Modeling Covid-19 in Massachusetts, Texas and Iowa

Allen, Justin S.; Clopper, Alexander J.; Salido, Javier

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Modeling Covid-19 in Massachusetts, Texas and Iowa

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CoViD-19 has rapidly spread around the world, and throughout the United States. The first case in the US was reported on January 19, in Washington State. It has already killed over 500,000 people in the US alone. Due to its rapid spread, it is difficult to research its epidemiology. New information comes to light at a speed that cannot be matched. Despite the thousands of papers written on its epidemiology and treatment, society is still struggling to control CoViD-19’s spread. In order to contribute to the research, we have chosen to use Tang et al.’s Mathematical Model on CoViD-19 spread, created using Markov Chain Monte Carlo Simulation. In proving the system of equations, we determined the Basic Reproduction Number formula. With this knowledge, we choose which parameters to research, based upon their importance in this calculation. Although Tang et al. provided parameter values based on Wuhan, this information required examination. For some parameters, our research matched up with the values found by Tang et al. We conducted this research through two avenues: online research, for parameters with consistency between states; and, data analysis. This required us to use statistics from Massachusetts, Texas, and Iowa, which we cleaned and smoothed. After we prepared the data, we performed Linear Regression Analysis and Constrained Non-Linear Optimization for Parameter Tuning. Our focus was on four of the parameters: c, β, q, and θ. In our data analysis, we developed alternative parameter sets, and determined which parameters have the most impact on the model. These new parameter sets were tested in the Basic Reproduction Number formula twice, once with Tang et al.’s original parameters, and once with the updated values. This tested their accuracy and gave insight into what R0 might be for CoViD-19. We hope that this information is helpful for future analysis of CoViD-19, especially in determining a more accurate Basic Reproduction Number. Doing so will help understand Herd Immunity, which, with the development of the Moderna, Pfizer, and Johnson & Johnson vaccines, is becoming especially important.

This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

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