Stability Analysis and Simulation of a Delayed Dengue Transmission Model with Logistic Growth and Nonlinear Incidence Rate

In this work, a dengue transmission model with logistic growth and time delay (tau) is investigated. Through detailed mathematical analysis, the local stability of a disease-free equilibrium and an endemic equilibrium is discussed, the existence of Hopf bifurcation and stability switch is established, and it is proved that the system is permanent if the basic reproduction number is greater than 1. On the basis of Lyapunov functional and LaSalle's invariance principle, sufficient conditions are derived for the global stability of the endemic equilibrium. The primary theoretical results are simulated numerically. In addition, when tau = 0, relevant properties of the Hopf bifurcation are analyzed. Finally, sensitivity analysis is given and data fitting is carried out to predict the epidemic development trend of dengue fever in Singapore in 2020.