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The Numerical Simulation and Mathematical Analysis on a Model Predicting and Preventing the Measles Epidemic

Undergraduate #247
Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics

Ashana Evans - North Carolina A&T State University
Co-Author(s): Melanie Payton and Liping Liu, NCAT



Measles is a viral infection that is serious for small children but is easily preventable by a vaccine. For the spread of this disease, there are various studies that have sought to understand the process by using the SVIR (Susceptible, Vaccinated, Infected and Recovered) models. This research utilizes a deterministic SI/SVI model for measles to investigate the process of how an epidemic of measles occurs within a closed population over the years where a portion of the population has been vaccinated. Since different age groups have different vaccination coverage rates and different activity types, it is necessary to divide the population into groups based on their ages. In addition, to model the endemic cycles, one has to consider the seasonal effects, which could be from the cultures, school periods as well as the calendar seasons. Therefore, our developed model takes into account these two major factors: age structure and seasonality. Various contact rates and transition rates among the groups are used to reflect the age and seasonality. Matlab programs are developed for numerical simulations. There are two major models in this study: the four age groups model for prediction, the eight age groups model for prevention with various vaccination strategies. The parameter values are estimated from the real data. The simulation results match reasonably well with the observation data. Using the model with the estimated parameters, we are able to capture the endemic cycles in the history and to predict the possible future outbreaks of measles under various vaccination strategies. Lastly, the parameter sensitivity analysis is conducted from some chosen parameters. This research will give me exposure to the synthesis of mathematical applications with computational software and simulation models. It will help me understand how computers and math are used to understand infections and how they spread.

Funder Acknowledgement(s): NSF HBCU-UP funded TALENT-21 Program at North Carolina A&T State University

Faculty Advisor: Liping Liu,

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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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