In this paper, we study and investigate the spread of the corona virus disease 2019 (COVID-19) in Egypt by using spectral analysis and Box-Jenkins's analysis of time series, taking into account mildly and symptomatically infected individuals reported daily by the Ministry of Health of Egypt. Many ARIMA models were considered and estimated their parameters, the best model used through the study. The period from 14 March 2020 to 3 November 2021 was studied. Three waves of COVID-19 epidemic are distinguished. A fourth wave is prospected, its main characteristics are presented
Another approach using Gaussian (normal) model is used to study the epidemic wave by wave. Its results cope with those of ARIMA model, we concluded that the length of the wave is 167 days using spectral analysis, so it is expected to reach its minimum (or vanishes) on 10 January 2022, it reaches 1077 new infections as its maximum on 16 October 2021 after 81 from its beginning.