Stochastic Modeling and Forecasting of Covid-19 Deaths: Analysis for the Fifty States in the United States

In this work, we study and analyze the aggregate death counts of COVID-19 reported by the United States Centers for Disease Control and Prevention (CDC) for the fifty states in the United States. To do this, we derive a stochastic model describing the cumulative number of deaths reported daily by CDC from the first time Covid-19 death is recorded to June 20, 2021 in the United States, and provide a forecast for the death cases. The stochastic model derived in this work performs better than existing deterministic logistic models because it is able to capture irregularities in the sample path of the aggregate death counts. The probability distribution of the aggregate death counts is derived, analyzed, and used to estimate the count's per capita initial growth rate, carrying capacity, and the expected value for each given day as at the time this research is conducted. Using this distribution, we estimate the expected first passage time when the aggregate death count is slowing down. Our result shows that the expected aggregate death count is slowing down in all states as at the time this analysis is conducted (June 2021). A formula for predicting the end of Covid-19 deaths is derived. The daily expected death count for each states is plotted as a function of time. The probability density function for the current day, together with the forecast and its confidence interval for the next four days, and the root mean square error for our simulation results are estimated.