Dynamical Analysis of an Age-Structured Sveir Model With Imperfect Vaccine

This paper proposes an imperfectly vaccinated SVEIR model for latent age. We calculate the equilibrium points and basic reproduction number of the model. The asymptotic smoothness, uniform persistence and the existence of the attractor of the semi-flow generated by the solutions of the system are addressed. Moreover, using LaSalle’s invariance set principle and constructing Volterra-type Lyapunov functions, we can prove the global asymptotic stability of both the disease-free equilibrium and the endemic equilibrium of the model. The conclusion is that if the basic reproduction number R0 is less than one, the disease will gradually disappear. On the other hand, if the number is greater than one, the disease will become endemic and persist. Finally, measures that can effectively control the ongoing transmission of the disease have been obtained.