Global dynamics of a vector-borne disease model with infection ages and general incidence rates

Abstract

A vector-borne disease model with general incidence rates is proposed and investigated in this paper, where both vector and host are stratified by infection ages in the form of a hyperbolic system of partial differential equations coupled with ordinary differential equations. The existence, uniqueness, nonnegativeness, and boundedness of solution of the model are studied for biologically reasonable purpose. Furthermore, a global threshold dynamics of the system is established by constructing suitable Lyapunov functionals, which is determined by the basic reproduction number $$\mathcal {R}_0$$ : the infection-free equilibrium is globally asymptotically stable when $$\mathcal {R}_0<1$$ while the endemic equilibrium is globally asymptotically stable when $$\mathcal {R}_0>1$$ .