Narrow Results

Atmospheric methane, emitted from agriculture sector such as production of rice paddies and farming of livestock populations, is one of the important factors responsible for increasing the average atmospheric temperature leading to global warming. It is, therefore, crucial to comprehend the dynamics of methane emission and its effect on global warming. In this paper, a nonlinear mathematical model is proposed and analyzed to study the increase of average atmospheric temperature (or average global warming temperature) caused by emission of methane due to various processes involved in the production of rice paddies and farming of livestock populations simultaneously. In the modeling process, six variables are considered, namely, the cumulative biomass density of rice paddies, the cumulative density of livestock populations, the cumulative density of methane formed by various processes involved in the production of rice paddies, the cumulative density of methane formed by various processes involved in the farming of livestock populations, the atmospheric concentration of methane and the average atmospheric temperature. It is assumed that both the cumulative biomass densities of rice paddies and livestock populations follow logistic models with their respective growth rates and carrying capacities. The growth rate of concentration of methane in the atmosphere is assumed to be directly proportional to the cumulative densities of various processes involved in the production of rice paddies as well as in the farming of livestock populations. This growth rate also increases with a constant rate from various natural sources such as wetlands, etc. The growth rate of average global warming temperature is assumed to be proportional to the increased level of methane 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 level caused by various natural factors such as rain fall, snowfall, etc.

The proposed model is analyzed using the stability theory of differential equations and numerical simulation. The analysis shows that as the emission of methane from various processes involved in the production of rice paddies and farming of livestock populations increase, the average global warming temperature increases considerably from its equilibrium level. The numerical simulation of the model confirms the analytical results.