Optimal control strategies for dynamical model of climate change under real data

Authors

  • Fatmawati
    Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia
  • Faishal F. Herdicho
    Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia
  • Nurina Fitriani
    Department of Biology, Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia
  • Norma Alias
    Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor Bahru, Johor, Malaysia
  • Mazlan Hashim
    Geoscience & Digital Earth Centre (INSTEG), Research Institute for Sustainable Environment (RISE), Universiti Teknologi Malaysia, Johor Bahru, Johor, Malaysia
  • Olumuyiwa J. Peter
    Department of Mathematics, Saveetha School of Engineering, SIMATS, Saveetha University, Chennai, Tamil Nadu, 602105, India

Keywords:

Climate change, cost-effectiveness analysis, mathematical model, optimal control, parameters estimation

Abstract

Climate change is primarily caused by increasing levels of carbon dioxide (CO$_2$) in the atmosphere, with significant impacts on global temperatures and ecosystems. The interplay between CO$_2$ levels, forest biomass, and temperature highlights how important it is to conserve these vital ecosystems in order to effectively combat climate change. In this study, we construct and analysis the Lotka-Volterra model to explore the interactions between concentration of CO$_2$, photosynthetic biomass density and atmospheric temperature. The results of the model analysis obtained four locally asymptotically stable equilibria under specific conditions and two unstable equilibria. Based on the results of the sensitivity analysis, the most influential parameters affecting changes in concentration number are intrinsic rate of accumulation of CO$_2$ and natural reduction rate of CO$_2$. Next to estimate the model parameters, we employ the least-squares method, enabling us to apply the model to actual temperature data from Surabaya city, Indonesia. The numerical simulation results show that CO$_2$ concentration is expected to range from 400 to 420 ppm, biomass density is estimated to be between 92 and 102 kg/m$^3$, and atmospheric temperature is projected around $28.1^o$C $- 29.1^o$C. Next, using the Incremental Cost-Effectiveness Ratio (ICER) calculation, implementing control strategy in the form of limiting access to private vehicles and reforestation is the best strategy to make the temperature better and cost efficiency. 

Dimensions

[1] Intergovernmental Panel on Climate Change (IPCC), Climate Change 2021: The Physical Science Basis, 2021. [Online]. https://www.ipcc.ch/report/ar6/wg1/.

[2] I. A. Anazonwu & M. Z. Fahmi, “Wastewater treatment, greenhouse gas emissions, and our environment”, Recent Advances in Natural Sciences 2 (2024) 121. https://doi.org/10.61298/rans.2024.2.2.121.

[3] R. Latha, K. Kakshminarayanachari & C. Bhaskar, “An analytical model for point source pollutants in an urban area with mesoscale wind and wet deposition”, Journal of the Nigerian Society of Physical Sciences 6 (2024) 2116. https://doi.org/10.46481/jnsps.2024.2116.

[4] Food and Agriculture Organization of the United Nations (FAO), “The state of the World’s forests 2020: Forests, biodiversity and people”, 2020. [Online]. https://www.fao.org/state-of-forests/en/.

[5] World Wildlife Fund (WWF), “Forest pathways report 2023”, 2023. [Online]. https://www.worldwildlife.org/publications/forest-pathways-report-2023.

[6] I. A. Pratiwi, E Prasetyo & H. D. Ardiansyah, “Greenhouse gas (GHG) emission reduction model in Surabaya”, Ecology, Environment and Conservation Paper 26 (2020) 1342. https://www.envirobiotechjournals.com/issues/article abstract.php?aid=10785&iid=316&jid=3.

[7] U. F. Kurniawati, C. Susetyo & P. T. Setyasa, “Institutional assesment through climate and disaster resilience initiative in Surabaya”, IOP Conf. Series: Earth and Environmental Science 562 (2020) 012025. https://iopscience.iop.org/article/10.1088/1755-1315/562/1/012025.

[8] H. A. Biswas, T. Rahman & N. Haque, “Modeling the potential impacts of global climate change in Bangladesh: an optimal control approach”, Journal of Fundamental and Applied Sciences 8 (2016) 1. http://dx.doi.org/10.4314/jfas.v8i1.1.

[9] S. Mandal, Md. S. Islam & Md. H. A. Biswas, “Modeling the potential impact of climate change in living beings near coastal areas”, Modeling Earth Systems and Environment 7 (2021) 1783. https://doi.org/10.1007/s40808-020-00897-5.

[10] E. A. D. Kurniawan, Fatmawati & Miswanto, “Modeling of global warming effect on the melting of polar ice caps with optimal control analysis”, AIP Conference Proceedings 2329 (2021) 040006. https://doi.org/10.1063/5.0042360.

[11] S. Mandal, Md. S. Islam, Md. H. A. Biswas & S. Akter, “Modeling the optimal mitigation of potential impact of climate change on coastal ecosystems”, Heliyon 7 (2021) e07401. https://doi.org/10.1016/j.heliyon.2021.e07401.

[12] S. Soldatenko, A. Bogomolov & A. Ronzhin, “Mathematical modelling of climate change and variability in the context of outdoor ergonomics”, Mathematics 9 (2021) 2920. https://doi.org/10.3390/math9222920.

[13] A. Din, F. M. Khan, Z. U. Khan, A. Yusuf & T. Munir, “The mathematical study of climate change model under nonlocal fractional derivative”, Partial Differential Equations in Applied Mathematics 5 (2022) 100204. https://doi.org/10.1016/j.padiff.2021.100204.

