This study is focused on the construction and analysis of a complex epidemiological practical model built on the basis of the Susceptible-Infected-Removed (SIR) model. The examples illustrate the behavior of the practical model in various scenarios and also compare this model and a similar model, taking into account migration. The nature of the behavior of the model is determined by parameters such as the rate of spread of infection, the coefficients of recovery, mortality, the intergroup transition and others with different values of influence.