Mathematical Modeling and Control of Gas Emissions, Ozone Depletion, and Ecological Sustainability
5 affiliations
- 1Department of Applied Sciences, Bharati Vidyapeeth’s College of Engineering, New Delhi 110063, India
- 2Sri Venkateswara College, University of Delhi, Delhi 110021, India
- 3Department of Civil, Environmental and Mechanical Engineering, University of Trento, 38123 Trento, Italy
- 4Department of Information Technology, Bharati Vidyapeeth’s College of Engineering, New Delhi 110063, India
- 5INTI International University, Persiaran Perdana BBN Putra Nilai, Nilai 71800, Malaysia
Abstract
The paper has re-modeled a nonlinear differential equation to investigate the relationship among human population growth, carbon dioxide accumulation, forest biomass depletion, and ozone-depleting gases. The stability around the equilibrium point of the system is analyzed both locally and globally. The study shows the nature of the stability state characterized by the high pollution rates and loss of the forest resources. In response, control measures are designed to limit emissions and conserve forests, which are formulated and examined in the context of optimal control theory. The Pontryagin maximum principle is used to derive the necessary conditions for optimality, and sensitivity analysis is used to investigate the effect of important parameters. Numerical simulations are performed to verify the outcomes. The study proves that proper intervention strategies are necessary to create a balance between the environment and human well-being.
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BibTeX
@article{arora2026mathematical,
title = {{Mathematical Modeling and Control of Gas Emissions, Ozone Depletion, and Ecological Sustainability}},
author = {Charu Arora and Sudhakar Yadav and Saurabh Kr Agrawal and Nishi Deepa Palo and Massimo Donelli and Achin Jain},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14193578},
url = {https://www.mdpi.com/2227-7390/14/19/3578},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Mathematical Modeling and Control of Gas Emissions, Ozone Depletion, and Ecological Sustainability
AU - Charu Arora
AU - Sudhakar Yadav
AU - Saurabh Kr Agrawal
AU - Nishi Deepa Palo
AU - Massimo Donelli
AU - Achin Jain
PY - 2026
DA - 2026/10/02
JO - Mathematics
DO - 10.3390/math14193578
UR - https://www.mdpi.com/2227-7390/14/19/3578
AB - The paper has re-modeled a nonlinear differential equation to investigate the relationship among human population growth, carbon dioxide accumulation, forest biomass depletion, and ozone-depleting gases. The stability around the equilibrium point of the system is analyzed both locally and globally. The study shows the nature of the stability state characterized by the high pollution rates and loss of the forest resources. In response, control measures are designed to limit emissions and conserve forests, which are formulated and examined in the context of optimal control theory. The Pontryagin maximum principle is used to derive the necessary conditions for optimality, and sensitivity analysis is used to investigate the effect of important parameters. Numerical simulations are performed to verify the outcomes. The study proves that proper intervention strategies are necessary to create a balance between the environment and human well-being.
SN - 2227-7390
ER -