The equilibrium states of a mathematical model of an infectious disease are studied in this paper under variable parameters. A simple SEIR model with a delay is presented under a set of parameters varying periodically, characteristic to the seasonality of the disease. The final equilibrium state, determined by these parameters, is obtained with a general method based on a Fourier analysis of the dynamics of the subpopulations proposed in this paper. Then the stability of these equilibrium

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... for the general and some particular cases will be contemplated, and simulations will be made in order to confirm the predictions. Mathematics Subject Classification: 37M05, 37M10, 65P40