In this review, we have discussed the different statistical modeling and prediction techniques for various infectious diseases including the recent pandemic of COVID-19. The distribution fitting, time series modeling along with predictive monitoring approaches, and epidemiological modeling are illustrated. When the epidemiology data is sufficient to fit with the required sample size, the normal distribution in general or other theoretical distributions are fitted and the best-fitted distribution is chosen for the prediction of the spread of the disease. The infectious diseases develop over time and we have data on the single variable that is the number of infections that happened, therefore, time series models are fitted and the prediction is done based on the best-fitted model. Monitoring approaches may also be applied to time series models which could estimate the parameters more precisely. In epidemiological modeling, more biological parameters are incorporated in the models and the forecasting of the disease spread is carried out. We came up with, how to improve the existing modeling methods, the use of fuzzy variables, and detection of fraud in the available data. Ultimately, we have reviewed the results of recent statistical modeling efforts to predict the course of COVID-19 spread.