Mathematical model for the dispersion of toxicity through commuters

Abstract

In the proposed paper, we consider three types of vehicle. One is those vehicles which are used for personal purposes called private vehicles. Second is for public transportation named as public vehicles. Third one is used for other activities known as cargo vehicles. These vehicles can be either polluted or non-polluted according to their fuel category. They produce toxic air pollutants which makes environment toxic. To compare the dispersion of toxicity through these vehicles, a mathematical model is formulated. In this model, dynamical system is developed with the help of non-linear differential equations. Threshold for each vehicle category is acquired and compared. Threshold and backward bifurcation govern the stability of the model. Simulation is prepared to brace the output.