A Mathematical Model of Solid Waste Accumulation and Treatment with a Varying Human Population Size

Abstract

Solid waste management has continued to be an increasing challenge worldwide and the situation has become worse in urban areas of developing countries. The rapid urban population growth, mainly due to high immigration and birth rates, has led to large amounts of solid waste, making it difficult for authorities to effectively manage the accumulated waste. Existing mathematical models of solid waste accumulation consider solid waste management by an external effort and do not address the contribution of the population in the management process. In this study, a mathematical model of solid waste accumulation is developed and analysed incorporating parameters for human immigration and solid waste recycling by particular population age groups. The solid waste is considered to be of two categories: biodegradable and non-biodegradable. Existence of equilibrium points is established and their stability analysed. Numerical simulations are done using MATLAB and Maple. Results show that solid waste increases with increasing human population and thus a solid waste free environment cannot be achieved. Sensitivity analysis suggests that improving the biodegradability of solid waste coupled with aiding solid waste decay and recycling reduces the final size of solid waste.