Optimal control strategies and global dynamics for a dengue disease model with waning vaccine-induced immunity and incubation delay

Dengue is one of the most serious vector-borne diseases in the world. Although there is still no effective method to control this rapidly spreading disease, dengue vaccine is the best control measure for the foreseeable future. Dengue vaccine development has made great progress, but a better understanding of how vaccine-induced immune responses are related to vaccine efficacy can accelerate development and testing, and improve potential risks. In this paper, we formulate a dengue disease model with waning vaccine-induced immunity and a time delay depicting the extrinsic incubation period of mosquitoes in dengue transmission. The basic reproduction number is obtained, which is the threshold for distinguishing between the disappearance and prevalence of dengue. By constructing appropriate Lyapunov functionals, the global asymptotic dynamics of the system are established. By using the Pontryagin's minimum principle with delay, we included five time-dependent controls to evaluate the impact of four different schemes on our model, which provides a theoretical basis for people to effectively prevent and control dengue disease. Finally, elasticity and sensitivity analysis are given and data fitting is conducted based on the number of weekly cases reported in Singapore in 2022. This helps one to understand the importance of vaccine-related parameters and provides some perspective on the development trend of the disease.