Dengue virus is transmitted by Aedes mosquitoes, posing threat to people's health and leading to great economic cost in many tropical and subtropical regions. We develop an ordinary differential equation model taking into account multiple strains of dengue virus. Using the model, we assess the effectiveness of human vaccination considering its waning and failure. We derive the lower bound and upper bound for the final size of the epidemic. Sensitivity analysis quantifies the impact of parameters on the basic reproduction number. Different scenarios of vaccinating humans show that it is better to vaccinate humans at early stages. We find that the cumulative number of infected humans is small when the vaccination rate is high or the waning rate is low for previously infected humans. We analyze the necessary conditions for implementing optimal control and derive the corresponding optimal solutions for mitigation dengue virus transmission by applying Pontryagin's Maximum Principle. Our findings may provide guidance for the public health authorities to implement human vaccination and other mitigation strategies.
Keywords: Dengue virus; Disease-free equilibrium; Optimal control; Sensitivity analysis; Vaccination.