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A Comparison of Measles Vaccination Regimes in a Stochastic Spatial SIR Model

Undergraduate #88
Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics

Amanda Reeder - Norfolk State University
Co-Author(s): Emily Nguyen, Muhlenberg College, Allentown, PA



Measles is a childhood disease that is still present in today’s society and the only way for measles to be under control is to implement a vaccination regime. We investigated four different vaccination regimes in a ‘country’ of 25 cities using a spatial, stochastic, and continuous time SIR model to determine which regime would lead optimally lead to herd immunity. We used the Gillespie SSA algorithm to implement the stochastic nature of our model and we ran the model over a time period of 20 years. We compared our four regimes when the mean proportion of vaccinated was relatively similar and further investigated the behavior of the model as herd immunity was approached.

We confirmed that eliminating measles in a country happened relatively quickly, however if there is a steady growth of susceptibles in the population large spikes of cases would be common if one infected person entered the population. We found that the mean proportion vaccinated does not reflect the qualitative behavior of the model over the 20 year time period. A steady, high vaccination rate eliminated cases and lead the country to herd immunity. In the future we would like to change the movements and population patterns to model different country dynamics. We would also add a death rate to the susceptible compartment, to simulate people in the population that stay susciptible their entire lives.

Funder Acknowledgement(s): Mathematical Biosciences Institute / NSF

Faculty Advisor: John Fricks,

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This material is based upon work supported by the National Science Foundation (NSF) under Grant No. DUE-1930047. Any opinions, findings, interpretations, conclusions or recommendations expressed in this material are those of its authors and do not represent the views of the AAAS Board of Directors, the Council of AAAS, AAAS’ membership or the National Science Foundation.

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