A basic general model of vector-borne diseases

Abstract

We propose a model that can translate the dynamics of vector-borne diseases, for this model we compute the basic reproduction number and show that if $\mathcal{R}_0<\zeta<1$ the DFE is globally asymptotically stable. For $\mathcal {R}_0>1$ we prove the existence of a unique endemic equilibrium and if $\mathcal {R}_0 \leq 1$ the system can have one or two endemic equilibrium, we also show the existence of a backward bifurcation. By numerical simulations we illustrate with data on malaria all the results including existence, stability and bifurcation.