Analysis, Identification, and Validation of Discrete-Time Epidemic Processes

TL;DR

This paper explores various discrete-time epidemic models, establishes conditions for their stability and parameter learning, and validates a network-dependent SIS model using historical and real-world datasets.

Contribution

It introduces new theoretical conditions for model stability and parameter identification, and validates models with real epidemic data.

Findings

Conditions for asymptotic stability of the healthy state

Necessary and sufficient conditions for parameter learning

Validation of SIS model with historical and real data

Abstract

Models of spread processes over non-trivial networks are commonly motivated by modeling and analysis of biological networks, computer networks, and human contact networks. However, identification of such models has not yet been explored in detail, and the models have not been validated by real data. In this paper, we present several different spread models from the literature and explore their relationships to each other; for one of these processes, we present a sufficient condition for asymptotic stability of the healthy equilibrium, show that the condition is necessary and sufficient for uniqueness of the healthy equilibrium, and present necessary and sufficient conditions for learning the spread parameters. Finally, we employ two real datasets, one from John Snow's seminal work on cholera epidemics in London in the 1850's and the other one from the United States Department of Agriculture, to validate an approximation of a well-studied network-dependent susceptible-infected-susceptible (SIS) model.