Stability and Hopf bifurcation of a vector-borne disease model with saturated infection rate and reinfection (Q2003636)

Summary: This paper established a delayed vector-borne disease model with saturated infection rate and cure rate. First of all, according to the basic reproductive number \(R_0\), we determined the disease-free equilibrium \(E_0\) and the endemic equilibrium \(E_1\). Through the analysis of the characteristic equation, we consider the stability of two equilibriums. Furthermore, the effect on the stability of the endemic equilibrium \(E_1\) by delay was studied, the existence of Hopf bifurcations of this system in \(E_1\) was analyzed, and the length of delay to preserve stability was estimated. The direction and stability of the Hopf bifurcation were also been determined. Finally, we performed some numerical simulation to illustrate our main results.