Modelo matemático para a simulação da produção de mel em municípios do Rio de Janeiro

Abstract

Brazil and Argentina amongst the world’s ten leading countries in honey exports. The two countries share in this commodity exports was about US$ 220 million dollars in 2011. Argentina is one of the world’s greatest producers, having reached 83,121 tons that year. That means that apiculture is a relevant activity to both countries’ agrobusiness network. All this amount of production and equivalente input were consequence of the joint effort of producers, research centres and development agencies. Thus, mathematical models which may allow a better understanding of honey production over time, under many factors influence, might be na important planning tool for the many actors involved in this scene. The aim of this work is to develop mathematical models, defined by ordinary differential equations, whose numerical solutions and parameters may allow one to have information about a certain municipality’s honey production. The central hipotesis is that it is possible to assess and predict a municipality’s honey production, by using mathematical models. A secondary hipotesis would be that these models’ paremeters could be important indices to this productive activity. The models deveploped here were based in Lucas Growth Model, which takes into account that human capital as an endogenous fundamental growth component. The parameter rescue and the models numerical solving were implemented through a software in Fortran 95 programming language. The software main guideline was to allow solutions to the models so that it was possible to offer anoptimalmuniciplaity’s honey production description, in a certain time period. The solution fitting of the system of differential equaions which define the models was made through a nonlinear least squares method. The solver to this method was BOBYQA, a software presented in Powell (2009). This algorithm was developed in Fortran 77, is derivative free and accepts box constraints. The model validation was made in two steps: in the first it was validated gedanken honey production data. In the second the models were applied to eightenn municipalities which represented honey production in Rio de Janeiro State microregions. Fifteen among the researched had good model fitting. There was no fitting in three cases of anomalous production.This way, the results allow one to conclude that the developed models may be efficient instruments to honey agorbusiness managers, by allowing good production predictions under certain conditions and crop estimate in harvest periods. Moreover, they may start important research about technology and productivity in this economic activity.