STUDY OF MATHEMATICAL METHODS AND MODELS USAGE IN THE PESTICIDE DEGRADATION AND RESIDUE PREDICTION

Pesticide was widely used in agriculture industry to ensure the crops’ yield and quality, followed that pesticide pollution had become one of the most serious issues for public health in the world. Therefore, it’s necessary to develop mathematical models for the prediction of pesticide degradation and residue. In this paper, we introduced four kinds of mathematical models in pesticide prediction, and offered the basis theories and practical applications for each model. Then we compared their advantages and disadvantages systematically by analyzing the roles of each one. Finally, present challenges and future perspectives in pesticide residue prediction fields were discussed.

According to the pesticides degradation regularity, the disappearance of pesticides in soil or on plants is like the decay of radioactive substances, which can be expressed by the firstorder reaction kinetics formula of biotic and abiotic factors, Exponential degradation model has the advantages including simple calculation, directly-viewed and easy understanding, which has important influence on the prediction of pesticide degradation. But the basic model is proposed in a relatively ideal situation, ignoring the nature environmental factors. Also, the predict results just describe the situation that the degradation rate is a monotonically decreasing function over time, which can't change following the special environments. It is limited in actual application due to its extremely idealization and simplification. ( According to the value, we set the bivariate function as following: t is time after pesticide application , a , b is undetermined coefficients. After the logarithm based on (3.1), we will get x  ,the formula of (3.2) can be translated into a binary linear regression equation,as following: Fang et al.
[0] studied the degradation of methamidophos on rice leaves, mimicking the dynamic mathematics model. The regression of this model is remarkable and conform to the law of degradation, then they proposed three modified Rayleigh models to predict the pesticide residues, which showed better results. Zhu et al.
[0] proposed a modified Rayleigh mathematics model for the degradation law of pesticide. In their study, parameter estimation method of modified Rayleigh model was introduced, which offered theoretical basis for the study on pesticide residue law.
Compared with exponential degradation model, Rayleigh dynamic model has more advantages like precision error, easyto-use and high fitting accuracy, which avoid complicated calculations and range of independent variables in polynomials. Rayleigh dynamic model performs effective results and it's a utility model.
(3) Grey prediction GM (1.1) Model Grey prediction is that the model using not the original data sequence but the generated data sequence. Based Grey Model, Grey prediction is a method that generates the approximate exponential law through accumulation (or other methods) of the original data and then carries out modeling.
Let pesticide residue sequence as  ) ( ) 1 ( k z is the adjacent to mean-generated sequence of Building the GM (1,1) model for pesticide residue sequence as (  is parameters sequence, then a is development coefficient and u is Grey action. Let the differential equation satisfying the data sequence generated by once accumulation as So parameter a and u can structure a matrix B , n Y Then the least squares estimation parameter column of .Let â into differential equation (10)   And the degradation of residual quinalfhosion in cowpea, the degradation of residual mancozeb in Lycopersicon esculentum miller, the degradation dynamics of triadimefon in ear of wheat and the dynamic dispelling of pirimicarb residue in cucumber fruit were predicted based on the IEA-GM (1.1) prediction model. GM (1.1) model has good accuracy in simulation and prediction, existing high practical application value. However, the solution of GM (1,1) model parameters involves matrix transpose, matrix multiplication and matrix inversion, which is too complex and not easy to apply, and has the characteristics of chaos.

4) Other Recent research models
In addition, many innovative research methods emerged for pesticide residues prediction. In 2016 Zuo et al.
[0] studied the pesticide residue prediction based on fuzzy system. The mathematic Fuzzy System was established by using the MRL values (maximum residue limits of all kinds of pesticides in food) of Matlab Fuzzy. Taking chlorpyrifos as an example, the analysis results showed that the application of fuzzy system for pesticide residue prediction was feasible and reasonable, and it was conductive to solve the problem of the using amounts of pesticides in the process of agricultural. In 2018, Li et al. [0] proposed a multi-section model based on principal components analysis (PCA) and neural network. They solve the problem that the modeling data characteristics changes obviously and experimental results show that the muti-section models built by Back Propagation(BP)/Radial Basis Function (RBF) network can significantly reduce the prediction error compared with the single models, and reduce the output error to 0.8 % and 0.4 % for establishing muti-section models BP and RBF respectively.
Conclusions. Pesticides provide a strong guarantee for the large-scale incremental production of crops, but excessive and continuous usage of pesticides have aroused much fear in our life [0]. With the development of science and our environmental awareness being strengthened, the harmful impact of pesticide residues and their degradation behavior have attracted more and more attention. The pesticide degradation and residue are a highly complex physical and biochemical processes. Even though variety dynamic models with high fitting degree for the residual degradation process of different pesticide are established, they could not meet the requirement of universality [0]. Therefore, it is of great practical significance to study the pesticides degradation law, and select appropriate mathematical models to describe the dynamic process of pesticide residues, then to do the analyse and prediction works. This paper summarizes four kinds of classic mathematics models in pesticide residues prediction, and compare their strengths and weaknesses based on mathematics theory and experiments results for each other. It turns out that there still exist more works to do in the future. As the development of computer technology, digital simulation and molecular biotechnology technologies, the studies on pesticide degradation and residues will continue to be further developed [0-22].