費爾哈斯特（Verhulst）模型是由德國生物數學家Verhulst於1837年提出的生物生長模型，其特性是模型之預測趨勢會趨向某固定數值而達極限穩定，人口成長亦不會無限制成長，將因環境與食物等限制因素而達極限穩定。灰費爾哈斯特模型便是將Verhulst模型之特性結合灰預測GM（1,1）模型，在灰預測模型中加入一個限制發展項，以推求人口可能之實際成長極限情況。灰預測是近幾年廣受發展之預測模型，因其僅需小樣本往往便可得到高預測精度（90%以上）。本研究以宜蘭縣1993∼2011年之人口資料為基礎，進而以灰費爾哈斯特模型推估宜蘭縣2013年之成長極限人口，以提供政府部門擬議人口發展政策之參考。

The Verhulst model about the growth of biology was proposed by a German bio-mathematician in 1837. Its characteristic was that the predictive trend will limit to fixed value and be saturated and stable. Traditional prediction model of long regulation often requires large of data and sometimes doesn't accord to the economic effect. Thus the grey predictive model which only depends on small data can acquire high accurate result (90%) is used more widely.The Grey Verhulst model was combined the characteristic both with the verhulst model and GM(1,1) of grey predictive model. It added a limited item of development into the GM(1,1) mode to satisfy the situation of realistic saturation. This study was on the basis of population of 1993~2011 in Yilan County, by means of a grey verhulst model to predict the population in 2013, in order to propose results to the government for reference when making decision in population policy.