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Uncertain age-dependent population equation with migration source

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Abstract

The age-dependent population equation with migration source is a partial differential equation describing the variation of population density in a given area over time. In the traditional age-dependent population equation with migration source, the strength of the migration source is deterministic. In practice, however, the migration source is often affected by noise caused by environmental, policy and other factors. To capture this noise, some scholars have applied the Wiener process. However, the prediction accuracy of the noise model based on the Wiener process may be low. This paper proposes the adoption of the Liu process in uncertainty theory as an alternative tool for modelling noise, which improves the prediction accuracy of the model. The paper then deduces the uncertain age-dependent population equation with migration source based on the Liu process. Furthermore, the analytic solution to the equation and its inverse uncertainty distribution are derived. Additionally, the parameters of the uncertain age-dependent population equation with migration source are estimated, and numerical examples are analysed to validate the model. This paper makes the following contributions: (1) describing the continuous migration source using a Liu process; (2) establishing a new type of uncertain differential equation depicting the variation in population density caused by migration noise in practice; (3) extending the applicability of uncertainty theory to demographic theory.

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Notes

  1. MATLAB R2020a, 9.8.0.1323502, maci64, Symbolic Math Toolbox,sym and solve functions.

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Acknowledgements

This work was supported by grants from the Key Program of the National Statistical Science Research (No.2021LZ28), Natural Science Foundation of Shaanxi Province of China (No.2022JQ-042), the Young Talent Support Program of Xi’an University of Finance and Economics, and the Yanta Scholars Fund of Xi’an University of Finance and Economics.

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Correspondence to Lu Yang.

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Yang, L. Uncertain age-dependent population equation with migration source. J Ambient Intell Human Comput 14, 7411–7425 (2023). https://doi.org/10.1007/s12652-022-04448-x

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