Infections are serious disturbing problem over the time. They are usually showing as a tsunami waves hitting the societies. COVID-19 and its followed variants are the recent pandemic in this decade. In this paper, a mathematical model is proposed to describe the wave propagation of COVID-19 daily cases and deaths. The model is applied to the data of Egyptian society which is representing the confirmed daily cases and deaths of COVID-19 and of its followed variants. The pandemic is studied as a successive flow of waves over the first three years. These waves are described by summation of sech-hyperbolic functions. The parameters of the model are estimated using Newton optimization method. Finally, the relation between cases and deaths is illustrated before and after vaccination to show the vaccination effect on society. Any pandemic data can be inserted to the proposed model, and then optimize the parameters for any country to fit the data inserted.