Threshold dynamics and optimal control of a dengue epidemic model with time delay and saturated incidence

In this paper, an epidemic model of dengue fever with time delay and saturated incidence rate is studied. The basic reproduction number is calculated by the next-generation matrix method. The local stability of each of feasible equilibria is obtained by analyzing the corresponding characteristic equations. Lyapunov functional method and LaSalle's invariance principle are used to prove that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is less than 1; when the basic reproduction number is greater than 1, the endemic equilibrium is globally asymptotically stable. Further, optimal control strategy for the prevention and control of dengue fever infection is suggested based on Pontryagin's minimum principle with delay. In addition, sensitivity analysis is carried out on basic reproduction number and numerical simulation of the dengue outbreak in Guangdong, in 2014, is given to illustrate the rationality of the model.