In this work, a Thai disability labor employment model was developed using a nonlinear delay-differential equation, with the delay term capturing policy implementation lags arising from administrative processes. In addition, we established theoretical results that guarantee the existence of equilibria and characterized the effect of implementation delays on long-term market stability. In particular, the global asymptotic stability under sufficient conditions was proved using a Lyapunov approach. To evaluate parameter influence, a normalized sensitivity analysis was conducted to identify the most significant factors for unemployment dynamics. Finally, numerical results were demonstrated in two stages. First, the numerical experiments were performed to validate the theoretical stability results. Second, the model parameters were estimated using historical Thai data for 2022–2025. To improve the model's consistency with observed data, the vacancy dynamics were refined by introducing additional variables. The proposed model provides a quantitative tool for analyzing policy delays and designing effective intervention strategies in the disability labor market.
Citation: Phachara Chanosot, Suttida Wongkaew, Tawatchai Petaratip, Piyapong Niamsup. Stability and impact of time-delay analysis of the disability labor model[J]. AIMS Mathematics, 2026, 11(6): 19286-19320. doi: 10.3934/math.2026784
In this work, a Thai disability labor employment model was developed using a nonlinear delay-differential equation, with the delay term capturing policy implementation lags arising from administrative processes. In addition, we established theoretical results that guarantee the existence of equilibria and characterized the effect of implementation delays on long-term market stability. In particular, the global asymptotic stability under sufficient conditions was proved using a Lyapunov approach. To evaluate parameter influence, a normalized sensitivity analysis was conducted to identify the most significant factors for unemployment dynamics. Finally, numerical results were demonstrated in two stages. First, the numerical experiments were performed to validate the theoretical stability results. Second, the model parameters were estimated using historical Thai data for 2022–2025. To improve the model's consistency with observed data, the vacancy dynamics were refined by introducing additional variables. The proposed model provides a quantitative tool for analyzing policy delays and designing effective intervention strategies in the disability labor market.
| [1] |
S. Al-Sheikh, R. Al-Maalwi, H. A. Ashi, A mathematical model of unemployment with the effect of limited jobs, Comptes Rendus. Math., 359 (2021), 283–290. https://doi.org/10.5802/crmath.164 doi: 10.5802/crmath.164
|
| [2] | G. N. Pathan, P. H. Bhathawala, A mathematical model for unemployment with effect of self employment, IOSR J. Math., 11 (2015), 37–43. |
| [3] |
H. Yang, Analyzing global stability of the delay viral model with general incidence rate, Differ. Equ. Dyn. Syst., 24 (2016), 319–328. https://doi.org/10.1007/s12591-016-0295-9 doi: 10.1007/s12591-016-0295-9
|
| [4] | P. Chanosot, S. Wongkaew, Stability analysis of unemployment model in Thailand after COVID-19 outbreak, MS. Thesis, Chiang Mai University, 2022. |
| [5] |
A. K. Misra, A. K. Singh, A delay mathematical model for the control of unemployment, Differ. Equ. Dyn. Syst., 21 (2013), 291–307. https://doi.org/10.1007/s12591-012-0153-3 doi: 10.1007/s12591-012-0153-3
|
| [6] |
T. Petaratip, P. Niamsup, Stability analysis of an unemployment model with time delay, AIMS Math., 6 (2021), 7421–7440. https://doi.org/10.3934/math.2021434 doi: 10.3934/math.2021434
|
| [7] |
A. K. Misra, M. Kumari, M. Sajid, Role of informal sector to combat unemployment in developing economy: a modeling study, Heliyon, 10 (2024), e33378. https://doi.org/10.1016/j.heliyon.2024.e33378 doi: 10.1016/j.heliyon.2024.e33378
|
| [8] |
P. K. Singh, K. Lata, A. K. Singh, A. K. Misra, Modeling the effect of unemployment augmented industrialization on the control of unemployment, Environ. Dev. Sustain., 25 (2023), 587–600. https://doi.org/10.1007/s10668-021-02069-6 doi: 10.1007/s10668-021-02069-6
|
| [9] | S. B. Munoli, S. Gani, S. R. Gani, A mathematical approach to employment policies: an optimal control analysis, Int. J. Stat. Syst., 12 (2017), 549–565. |
| [10] |
