Computational Ecology and Software, 2022, 12(2): 23-37
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Impact of carbon dioxide emissions caused by human activities on atmospheric temperature: A mathematical model

Shyam Sundar1, Ashish Kumar Mishra1, Ram Naresh2, J. B. Shukla3
1Department of Mathematics, Pranveer Singh Institute of Technology, Kanpur-209305, India
2Department of Mathematics, School of Basic and Applied Sciences, Harcourt Butler Technical University, Kanpur-208002, India
3Indian Institute of Technology, Kanpur-208017, India

Received 28 December 2021;Accepted 8 February 2022;Published 1 June 2022

Various human activities have increased the concentration of carbon dioxide in the atmosphere leading to increase in average atmospheric temperature causing global warming. It threatens our environment as well as health and basic needs of human beings. Therefore, in this paper, a mathematical model is developed to study the effects of carbon dioxide emissions caused by human activities on average atmospheric temperature contributing global warming considering four dependent variables namely, the density of human population, cumulative density of human activities such as industries, automobiles, and power plants etc., the concentration of carbon dioxide and the average atmospheric temperature. The model is analyzed using stability theory of ordinary differential equations. Local and global stability conditions are established to study the feasibility of the model system. The growth rate of average atmospheric temperature is assumed to be proportional to the increased level of carbon dioxide concentration in the atmosphere from its equilibrium value. It is also assumed that this temperature decreases with a rate proportional to its enhanced level from its equilibrium value caused by various natural factors such as rain fall, snow fall, etc. The analysis shows that as the emission of carbon dioxide from human activities increases the average atmospheric temperature increases considerably from its equilibrium level.

Keywords mathematical model;carbon dioxide;average atmospheric temperature;stability analysis.

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