Dinâmica da dengue em áreas de risco no Brasil: uma análise epidemiológica baseada no modelo de Ornstein-Uhlenbeck

Abstract

Dengue is one of the most alarming arboviral diseases, affecting millions of people annually and posing a significant challenge to public health on a global scale. With four distinct virus serotypes (DENV-1, DENV-2, DENV-3, and DENV-4), the disease is transmitted through the bites of female Aedes aegypti and Aedes albopictus mosquitoes. Mathematical models can aid in understanding the dynamics of dengue spread, especially when considering how human mobility and interactions among different population groups influence the propagation of the disease. In this context, an analytical reaction-advection-diffusion model in closed form, based on the Ornstein-Uhlenbeck stochastic process in continuous time and space, is proposed to estimate the spatiotemporal distribution of the rate of new infections and, consequently, the infection risk rate for a host within the region under study. For the analysis, a population of susceptible individuals initially distributed uniformly in space was considered. Subsequently, as an initial condition, a new infection hotspot was introduced at point x , disrupting the homogeneous distribution. Through this modeling, essential epidemiological parameters in the dynamics of dengue spread were determined, including the basic reproduction number (R 0 ) and the generation time of the disease. For the study, states from each of Brazil’s regions were selected: Amazonas and Pará (North); Bahia and Pernambuco (Northeast); Paraná and Rio Grande do Sul (South); Minas Gerais, Rio de Janeiro, and São Paulo (Southeast); and Goiás and the Federal District (Central-West). Epidemiological data on dengue cases were extracted from the DataSUS platform, covering the period from 2014 to 2024, focusing on epidemiological weeks 1 to 7 of each year. The R 0 values found were consistently greater than 1, ranging from 1 to 2.5 throughout the study period. The results show that the R values and the mean generation time of 18.77 days are consistent with previous studies. Regarding the risk area, the results indicate that the highest intensity in the risk scale is concentrated near the central infection point. This suggests that the highest transmission risk occurs within a very small radius. Therefore, targeted actions within a radius of less than 0.2 km around identified cases should be prioritized.