On the stability of an SEIR epidemic model with distributed time-delay and a general class of feedback vaccination rules

This paper discusses and formulates a continuous-time SEIR -type epidemic model of pseudo-mass action type with finitely distributed delays under a very general, potentially time-varying, vaccination control rule which eventually generates feedback actions on the susceptible, infectious and recovered subpopulations. A lot of particular vaccination laws can be got from the proposed general one. The disease-free and endemic equilibrium points are characterized and their local stability properties discussed depending on the limits of the vaccination control gains provided that they converge asymptotically. Then, the global asymptotic stability to the disease-free equilibrium point is studied under an infective transmission rate below a certain maximum threshold. Later on, an extended SEIR epidemic model is discussed through simulated examples with stochastic Wiener-type perturbations around the equilibrium points.