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Motivated by the current Coronavirus Disease (COVID-19) pandemic, which isdue to the SARS-CoV-2 virus, and the important problem of forecasting dailydeaths and cumulative deaths, this paper examines the construction ofprediction regions or intervals under the Poisson regression model and for anover-dispersed Poisson regression model. For the Poisson regression model,several prediction regions are developed and their performance are comparedthrough simulation studies. The methods are applied to the problem offorecasting daily and cumulative deaths in the United States (US) due toCOVID-19. To examine their performance relative to what actually happened,daily deaths data until May 15th were used to forecast cumulative deaths byJune 1st. It was observed that there is over-dispersion in the observed datarelative to the Poisson regression model. An over-dispersed Poisson regressionmodel is therefore proposed. This new model builds on frailty ideas in SurvivalAnalysis and over-dispersion is quantified through an additional parameter. ThePoisson regression model is a hidden model in this over-dispersed Poissonregression model and obtains as a limiting case when the over-dispersionparameter increases to infinity. A prediction region for the cumulative numberof US deaths due to COVID-19 by July 16th, given the data until July 2nd, ispresented. Finally, the paper discusses limitations of proposed procedures andmentions open research problems, as well as the dangers and pitfalls whenforecasting on a long horizon, with focus on this pandemic where events, bothforeseen and unforeseen, could have huge impacts on point predictions andprediction regions.

Prediction Regions for Poisson and Over-Dispersed Poisson Regression  Models with Applications to Forecasting Number of Deaths during the COVID-19  Pandemic