Abstract
We propose and study a stochastic capital-labour model with logistic growth function. First, we show that the model has a unique positive global solution. Then, using the Lyapunov analysis method, we obtain conditions for the extinction of the total labour force. Furthermore, we also prove sufficient conditions for their persistence in mean. Finally, we illustrate our theoretical results through numerical simulations.
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References
Becker, T.: A decomposition heuristic for rotational workforce scheduling. J. Sched. 23(5), 539–554 (2020)
Göttlich, S., Knapp, S.: Uncertainty quantification with risk measures in production planning. J. Math. Ind. 10 (2020), Paper No. 5, p. 21
Winberry, T.: A method for solving and estimating heterogeneous agent macro models. Quant. Econ. 9(3), 1123–1151 (2018)
Zine, H., Torres, D.F.M.: A stochastic fractional calculus with applications to variational principles. Fractal Fract. 4(3), Art. 38, 11 (2020)
Lotfi, E.M., Hattaf, K., Yousfi, N.: Stability and Hopf bifurcation of an epidemic model with logistic growth and delay. Discontin. Nonlinearity Complex 8(4), 379–389 (2019)
Mahrouf, M., Boukhouima, A., Zine, H., Lotfi, E.M., Torres, D.F.M. Yousfi, N.: Modeling and forecasting of COVID-19 spreading by delayed stochastic differential equations. Axioms 10(1), Art. 18, 16 (2021)
Zine, H., Boukhouima, A., Lotfi, E.M., Mahrouf, M., Torres, D.F.M., Yousfi, N.: A stochastic time-delayed model for the effectiveness of Moroccan COVID-19 deconfinement strategy. Math. Model. Nat. Phenom. 15 (2020), Paper no. 50, p. 14
Mao, X.: Stochastic Differential Equations and Applications, 2nd edn. Horwood Publishing Limited, Chichester (2008)
Dalal, N., Greenhalgh, D., Mao, X.: A stochastic model of AIDS and condom use. J. Math. Anal. Appl. 325(1), 36–53 (2007)
Gray, A., Greenhalgh, D., Hu, L., Mao, X., Pan, J.: A stochastic differential equation SIS epidemic model. SIAM J. Appl. Math. 71(3), 876–902 (2011)
Higham, D.J.: An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 43(3), 525–546 (2001)
Riad, D., Hattaf, K., Yousfi, N.: Dynamics of capital-labour model with Hattaf-Yousfi functional response. J. Adv. Math. Comput. Sci. 18(5), 1–7 (2016)
Acknowledgements
This research is part of first author’s Ph.D. project, which is carried out at University of Aveiro under the Doctoral Program in Applied Mathematics of Universities of Minho, Aveiro, and Porto (MAP-PDMA). It was partially supported by the Portuguese Foundation for Science and Technology (FCT) within project UIDB/04106/2020 (CIDMA).
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Zine, H., Danane, J., Torres, D.F.M. (2022). A Stochastic Capital-Labour Model with Logistic Growth Function. In: Tchemisova, T.V., Torres, D.F.M., Plakhov, A.Y. (eds) Dynamic Control and Optimization. DCO 2021. Springer Proceedings in Mathematics & Statistics, vol 407. Springer, Cham. https://doi.org/10.1007/978-3-031-17558-9_13
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