Network Models in Epidemiology: Considering Discrete and Continuous Dynamics

TL;DR

This paper explores network models in epidemiology, comparing discrete and continuous dynamics, and introduces a discrete dynamical system for modeling infection and recovery processes in populations.

Contribution

It presents a novel discrete dynamical system for epidemiological modeling and discusses the benefits and computational methods of network-based approaches.

Findings

Development of a discrete dynamical system for infection and recovery

Discussion of advantages of network models over traditional compartmental models

Outline of a computational scheme for model iteration

Abstract

Discrete and Continuous Dynamics is the first in a series of articles on Network Models for Epidemiology. This project began in the Fall quarter of 2014 in my continuous modeling course. Since then, it has taken off and turned into a series of articles, which I hope to compile into a single report. The purpose of the report is to explore mathematical epidemiology. In this article, we discuss the historical approach to disease modeling with compartmental models. We discuss the issues and benefits of using network models. We build a discrete dynamical system to describe infection and recovery of individuals in the population. Lastly, we detail the computational scheme for iterating this model.