Analysis and Applications of Population Flows in a Networked SEIRS Epidemic Process

TL;DR

This paper models the spread of infectious diseases through transportation networks using a networked SEIRS epidemic process, providing stability analysis, conditions for endemic states, and practical tools for real-world data application, exemplified by COVID-19 data from Minnesota.

Contribution

It introduces a novel networked SEIRS model incorporating population flows, with stability analysis and methods for parameter estimation and disease prediction in real-world scenarios.

Findings

Stable healthy states under certain conditions

Existence and uniqueness of endemic states established

Effective tools for disease spread prediction demonstrated

Abstract

Transportation networks play a critical part in the spread of infectious diseases between populations. In this work, we define a networked susceptible-exposed-infected-recovered epidemic process with loss of immunity over time (SEIRS) that explicitly models the flow of individuals between sub-populations, which serves as the propagating mechanism for infection. We provide sufficient conditions for local stability and instability of the healthy state of the system and show that no perturbation of population flows can change the local stability of any healthy state. We also provide sufficient conditions for the existence and uniqueness of an endemic state. We then develop tools and methods for applying our model to real-world data, including spreading parameter estimation and disease arrival time prediction, and apply them in a case study using both travel and infection data from counties in Minnesota during the first year of the COVID-19 pandemic.