Title: Applications of the dynamic system and differential equations to Taiwan mortality

Authors: Yong-Shiuan Lee; Meng-Rong Li; Jengnan Tzeng; Tsung-Jui Chiang-Lin

Addresses: Department of Statistics, National Chengchi University, Taipei, 116, Taiwan ' Department of Mathematical Sciences, National Chengchi University, Taipei, 116, Taiwan ' Department of Mathematical Sciences, National Chengchi University, Taipei, 116, Taiwan ' Graduate Institute of Applied Physics, National Chengchi University, Taipei, 116, Taiwan

Abstract: Modelling mortality is an important part of demographic researches. Since most developed countries have experienced rapid declines in mortality rates and population aging lately, it requires a more accurate mortality model to characterise and explain the phenomenon. Rather than stochastic models, the approach of the dynamic system and differential equations which is popular in natural sciences is applied in this study. The proposed model emphasises the mean reversion of the mortality where the mean stands for a hypothetical minimum rate. The model also depicts the speed of the convergence toward the minimum as the logistic curve. The empirical study shows that the model possesses reasonable characterisation and forecasts of Taiwan male and female age-specific mortalities. Subject to the algorithm the errors suggest that the model is comparatively better than Lee-Carter model, the benchmark model, for the ages from 15 to 70. Modelling the coefficients and modifying the algorithm will be the future work to raise the forecasting ability of the model.

Keywords: dynamic systems; differential equations; Taiwan; mortality; age-specific mortality; modelling; forecasting; demography; Lee-Carter model; mean reversion; Newton's law of cooling; logistic growth.

DOI: 10.1504/IJCSM.2021.116761

International Journal of Computing Science and Mathematics, 2021 Vol.13 No.3, pp.245 - 266

Received: 15 Feb 2018
Accepted: 01 May 2018
Published online: 02 Aug 2021 *

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