Publication Title

Royal Society Open Science

Document Type

Article

Department or Program

Mathematics

Second Department or Program

Geology

Publication Date

1-2020

Keywords

emergence, smallpox, epidemic, mathematical model, oscillation, data

Abstract

A simple susceptible–infectious–removed epidemic model for smallpox, with birth and death rates based on historical data, produces oscillatory dynamics with remarkably accurate periodicity. Stochastic population data cause oscillations to be sustained rather than damped, and data analysis regarding the oscillations provides insights into the same set of population data. Notably, oscillations arise naturally from the model, instead of from a periodic forcing term or other exogenous mechanism that guarantees oscillation: the model has no such mechanism. These emergent natural oscillations display appropriate periodicity for smallpox, even when the model is applied to different locations and populations. The model and datasets, in turn, offer new observations about disease dynamics and solution trajectories. These results call for renewed attention to relatively simple models, in combination with datasets from real outbreaks.

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

Copyright Note

This is the publisher's version of the work. This publication appears in Bates College's institutional repository by permission of the copyright owner for personal use, not for redistribution.

Required Publisher's Statement

Original version is available from the publisher at: https://doi.org/10.1098/rsos.191187

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