This article talks about a model of fractional differential equations to describe how COVID-19 is spread in the world in general and Iraq in particular. The model contains five fractional differential equations. Moreover, we have proven the existence and uniqueness of the solution of the model, found the equilibrium points of the model and checked its stability. Then we solved it using a fractional linear multi-step method. When we compare the results with the data documented by the World Health Organisation (WHO), we find that the total number of active cases in the world are equal to 584498294 on 3/8/2022, and it is similar to what was done with the system. The number of those who have recovered and died  from the disease has also been calculated. For Iraq, the total number of active cases is 2448484 and the total number of active cases calculated by the model is 2628000. In comparison, the calculated number is slightly  higher than what is given in the data. This is quite normal because not all infected patients go to the health centres and it is difficult to record them as active cases.