In this paper, a discrete fractional Susceptible-Infected-Treatment-Recovered-Susceptible (SITRS) model for simulating the coronavirus (COVID-19) pandemic is presented. The model is a modification to a recent continuous-time SITR model by taking into account the possibility that people who have been infected before can lose their temporary immunity and get reinfected. Moreover, a modification is suggested in the present model to correct the improper assumption that the infection rates of both normal susceptible and old aged/seriously diseased people are equal. This modification complies with experimental data. The equilibrium points for the proposed model are found and results of thorough stability analysis are discussed. A full numerical simulation is carried out and gives a better analysis of the disease spread, influences of model’s parameters, and how to control the virus. Comparisons with clinical data are also provided.