Abstract Dengue has emerged as the most widespread mosquito-borne ailment in humans, causing an estimated 390 million infections within the endemic regions of the world annually. In this paper, a novel mathematical model is proposed for three strains of dengue virus with vaccination measures. Some of the important qualitative analysis carried out are as follows: The dengue serotypes 1, 2 and 3 sub-models are qualitatively analyzed, using well constructed candidates of Lyapunov function. The sub-models' infection-free equilibria are proven to be locally asymptotically stable.The infection-free and endemic equilibria of the sub-models are established to be globally asymptotically stable. The complete model's infection-free equilibrium is proven to be locally and globally asymptotically stable. Also, simulations are also presented to validate the theoretical analysis in the paper. The solution profiles of all epidemiological compartments when the reproduction numbers are both below one and greater than one are graphically presented. It was observed that, for the scenarios when the dengue reproduction number $\mathcal{R}_{0}$ is below and above one, the solution trajectories converge to the infection-free and dengue-endemic steady states, respectively. Sensitivity analyses using the Latin Hypercube Sampling (LHS), and also using contour plots and surface plots are performed on the dengue serotypes associated reproduction numbers. The impact of influential parameters are graphically presented. Worthy of mention, is the significant impact of dengue transmission rates (positively correlated) and dengue vaccination rates and vaccine effectiveness levels (negatively correlated). Different scenario analyses to investigate the impact of dengue vaccination measures are presented. It was observed that enhanced dengue vaccination programme under the administration of safe and highly effective vaccine could curtail the spread and co-circulation of different dengue serotypes within the population.
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