3 resultados para Matrix fractional order differential equation


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The model presented allows simulating the pesticide concentration in fruit trees and estimating the pesticide bioconcentration factor in fruits of woody species. The model allows estimating the pesticide uptake by plants through the water transpiration stream and also the time in which maximum pesticide concentration occur in the fruits. The equation proposed presents the relationships between bioconcentration factor (BCF) and the following variables: plant water transpiration volume (Q), pesticide transpiration stream concentration factor (TSCF), pesticide stem-water partition coefficient (KWood,w), stem dry biomass (M) and pesticide dissipation rate in the soil-plant system (kEGS). The modeling started and was developed from a previous model ?Fruit Tree Model? (FTM), reported by Trapp and collaborators in 2003, to which was added the hypothesis that the pesticide degradation in the soil follows a first order kinetic equation. The model fitness was evaluated through the sensitivity analysis of the pesticide BCF values in fruits with respect to the model entry data variability.

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We presented a model that estimates the bioconcentration factor (BCF) of pesticides in potatoes supposing that the pesticide in the soil solution is absorbed by the potato by passive diffusion, following Fick?s second law. The pesticides in the model are nonionic organic substances, traditionally used in potato crops that degrade in the soil according to a first order kinetic equation. This presents an expression that relates BCF with the pesticide elimination rate by the potato, with the pesticide accumulation rate within the potato, with the rate of growth of the potato and with the pesticide degradation rate in the soil. BCF was estimated supposing steady state equilibrium of the quotient between the pesticide concentration in the potato and the pesticide concentration in the soil solution. It is suggested that a negative correlation exists between the pesticide BCF and the soil sorption partition coefficient. The model was built based on the work of Trapp et al. (2007), [Diffusion of PAH in Potato and Carrot Slices and Applications for a Potato Model] in which an expression to calculate the diffusivity of persistent organic substances in potatoes is presented. The model consists in adding to the expression of Trapp et al. (2007) the hypothesis that the pesticide degrades in the soil. The value of BCF suggests which pesticides should be monitored in potatoes.

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RESUMO - O Huanglongbing (HLB ou Greening) é a doença mais importante e destrutiva da citricultura mundial. Presente de forma endêmica nos continentes asiático e africano há várias décadas, essa doença foi constatada no Brasil em 2004, sendo transmitida pelo psilídeo Diaphorina citri e causada por bactérias de floema Candidatus Liberibacter spp. Para auxiliar o estudo da doença, foram desenvolvidos modelos matemáticos para avaliação da propagação do HLB Citros. Este trabalho tem por objetivo a criação de um sistema para execução via web de um destes modelos, permitindo aos profissionais de diversas formações, em especial os das áreas biológicas, que são os especialistas do domínio em estudo, acesso rápido aos resultados fornecidos pelo modelo matemático, eliminando ainda a necessidade de conhecimento prévio em alguma linguagem de programação ou de métodos de resolução de equações diferenciais. O sistema foi completamente implementado em R, tendo sido o pacote deSolve usado para solução do modelo matemático e o framework web Shiny para a interface com usuário, sendo todos open source.