These equations can be further modified to account for various other factors (e.g., pathogen-induced mortality) by the inclusion of more parameters in the ODEs, or they can be adapted to reflect different infectious dynamics (e.g., waning immunity)

Methods

Results

Conclusion