两类生长曲线模型的参数辨识及对疫情数据的拟合

Parameter Identification and Epidemic Data Fitting of Two Types of Growth Curve Models

本文研究了Logistic和Richards两类种群生长模型的差异。Logistic方程是Richards方程异速增长参数取定值2的特例。从微分方程出发,我们求出了两类生长方程的显式通解,通过取对数、求导、换元和差分等操作,利用线性最小二乘法对参数进行估计,最后结合湖南省的新冠疫情实例对比说明Logistic和Richards增长曲线方程的适用性及参数估计的有效性。

The differences between Logistic and Richards population growth models were studied. The Logistic equation is a special case of the constant value 2 of allometric growth parameter of Richards equation. Starting from the differential equation, we calculate the growth equations of the two kinds of explicit conditions and by the exponential, derivation, changing and difference operations such as, using the linear least square method to estimate the parameters, and finally combined with the outbreak of the new champions league of Hunan Province to explain the applicability of Logistic and Richards growth curve equation and the validity of parameter estimation.