Spatial dynamics of dengue fever spreading for the coexistence of two serotypes with an application to the city of São Paulo, Brazil

Abstract

Background and objective:Dengue fever is a disease in which individuals’ spatial distribution and Aedes aegypti mosquitoes breeding places are important factors for the disease dynamics. Typically urban, dengue is a problem for least developed countries due to the ineffectiveness in controlling the vector and disorderly urbanization processes. The result is a composition of urban sanitation problems and areas with high demographic densities and intense flows of people. This paper explores the spatial distribution of vector breeding places to evaluate introducing a new dengue serotype to a population at equilibrium for a pre-existing serotype. The paper’s objective is to analyze the spatial dynamics of dengue using variations of the basic reproduction number.Methods:A model based on probabilistic cellular automata is proposed to permitting the necessary flexibility to consider some spatial distributions of vector breeding places. Then, ordinary differential equations are used as a mean-field approach of the model, and the basic reproduction number (R0) is derived considering the next-generation matrix method. A spatial approach for R0 is also proposed, and the model is tested in a neighbourhood from the city of São Paulo, Brazil, to examine the potential risks of vector breeding cells distribution.Results:The results indicated that the more spread out these places, the higher are the values of R0. When the model is applied to a neighbourhood in São Paulo, residential areas may boost the infections and must be under public vigilance to combat vector breeding sites.Conclusions:Considering the mean-field approximation of the cellular automata model by ordinary differential equations, the basic reproduction number derived returned an estimative of the disease dynamics in the population. However, the spatial basic reproduction number was more assertive in showing areas with a higher disease incidence. Moreover, the model could be easily adapted to be used in real maps enabling simulations closer to real problems.