Modelling Air Pollution Dynamics and Mitigation Strategies: A Mathematical Approach

Abstract

In this paper, we explore the intricate dynamics of air pollution using a deterministic mathematical model. Our objective is to comprehensively analyse the factors that contribute to both pollution-free and endemic equilibria. The model, carefully designed, serves as a valuable tool for understanding air quality dynamics and its evolution over time. Here, we constructed a three-dimensional mathematical model, namely general air class A(t), the polluted air class P(t) and the class of clean air C(t). The key focus of our investigation is the stability analysis of equilibrium points. Our model has two equilibrium points, pollution-free and endemic equilibrium. Specifically, we examine local asymptotic stability, identifying conditions on key parameters that determine the stability of both pollution-free and endemic equilibria. This analysis provides crucial insights into the resilience or vulnerability of the system under different conditions, offering a deeper understanding of the factors influencing air pollution dynamics. Also, we obtained a basic reproduction number for our model, using the next-generation matrix method. To further support the credibility and applicability of our conclusions, we verify our theoretical results through computing simulations, bridging the gap between mathematical abstraction and real-world scenarios.