Global stability and a comparison of SVEIP and delayed SVIP epidemic models with indirect transmission

The latent period is one of the important risk factors considered in epidemiological research literatures. In general, a latent period can be modelled by incorporating a delay effect (delay system), or by introducing an exposed class defined as E. In this paper, a susceptible-vaccinated-exposed-infectious-pathogen (SVEIP) dynamic model and its corresponding delayed SVIP model are proposed. Under biologically motivated assumptions, the stability of equilibria is investigated by the global Lyapunov functions and functionals, and the dynamical properties of two systems are found to depend entirely on the basic reproduction numbers R 0 1 and R 0 2 : if R 0 1 ( R 0 2 ) ≤ 1 , the disease-free equilibrium is globally asymptotically stable; if R 0 1 ( R 0 2 ) > 1 , the endemic equilibrium exists and is globally asymptotically stable, which implies time delay span has no effect on the stability of equilibria in delay system. Finally, a comparison between SVEIP and delayed SVIP epidemic model is made by numerical analysis, elaborating the epidemiological significance of these results.