Global dynamics of an SVEIR epidemic model with distributed delay and nonlinear incidence

• A novel delay SVEIR epidemic model is formulated.
• The uniform persistence and global stability of the system are discussed.
• Some good results and efficient approach are presented.

An SVEIR epidemic model with imperfect vaccination and nonlinear incidence, and a general latent distribution is formulated. By constructing Lyapunov functionals, it is shown that the disease will die out if the vaccination reproduction number Rvac≤1Rvac≤1 and the disease becomes endemic if Rvac>1Rvac>1. Furthermore, vaccination effects are analyzed. Two special forms the probability of remaining in latent class are discussed. When the probability is negatively exponentially distributed, we present an efficient approach of proving global stability of the endemic equilibrium of the SVEIR system of ordinary differential equations (ODEs), which may improve some known approaches. When the probability is a step-function, the delay differential equation (DDE) system derived is used to study the impacts of vaccination and saturated incidence on the mumps transmission.