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Computational Ecology and Software, 2021, 11(2): 54-68
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Article

Stability analysis of a mathematical model for the abatement of methane: Effect of mitigation options

Ashish Kumar Mishra1, Shyam Sundar1, 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-208016, India

Received 8 January 2021;Accepted 15 February 2021;Published 1 June 2021
IAEES

Abstract
Atmospheric methane is one of the main greenhouse gases which contribute significantly to increase the burden of global warming. The production of rice paddies and livestock farming are the major sources of methane emissions in the atmosphere. The control of methane emissions using some efficient mitigation options is crucial to lower the concentration of methane in the atmosphere so that the adverse effects of global warming can be reduced to some extent. In this paper, a nonlinear mathematical model is proposed to study the effects of mitigation options on abatement of methane discharged by rice paddies and livestock populations in the atmosphere. In the modeling process, four nonlinearly interacting variables namely, the cumulative density of rice paddies, the cumulative density of livestock populations, the atmospheric concentration of methane and the cumulative density of mitigation options are considered. The cumulative density of mitigation options is assumed to be proportional to the increased level of atmospheric methane concentration from its equilibrium. The proposed nonlinear model is analyzed using the stability theory of differential equations and computer simulations. The study shows that without implementation of mitigation options, the concentration of methane in the atmosphere increases continuously with increase in the rates of its emissions by rice paddies and livestock populations. This increase in the atmospheric methane can be reduced considerably by efficient management of mitigation options. The increase in the implementation rate coefficient of various mitigation options and depletion rate coefficient due to net effectiveness of mitigation options further reduces the atmospheric methane concentration. The numerical simulation of the model confirms the analytical findings.

Keywords mathematical model;methane;rice paddies;livestock populations;mitigation options;stability analysis;numerical simulation.


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