Non–extenstive statistics play a significant role in studying the dynamic behaviour of COVID-19 to assist epidemiological scientists to take appropriate decisions about pandemic planning. Generic non–extensive and modified–Tsallis statistics are used to analyze and predict the morbidity and mortality rates in future. The cumulative number of confirmed infection and death in Egypt at interval from 4 March 2020 till 12 April 2022 are analyzed using both non–extensive statistics. Also, the cumulative confirmed data of infection by gender, death by gender, and death by age in Egypt at interval from 4 March 2020 till 29 June 2021 are fitted using both statistics. The best fit parameters are estimated. Also, we study the dependence of the estimated fit parameters on the people gender and age. Using modified–Tsallis statistic, the predictions of the morbidity rate in female is more than the one in male while the mortality rate in male is greater than the one in female. But, within generic non-extensive statistic we notice that the gender has no effect on the rate of infections and deaths in Egypt. Then, we propose expressions for the dependence of the fitted parameters on the age. We conclude that the obtained fit parameters depend mostly on the age and on the type of the statistical approach applied and the mortality risk increased with people aged above 45 years. We predict - using modified–Tsallis - that the rate of infection and death in Egypt will begin to decrease till stopping during the first quarter of 2025.