  A four-dimensional delay differential equations (DDEs) model of malaria with
standard incidence rate is proposed. By utilizing the limiting system of the
model and Lyapunov direct method, the global stability of equilibria of the
model is obtained with respect to the basic reproduction number ${R}_{0}$.
Specifically, it shows that the disease-free equilibrium ${E}^{0}$ is globally
asymptotically stable (GAS) for ${R}_{0}<1$, and globally attractive (GA) for
${R}_{0}=1$, while the endemic equilibrium $E^{\ast}$ is GAS and ${E}^{0}$ is
unstable for ${R}_{0}>1$. Especially, to obtain the global stability of the
equilibrium $E^{\ast}$ for $R_{0}>1$, the weak persistence of the model is
proved by some analysis techniques.
