Sample NLPDE and NLODE Social-Media Modeling of Information Transmission for Infectious Diseases:Case Study Ebola

TL;DR

This paper models the spread of Ebola-related information on Twitter using epidemic-inspired differential equations, linking stochastic tweet dynamics to deterministic models to inform epidemic containment strategies.

Contribution

It introduces a novel approach connecting Twitter meme propagation with epidemic models through Markov chains and differential equations, providing a new framework for analyzing information spread during epidemics.

Findings

Modified four-parameter model fits Ebola Twitter meme data

Temporal and spatial evolution equations inform epidemic spreading understanding

Models can aid decision makers in containment strategies

Abstract

We investigate the spreading of information through Twitter messaging related to the spread of Ebola in western Africa using epidemic based dynamic models. Diffusive spreading leads to NLPDE models and fixed point analysis yields systems of NLODE models. When tweets are mapped as connected nodes in a graph and are treated as a time sequenced Markov chain, TSMC, then by the Kurtz theorem these specific paths can be identified as being near solutions to systems of ordinary differential equations that in the large N limit retain many of the features of the original Tweet dynamics. Constraints on the model related to Tweet and re-Tweet rates lead to different versions of the system of equations. We use Ebola Twitter meme based data to investigate a modified four parameter model and apply the resulting fit to an accuracy metric for a set of Ebola memes. In principle the temporal and spatial evolution equations describing the propagation of the Twitter based memes can help ascertain and inform decision makers on the nature of the spreading and containment of an epidemic of this type.