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Background  The new coronavirus disease appeared at the end of 2019, and it is now a global problem over the world. There are multiple epidemiologic indicators used for discussing the spread of pandemics, one of these indicators is the basic reproductive ratio which indicates whether the pandemic is going to spread more or relax, and the aim of this work is estimating this ratio for the Middle East countries for two stages of the pandemic.    Main body of the abstract  We employ Runge–Kutta method on SEIR model to simulate the basic reproductive ratio values of SARS-CoV-2 disease by using the recorded data of the disease for two stages, up to date May 29, 2020, in the first stage and up to date September 7, 2020, in the second stage. We estimate the coefficient of exposing rate, the coefficient of infection rate, the coefficient of recovery rate and the coefficient of mortality rate of the new coronavirus disease in addition to the basic reproductive ratio values of the disease in the Middle East countries, namely Bahrain, Cyprus, Egypt, Iran, Iraq, Jordan, Kuwait, Lebanon, Oman, Qatar, Saudi Arabia, the Syrian Arab Republic, the United Arab Emirates, Turkey and Yemen where we apply the SEIR epidemic model.    Short conclusion  We find that the values of the basic reproductive ratio of the new coronavirus disease based on the used model in the Middle East countries start from 1.5583 to 3.0395 in the first stage and from 1.0001 to 4.5757. Besides, we find that the problem of the new coronavirus disease in Lebanon and in the Syrian Arab Republic is not good at all in the recent stage based on the values of the basic reproductive ratio comparing with other Middle East countries. Also, we find that the value of the basic reproductive ratio for the second stage is near one; however, if we apply the method for the following stages, we find that the values return to be larger because lots of people in that stage and after did not follow the governmental procedures for stopping the spreading of the disease.

The COVID-19 basic reproductive ratio using SEIR model for the Middle East countries and some other countries for two stages of the disease