Dynamics of a dengue epidemic model with class-age structure

Abstract

We introduce the class-age-dependent rates of the infected and vaccinated class in the compartmental model of dengue transmission. An age-structured host-vector interaction model incorporating vaccination effects is formulated and analyzed for the spread of dengue. Moreover, the basic reproduction number is derived, which serves as a threshold value determining the stability of the equilibrium points. By constructing suitable Lyapunov functional, the global asymptotic stability of the equilibria of the model is established in terms of the basic reproduction number. In particular, the disease-free equilibrium of the model is globally asymptotically stable if the basic reproduction number is less than one, while the disease persists and the unique endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than one. The analysis of our model indicates that our model is realistic to give a hint to control the transmission of dengue. Furthermore, it follows from the formulation of the infection-free equilibrium of susceptible humans [Formula: see text] and the basic reproduction number [Formula: see text] that both of them are decreasing with respect to the vaccination parameter [Formula: see text], which indicates that appropriate vaccinating program may contribute to prevent the transmission of Dengue disease.