UCLA

Starting late in 2019 in the Wuhan province of China, COVID-19 has become a pandemic in the last few years. We use mathematical and statistical modeling in the hope of proving that self-exciting models perform better than SIR-family models when it comes to modeling in Epidemiology. We take a look at two models, the SQUIDER compartmental differential equation model, and also the HawkesN self exciting process model. For training the SQUIDER model, we minimize the Sum of Square Errors between actual and predicted cumulative cases and deaths, and use weights to account for the cumulative cases, and cumulative deaths, respectively. In forecasting, we use fitted parameter values and the true case counts at the end of each lag, and forecast forward 3-days, and take the RMSE between the estimate forecast and the actual case counts of COVID-19. We fit the HawkesN model by using a Least Squares algorithm to fit the data we have and use an algorithm proposed in another paper to simulate the HawkesN method. Similar to the forecasting of the SQUIDER model, we take 10 3-day forecasting periods with a lag of 1 day through 10 days, and then calculate the RMSE. Taking a look at data from the CDC website, we fit and forecast for Oregon, South Carolina, and Washington State, and indeed see that except for a very few cases, overall the HawkesN process performs a lot better than the SQUIDER model in forecasting the daily cases of COVID-19.