Research On Grey Verhulst Model Based On Structural Optimization And Its Application

Grey Verhulst model is one of the important prediction models of grey system theory.It can be used to describe saturated S-shaped series and single-peak inverted U-shaped series.It is widely used in population prediction,biological growth,economic analysis and other fields.However,with the expansion of application fields,the existing grey Verhulst model has exposed some problems that need to be solved urgently,and it still needs to be optimized and improved.In this paper,two grey Verhulst models with optimized structure were constructed to reduce parameter mislocation error and broaden applicable sequence types,and the optimized models were applied to predict the incidence of infectious diseases,which provides theoretical support for studying the epidemic trend of infectious diseases and formulating relevant epidemic prevention strategies.Firstly,in view of the unstable performance of the traditional grey Verhulst model due to the inability to use quantitative methods to determine the sequence type,a grey Verhulst simulated annealing model was constructed.A variable constant term was introduced into the whitenization equation of the traditional model,so that the model can be adapted to the S-shaped and inverted U-shaped sequences.The simulated annealing algorithm was used to optimize the variable constant value,which broadened the scope of application and improved the stability of the model.The trapezoidal formula was used to optimize the grey derivative,so that the parameters of the difference equation were consistent with those of the differential equation.Through case analysis,the improved grey Verhulst simulated annealing model has sequence adaptability and can achieve high simulation prediction accuracy.Secondly,the Grey discrete swing Verhulst model was constructed for saturated S-shaped and inverted U-shaped sequences with fluctuation.The grey discrete Verhulst model was used as the base model to avoid the parameter misplacement problem of the traditional model.Based on the building process of GM(1,1)swing model,the prediction residual of grey discrete Verhulst model was discretized by Fourier finite.Genetic algorithm was used to solve the optimal grey frequency value and improve the prediction accuracy of the model.The comparison model was established with two examples,and the effectiveness of the model was illustrated by comprehensive evalucation indexes such as MAPE,MAE,U1,U2,IA and R.Finally,two optimization models were used to fit and predict the incidence data of four notifiable diseases in China from 2000 to 2020.Grey Verhulst simulated annealing model was established for typhoid fever and dysentery with inverted U-shape trend,grey discrete swinging Verhulst model was established for leptospirosis and JE with inverted U-shape trend,and the incidence data of four infectious diseases in the next five years were predicted.The results showed that the incidence of four infectious diseases showed a steady decline in the future.