A study of the spread of dengue using partial differential equations and fuzzy logic / Um estudo sobre o espalhamento da dengues usando equações diferenciais parciais e logica fuzzy

AUTOR(ES)
DATA DE PUBLICAÇÃO

2009

RESUMO

The aim of this work is to study dengue and, with this purpose, some mathematical models were created to simulate its evolution in the southern district of the city of Campinas. The human population was subdivided into three compartments, according to the state of the individuals { susceptible, infectious or recovered. The interaction between these different populations and the Aedes aegypti mosquito population establishes the behaviour of the disease in the specified domain. The state variables of the models are the human populations and the mosquito population, whose compartmental division depends on the adopted model. Its values are deterministic and represent population densities in each point of the domain. This work takes into account specialists information concerning the behaviour of the disease and the conditions of the proliferation and spread of the mosquito vector. These conditions, whose nature is considered uncertain, determine the risk of contraction of the disease and, consequently, the model parameters. The modelling results in systems of partial differential equations with some of its parameters being uncertain. To obtain the solutions (variable values according to time and the cited domain), numerical solution tools are used (Finite Elements and Crank-Nicolson methods). Parameters related to the behaviour of mosquito populations are evaluated through the Fuzzy Rules Based Systems, to which are provided, as entries, the specialists information with respect to the environmental conditions

ASSUNTO(S)

differential equations finite element method logica fuzzy dengue equação diferencial parcial epidemiology metodo de elementos finitos dengue epidemiologia - matemática partial fuzzy logic

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