S. B. Munoli, S. Gani, Optimal control analysis of a mathematical model for unemployment, Optim. Control Appl. Methods, 37 (2016), 798–806. https://doi.org/10.1002/oca.2195 doi: 10.1002/oca.2195
|
| [11] |
S. A. Somma, R. O. Omotinuwe, N. O. Abdurrahman, Mathematical model for the control of unemployment in Nigeria incorporating vocational education and apprenticeship, Al-Mustansiriyah J. Sci., 36 (2025), 1–17. https://doi.org/10.23851/mjs.v36i2.1655 doi: 10.23851/mjs.v36i2.1655
|
| [12] |
A. K. Misra, A. K. Singh, A mathematical model for unemployment, Nonlinear Anal., 12 (2011), 128–136. https://doi.org/10.1016/j.nonrwa.2010.06.002 doi: 10.1016/j.nonrwa.2010.06.002
|
| [13] |
L. Harding, M. Neamţu, A dynamic model of unemployment with migration and delayed policy intervention, Comput. Econ., 51 (2018), 427–462. https://doi.org/10.1007/s10614-016-9610-3 doi: 10.1007/s10614-016-9610-3
|
| [14] |
Z. Aamer, S. Jawad, B. Batiha, A. H. Ali, F. Ghanim, A. A. Lupaş, Evaluation of the dynamics of psychological panic factor, glucose risk and estrogen effects on breast cancer model, Computation, 12 (2024), 160. https://doi.org/10.3390/computation12080160 doi: 10.3390/computation12080160
|
| [15] | M. Ahmed, S. Jawad, The role of antibiotics and probiotics supplements on the stability of gut flora bacteria interactions, Commun. Math. Biol. Neurosci., 2023 (2023), 33. |
| [16] |
E. Hakeem, S. Jawad, A. H. Ali, M. Kallel, H. A. Neamah, How mathematical models might predict desertification from global warming and dust pollutants, MethodsX, 14 (2025), 103259. https://doi.org/10.1016/j.mex.2025.103259 doi: 10.1016/j.mex.2025.103259
|
| [17] | J. K. Hale, Ordinary differential equations, Courier Corporation, 2009. |
| [18] | M. W. Hirsch, S. Smale, R. L. Devaney, Differential equations, dynamical systems, and an introduction to chaos, 3 Eds., Academic Press, 2013. https://doi.org/10.1016/C2009-0-61160-0 |
| [19] | J. K. Hale, S. M. V. Lunel, Introduction to functional differential equations, Vol. 99, Springer Science & Business Media, 2013. |
| [20] | H. Smith, An introduction to delay differential equations with applications to the life sciences, Vol. 57, Springer New York, 2011. https://doi.org/10.1007/978-1-4419-7646-8 |
| [21] | H. K. Khalil, J. W. Grizzle, Nonlinear systems, Vol. 3, Upper Saddle River, Prentice Hall, 2002. |
| [22] | A. Patil, Routh-Hurwitz criterion for stability: an overview and its implementation on characteristic equation vectors using MATLAB, In: A. E. Hassanien, S. Bhattacharyya, S. Chakrabati, A. Bhattacharya, S. Dutta, Emerging technologies in data mining and information security, Advances in Intelligent Systems and Computing, Springer, Singapore, 1286 (2021), 319–329. https://doi.org/10.1007/978-981-15-9927-9_32 |
| [23] |
S. Ruan, J. Wei, On the zeros of a third degree exponential polynomial with applications to a delayed model for the control of testosterone secretion, IMA J. Math. Appl. Med. Biol., 18 (2001), 41–52. https://doi.org/10.1093/imammb/18.1.41 doi: 10.1093/imammb/18.1.41
|
| [24] | L. Perko, Differential equations and dynamical systems, Vol. 7, Springer Science & Business Media, 2013. |
| [25] | J. P. La Salle, The stability of dynamical systems, Society for Industrial and Applied Mathematics, 1976. |
| [26] | L. Arriola, J. M. Hyman, Sensitivity analysis for uncertainty quantification in mathematical models, In: G. Chowell, J. M. Hyman, L. M. A. Bettencourt, C. Castillo-Chavez, Mathematical and statistical estimation approaches in epidemiology, Springer, 2009,195–247. https://doi.org/10.1007/978-90-481-2313-1_10 |
| [27] | Department of Empowerment of Persons with Disabilities, Report on the situation of persons with disabilities in Thailand, Ministry of Social Development and Human Security (Data retrieved as of March 31, 2025), 2025. |
| [28] | National Statistical Office of Thailand, The 2025 disability survey, Ministry of Digital Economy and Society, Quarterly Labor Force Statistics, 2025. |
| [29] |
N. Chitnis, J. M. Hyman, J. M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull. Math. Biol., 70 (2008), 1272–1296. https://doi.org/10.1007/s11538-008-9299-0 doi: 10.1007/s11538-008-9299-0
|
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Phachara Chanosot, Suttida Wongkaew, Tawatchai Petaratip, Piyapong Niamsup. Stability and impact of time-delay analysis of the disability labor model[J]. AIMS Mathematics, 2026, 11(6): 19286-19320. doi: 10.3934/math.2026784
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