Effects of stochastic perturbation and vaccinated age on a vector-borne epidemic model with saturation incidence rate

Abstract

For reasons that the universality of stochastic perturbation and heterogeneity in the spread of vector-borne epidemic diseases, we formulate a stochastic vector-borne epidemic model with age-structure to discuss the effects of these factors. By constructing appropriate Lyapunov functions, the existence and uniqueness of global positive solutions of this model are derived. Further, we obtained some sufficient conditions for the extinction of the disease. In addition, the existence of a unique stationary distribution is studied which leads to the persistence of disease. Some numerical simulations are carried to explain our theoretical results. This implicates that, under the effects of these factors, the intensity and timing of outbreaks of the disease are unpredictable.