Global dynamics of a SEIR model with information dependent vaccination and periodically varying transmission rate

This paper is devoted to the investigation of the global dynamics of a SEIR model with information dependent vaccination. The basic reproduction number R0 is derived for the model, and it is shown that R0 gives the threshold dynamics in the sense that the disease-free equilibrium is globally asymptotically stable and the disease dies out if R0<1, while there exists at least one positive periodic solution and the disease is uniformly persistent when R0>1. Further, we give the approximation formula of R0. This answers the concerns presented in [B. Buonomo, A. d'Onofrio, D. Lacitignola, Modeling of pseudo-rational exemption to vaccination for SEIR diseases, J. Math. Anal. Appl. 404 (2013) 385-398]. Copyright (c) 2014 John Wiley & Sons, Ltd.