MSIRV Simulation for Dengue with Vaccination in a Complex Urban Domain

This research investigates the spatiotemporal dynamics of dengue propagation using an MSIRV (Mosquito-Susceptible-Infected-Recovered-Vaccinated) epidemiological model. The central focus is the application of numerical methods (Finite Element Method, Crank-Nicolson Method, and Newton Method) to the model in real scenarios, integrating vaccination dynamics as a control parameter. The structure of the MSIRV model consists of a system of nonlinear partial differential equations. The computational implementation of the methods is verified using the Manufactured Solutions Method, which analyzes spatial convergence rates before their applicability to dynamic scenarios. The continuous spatial domain corresponds to the municipality of Seropédica (RJ). The simulations demonstrate that including the vaccination component significantly alters the viral infection rate. The model proved to be an effective prognostic tool for intervention planning and epidemic control. This research was conducted with the support of the Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro - FAPERJ.