Age-structured model of dengue transmission dynamics with time-varying parameters, and its application to Brazil

An age structured mathematical model with time dependent parameters is developed to investigate the dynamics of dengue transmission. Its properties are thoroughly analyzed in the first part of this work, as for example its disease free steady state, the corresponding effective reproduction numbers, its basic reproduction number (obtained via the Euler and Lotka equation and the next generation matrix approach). We also provide formulas for the time-varying effective reproduction number, and draw relations with the instantaneous growth rate. In the second part, we apply this model to Brazil and use weekly time series data from this country. Various medical parameters are firstly evaluated from these data, and an extensive numerical simulations for the period 2021 to 2024 is then carried out. Estimation of the transmission rates are derived both from epidemiological data and from environmental data such as temperature and humidity. The time-varying effective reproduction numbers are then estimated on these data, following the theoretical investigations performed in the first part. The sensitive parameters that significantly affect the model dynamics are presented graphically. Model predictions for following year by using different transmission rates are finally presented. Our findings show the importance of population age distribution, vector population dynamics, and climate, contributing to a deeper understanding of dengue transmission dynamics in Brazil.