Mathematical modeling and analysis of emission and mitigation of methane from the integrated rice-livestock farming system

Controlling the elevated levels of methane ($\textrm{CH}_{4}$) in the atmosphere is crucial to tackling the problem of climate change. Both rice paddies and livestock farming are substantial contributors to this elevated methane. The integrated rice-livestock farming system is an agricultural practice designed to optimize the use of agricultural waste, while concurrently boosting rice and livestock productivity. Achieving the dual objectives of food security and mitigating climate change demands formulation and implementation of strategies that are aimed at managing the methane emissions from the rice-livestock farming system. This study introduces a nonlinear mathematical model of the emission and mitigation of methane in the integrated rice-livestock farming system. Through qualitative analysis, the model's dynamic behavior is thoroughly explored, identifying conditions for reduction and stabilization of atmospheric methane concentrations. Model parameters are estimated using secondary data on atmospheric methane concentration, rice yield and livestock population. A sensitivity analysis is presented to evaluate the influence of variations in crucial parameters on the system's behavior. Numerical simulations are conducted to confirm the validity of the theoretical results.