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Original GM(1,1) and Tan's modified GM(1,1) model are employed in this research to forecast the disability rate of the aged and the number of aged in the total population. However, the original GM(1,1) model outperforms Tan's modified GM(1,1) model. The results reveal that the continual increase in the disability rate of the aged leads in turn to growth rates of 1462.44% in the number of aged demanding long-term care services over the period 1991 -- 2011, far exceeding the growth rate of the aged population over the same period. In 2011 the total number of the aged in Taiwan demanding long-term care services is estimated to be 606,305; the number of the aged demanding services in home is estimated to be 424,413; while the number of the aged demanding institutional services is estimated to be 181,891.