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.
Recommended Citation
Greer, M.L., Saha, R., Gogliettino, A., Yu, C. and Zollo-Vanecek, K. 2020, Emergence of oscillations in a simple epidemic model and demographic data, Royal Society Open Science, 7(1). https://doi.org/10.1098/rsos.191187
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International 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