Analysis of the dengue risk by means of a Takagi–Sugeno-style model

Abstract

Dengue is an infectious disease caused by an arbovirus (transmitted by the bite of the Aedes aegypti mosquito), which occurs mainly in tropical and subtropical areas, including Brazil. Nowadays it constitutes a major public health problems in the world. This paper proposes analysis of the evolution of dengue risk, from a model of the kind Takagi–Sugeno where the consequence of each fuzzy rule is a partial differential equation – PDE. The uncertainty parameters κi, related to the risk of spread of dengue, are directly linked to the behavior of the mosquito population and they were evaluated by making use of a system based on fuzzy rules and information provided by experts. These parameters depend on the population of humans, which provides blood to the maturation of eggs, and potential mosquito breeding containers and still depend on the rainfall. The amount of rainfall presents stochastic dependence in the sampled values, and for this reason we chose the Markov chain method to model it. Researchers at the Laboratory for Spatial Analysis of Epidemiological Data (epiGeo – UNICAMP) performed studies on the dengue risk in the southern region of the city of Campinas (São Paulo state, Brazil) between 2006 and 2007, by means of statistical methods and provided information to begin this study. The numerical solution of differential equation resulting from Takagi–Sugeno inference was obtained using the weighted essentially non-oscillatory schemes, the fifth order (WENO-5) not smooth for regions of the domain and centered finite difference schemes of high order for the smooth regions, in the space discretization. Also a lifting scheme was made to define smoothness in the regions. For the time evolution we have chosen Runge–Kutta TVD (Total Variation Diminishing), of the third order. Simulations corresponding to a period of summer (December, January and February) were performed and the results have showed that an effective action to reduce the risk of dengue is to severely combat the potential mosquito breeding sites.