MODELING THE SURVIVAL OF HUMAN POPULATION IN A STRESSED ENVIRONMENT: EFFECT OF GLOBAL WARMING DUE TO TRAFFIC EMISSIONS

Abstract

The survival of human population is adversely affected by the global warming due to increasing temperature of earth surface caused by emissions of various gases (such as carbon dioxide, methane, etc.) and particulate matters from vehicles in the traffic. These gases, called greenhouse gases, present in the atmosphere above a certain threshold result to elevate the average temperature of earth surface affecting the human population. To comprehend this problem, in this paper, a nonlinear mathematical model is proposed to study the detrimental effects on human population of the increased earth surface temperature caused by traffic emissions. In the model formulation, five nonlinearly interacting variables namely; the cumulative densities of human population and vehicles in traffic, cumulative concentration of greenhouse gases and particulate matters due to traffic emissions and average global warming temperature of earth surface have been used. Using stability theory, certain inferences have been drawn regarding the local and nonlinear stability behaviour of the equilibrium points. It is shown that as the cumulative concentration of greenhouse gases emitted from vehicles in the traffic reaches beyond its threshold level, the average temperature of earth surface rises above its threshold value leading to global warming with diminishing effects on the growth of human population density. The growth of human population is further declined with increase in the cumulative concentration of particulate matters emitted from vehicles in traffic. Numerical simulations have also been performed to validate the analytical findings.