Mathematical modeling on the dynamics of dengue fever with vaccination and transovarial transmission with real statistical data

Abstract

In this work, we developed a deterministic mathematical model to investigate the transmission dynamics of dengue fever while also incorporating both vaccination and transovarial transmission within the mosquito population. We conducted a mathematical analysis of the model, estimated the basic reproduction number, and examined the stability of the equilibria. By using the Center Manifold Theory, our analysis indicates the potential occurrence of backward bifurcation at the endemic equilibrium. To validate the model, we employed the actual dengue case data from Brazil during the first 30 weeks of 2024. The validation results showed strong agreement between the model projections and the observed data, which was then used for forecasting purposes. A sensitivity analysis was also carried out to identify the parameters with the most significant influence on transmission. Furthermore, the model was extended to assess two time-dependent control strategies: the use of mosquito bed nets to minimize human exposure and environmental sanitation to eliminate mosquito breeding habitats. Finally, numerical simulations demonstrated that implementing both control strategies concurrently offers a significantly greater reduction in dengue virus transmission than using either intervention individually.