Periodic equilibrium states in a SEIR mathematical model of an infectious non-lethal disease

The periodic regime in a SEIR model with a delay is studied in this paper. The model is studied first under a simple set of constant parameters and then a more complex solution is proposed, depending on a set of periodic parameters related to the variable risk of contracting the disease and the different vaccination strategies applied in order to prevent it. Both the periodic parameters and the subpopulations obtained in the periodic solution proposed are defined as generic Fourier series, so the solution is valid for any possible periodic parameters. The stability of such periodic regimes are studied. A complementary numerical simulation of this model under periodic parameters is also included.