MODELING THE INFLUENCE OF HUMAN POPULATION AND HUMAN POPULATION AUGMENTED POLLUTION ON RAINFALL

Abstract

Worldwide, human population is increasing continuously and this has magnified the level of pollutants in the environment. Pollutants affect the human population as well as the environmental ecology including rainfall. Here, we formulate a mathematical model comprising ordinary differential equations to see the effect of human population and pollution caused by human population on the dynamics of rainfall. In the modeling process, it is assumed that the augmentation in the density of human population increases the concentration of pollutants; however, decreases the rate of formation of cloud droplets. It is also assumed that pollutants have negative impact on human population and affect the precipitation. The feasibility of all equilibrium and their stability properties are discussed. Further, to capture the effect of environmental randomness, the proposed model is also analyzed by incorporating white noise terms. For the proposed stochastic model, we have established the existence and uniqueness of global positive solution. It is also shown that system possesses a unique stationary distribution with some restrictions. The model analysis reveals that rainfall may decrease or increase due to the anthropogenic emission of pollutants in the atmospheric environment. Finally, for the validation of analytical findings, numerical simulations are presented.