Abstract

Purpose of the Study: The Verhulst model is a biological growth model proposed by the German biomathematician Verhulst in 1837. Population growth will also be limited by environmental and other development factors and tend to be stable. Its characteristic is that the trend predicted by the model will tend to a fixed value and reach stability. The gray Verhulst model combines the characteristics of the gray prediction GM(1,1) model and the Verhulst model, and adds restrictive development factors to the gray prediction model to infer the possible stable growth and development of the population.

Methodology: The research method of this study is the gray Verhulst model, which combines the characteristics of the gray prediction GM(1,1) model and the Verhulst model.

Main Findings: Gray prediction is a prediction model that has been widely promoted in recent years because it often requires only a small number of samples to obtain high prediction accuracy (more than 90%). This study is based on the population data of Nantou County, Taiwan from 2003 to 2020, and uses the Gray Fairhast model to estimate the number of elderly people and the growth of elderly families in Nantou County, Taiwan. The results show that the number of elderly households in Nantou County, Taiwan is expected to increase by 313 households in 2023, bringing the total number of elderly households to 14,853. The elderly population is expected to increase by 1,881 people, bringing the total number of elderly people to 93,424.

Applications of this study: This project provides a unique perspective, based on the biological growth model proposed by German biomathematician Verhulst in 1837. The trend predicted by the model will tend to a fixed value and reach stable characteristics, and population growth will also be affected by environmental and other developments. factors to predict future population development.

Novelty of this Study: The new contribution offered here is a reference for government departments to propose elderly population policy and investment in public facilities construction.