Limit periodic solutions of a SEIR mathematical model for non-lethal infectious disease

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 states for the general and some particular cases will be contemplated, and simulations will be made in order to confirm the predictions.