A Dengue Fever Epidemiological Model With Vaccination and Vaccine Inefficacy

The global impact of dengue has prompted the development of numerous mathematical models aimed at understanding and controlling the pandemic. The Qdenga vaccine was introduced in 2022 to prevent dengue infection. Building on this, we develop a threshold-based dynamical model of the dengue fever epidemic that incorporates vaccination, vaccine inefficacy, and asymptomatic carriers. We first formulate the arithmetic expression for the control reproduction number R-0 and then use properties of complex modulus and proof by contradiction to establish the local asymptotic stability of both dengue-free equilibrium and dengue-infected equilibrium of the model. Furthermore, by constructing appropriate Lyapunov functions and applying the generalized Lyapunov-LaSalle theorem, we obtain the global dynamic properties of the two equilibria. In particular, we confirm weak persistence for R-0>1 to achieve the global attractivity of the dengue-infected equilibrium. Notably, we conduct numerical simulations and analyze the transmission dynamics of the disease in conjunction with official data from Brazil and the results of parameter estimation. These numerical findings are consistent with our theoretical results. Additionally, sensitivity analysis using MATLAB is carried out to identify parameters with significant impact on our model. Our numerical simulation results suggest that taking into account vaccination and potential vaccine inefficacy can lead to more accurate simulations of real-world scenarios. This consideration also plays a significant role in devising feasible epidemic control strategies and enhancing targeted vaccine development. Specifically, Qdenga received approval for use in Brazil in March 2023. Relevant authorities in Brazil are encouraged to actively promote vaccination campaigns in order to reduce the infection rate.