改进简单催化模型中感染力函数的判别准则

Discriminant criterion for choosing infective force functions of modified simple catalytic model

针对改进简单催化模型中感染力函数[r(t)]的选择问题,作者作了分析.结果表明,可根据3个特定值的分布来确定r(t)的形式.当S值呈水平线、直线及二次曲线分布时,可分别选r(t)为常数、线性函数及二次函数;当T值呈直线分布时,选r(t)为指数函数;当u值呈“S”形分布时,选r(t)为Logistic函数,此时r(t)=u’(t)/u(t).结合实际资料,对r(t)的选择及模型的拟合过程作了解释.

This paper discusses the choice about infective force function [r(t)] of modified simple catalytic model(MSG model). The results indicate that r(t)can be determined by the distributions of three specific values called S, T and u. When the distribution of S value appears to be a constant, a straight line or a conic curve, the r(t) can be chosen correspondingly as a constant, a linear function or a conic function. When the distribution of T value is approximatively at a straight line, the r(t)will be chosen as an exponential function. When the u value appear to be a Logistic distribution, the Logistic function will be chosen as r(t). Finally, according to the real data, an example is given to demonstrate the choice of r(t) and to fit a MSG model.