Global dynamics of an nonautonomous SEIRS epidemic model with
vaccination and nonlinear incidence
In this paper, a class of nonautonomous SEIRS epidemic models with
vaccination and nonlinear incidence is investigated. Under some quite
weak assumptions, a couple of new threshold values in the form of
integral, i.e., $R_1$, $R^*_1$, $R_2$ and $R^*_2$ on
the extinction and permanence of disease for the model are established.
As special cases of our model, the autonomous, periodic and almost
periodic circumstances are discussed respectively. The nearly necessary
and sufficient criteria of threshold on the extinction and permanence of
disease for above cases are obtained as well. Numerical examples and
simulations are presented to illustrate the analytic results.