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Abstract

Influenza is a respiratory infection that places a substantial burden in the world population each year. In this project, we study and interpret a data set from a flu outbreak in a British boarding school in 1978 with mathematical modeling. First, we propose a generalization of the SIR model based on the quarantine measure in place and establish the long-time behavior of the model. By analyzing the model mathematically, we determine the analytic formulas of the basic reproduction number, the long-time limit of solutions, and the maximum number of infection population. Moreover, we estimate the parameters of the model based on the data set. Finally, we evaluate the effect of the quarantine measure by numerical computations with various alternative sets of parameters in the model.

Author Bio

Theadora Baker-Wallerstein, Mikenna Dew, and Amanda Langosch conducted the research detailed in “Modeling an infection outbreak with quarantine: The SIBKR Model” during the summer of 2023 under the direction of their favorite professor, King-Yeung Lam. This project was funded by the REU program at The Ohio State University under grant DMS-2325195.

TBW is a pre-med mathematics major on a biology track. Outside of the mathematical sciences, she enjoys reading and traveling. She plans to pursue a career in a biology field laboratory upon graduation.

MD is a pre-med biology major with a minor in mathematics. During her undergraduate career, she played ACHA D2 women’s ice hockey. She anticipates pursuing a PharmD.

AL is a pre-PA public health major with an environmental specialization and a minor in mathematics. She enjoys going to concerts and traveling to visit her friends in her free time. In the future, she plans to pursue the PA profession.

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