[14] P. U. Achimugwu, M. N. Kinyanjui & D. M. Malonza, “Mitigation of climate change due to excessive carbon dioxide emission and accumulation: a mathematical model approach”, Communications in Mathematical Biology and Neuroscience 2023 (2023) 70. https://doi.org/10.28919/cmbn/8027.

[15] A. Sangwan, S. Choudhary, V. Anand, N. Kumar, A. Kumar, M. K. Jat & R. Ahmed, “A mathematical model for temperature-reducing potential of urban greenspaces”, Earth Science Informatics 16 (2023) 4199. https://doi.org/10.1007/s12145-023-01166-6.

[16] K. L. Atoyev & P. S. Knopov, “Mathematical modeling of climate change impact on relationships of economic sectors”, Cybernetics and Systems Analysis 59 (2023) 535. https://doi.org/10.1007/s10559-023-00589-9.

[17] F. O. Ochieng, “A novel data-driven dynamical model for predicting future climate trends”, Modeling Earth Systems and Environment 10 (2024) 4599. https://doi.org/10.1007/s40808-024-02021-3.

[18] I. Shahid, R. A. Naqvi, M. Yousaf, A. M. Siddiqui & A. Sohail, “Controlling carbon emissions through modeling and optimization: addressing an earth system and environment challenge”, Modeling Earth Systems and Environment 10 (2024) 6003. http://dx.doi.org/10.1007/s40808-024-02096-y.

[19] S. Kutala, H. Awari, S. Velu, A. Anthonisamy, N. J. Bathula & S. Inthiyaz, “Hybrid deep learning-based air pollution prediction and index classification using an optimization algorithm”, AIMS Environmental Science 11 (2024) 551. https://doi.org/10.3934/environsci.2024027.11

[20] P. van den Driessche & J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartemental models of disease transmission”, Mathematical Biosciences 180 (2002) 29. https://doi.org/10.1016/s0025-5564(02)00108-6.

[21] Satu Data, Statistik Sektoral Kota Surabaya Tahun 2021-2023, 2021-2023. [Online]. https://satudata.surabaya.go.id/statistik-sektoral.

[22] N. Chitnis, J. M. Hyman & J. M. Cushing, “Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model”, Bulletin of Mathematical Biology 70 (2008) 1272. https://doi.org/10.1007/s11538-008-9299-0.

[23] L. S. Pontryagin, The Mathematical Theory of Optimal Processes, CRC Press, Boca Raton, USA, 1987. https://api.pageplace.de/preview/DT0400.9781351433075_A37629368/preview-9781351433075 A37629368.pdf.

[24] S. Lenhart & J. T. Workman, Optimal Control Applied to Biological Models, Chapman and Hall/CRC, Boca Raton, USA, 2007. https://doi.org/10.1201/9781420011418.

[25] B. Buonomo & R. D. Marca, “Optimal bed net use for a dangue disease model with mosquito seasonal pattern”, Mathematical Methods in the Applied Sciences 41 (2017) 573. https://doi.org/10.1002/mma.4629.

[26] Fatmawati, C. W. Chukwu, R. T. Alqahtani, C. Alfiniyah, F. F. Herdicho & Tasmi, “A Pontryagin’s maximum principle and optimal control model with cost-effectiveness analysis of the COVID-19 epidemic”, Decision Analytics Journal 8 (2023) 100273. https://doi.org/10.1016/j.dajour.2023.100273.

[27] S. S. Musa, S. Zhao, I. Abdulrashid, S. Qureshi, A. Colubri & D. He, “Evaluating the spike in the symptomatic proportion of SARS-CoV-2 in China in 2022 with variolation effects: a modeling analysis”, Infectious Disease Modelling 9 (2024) 601. https://doi.org/10.1016/j.idm.2024.02.005.

[28] D. Baleanu, S. Qureshi, A. Yusuf, A. Soomro & M. S. Osman, “Bi-modal COVID-19 transmission with Caputo fractional derivative using statistical epidemic cases”, Partial Differential Equations in Applied Mathematics 10 (2024) 100732. https://doi.org/10.1016/j.padiff.2024.100732.

[29] P. A. Naik, B. M. Yeolekar, S. Qureshi, M. Yeolekar & A. Madzvamuse, “Modeling and analysis of the fractional-order epidemic model to investigate mutual influence in HIV/HCV co-infection”, Nonlinear Dynamics 112 (2024) 11679. https://doi.org/10.1007/s11071-024-09464-9.

[30] A. Padder, L. Almutairi, S. Qureshi, A. Soomro, A. Afroz, E. Hincal & A. Tassaddiq, “Dynamical analysis of generalized tumor model with Caputo fractional-order derivative”, Fractal and Fractional 7 (2023) 258. https://doi.org/10.3390/fractalfract7030258.

[31] A. Atangana & S. Qureshi, “Modeling attractors of chaotic dynamical systems with fractal–fractional operators”, Chaos, Solitons & Fractals 123 (2019) 320. https://doi.org/10.1016/j.chaos.2019.03.003.

Published

2025-08-01

How to Cite

Optimal control strategies for dynamical model of climate change under real data. (2025). Journal of the Nigerian Society of Physical Sciences, 7(3), 2572. https://doi.org/10.46481/jnsps.2025.2572

Issue

Volume 7, Issue 3, August 2025

Section

Mathematics & Statistics
Copyright & Licensing

Copyright (c) 2025 Fatmawati, Faishal F. Herdicho, Nurina Fitriani, Norma Alias, Mazlan Hashim, Olumuyiwa J. Peter

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Optimal control strategies for dynamical model of climate change under real data. (2025). Journal of the Nigerian Society of Physical Sciences, 7(3), 2572. https://doi.org/10.46481/jnsps.2025.2572

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