Global stability of an SEIR epidemic model with vertical transmission and saturating contact rate

In this paper, the SEIR epidemic model with vertical transmission and the saturating contact rate is studied. It is proved that the global dynamics are completely determined by the basic reproduction number R0(p, q), where p and q are fractions of infected newborns from the exposed and infectious classes, respectively. If R0(p, q) ⩽ 1, the disease-free equilibrium is globally asymptotically stable and the disease always dies out. If R0(p, q) > 1, a unique endemic equilibrium exists and is globally stable in the interior of the feasible region, and the disease persists at the endemic equilibrium state if it initially exists.