Coronavirus disease (COVID-19) is an acute disease that affects the respiratory system which initially appeared in Wuhan, China. In Feb 2019 the sickness began to spread swiftly throughout the entire planet, causing significant health, social, and economic problems. Time series is an important statistical method used to study and analyze a particular phenomenon, identify its pattern and factors, and use it to predict future values. The main focus of the research is to shed light on the study of SARIMA, NARNN, and hybrid models, expecting that the series comprises both linear and non-linear compounds, and that the ARIMA model can deal with the linear component and the NARNN model can deal with the non-linear component. The models were applied in the health sector to predict the numbers of people infected with the Covid-19 virus in Iraq where the data were collected via the website of the Iraqi Ministry of Health through the daily epidemiological situation of all Iraqi provinces for the period (2021\3\28 to 2021\8\15). When analyzing, studying, and comparing these models, the researcher noted that the hybrid model outperformed other models because it had the lowest value for the MSE, RMSE, MAE, and MAPE so it was used to predict future values.