Mathematical Model for the Cyclical Dynamics of Plastic Waste Management: A Two-state Closed Model

Abstract

The transition to circular economy has become a sustainable technique to plastic waste management. This makes recycling a key driving machinery for achieving sustainable plastic waste management. However, most of the models that predict the volume of plastic products and its waste generation do not reflect the role of the recycling rate and its correlates. The objective of this study is to develop a simple two-dimensional cyclical dynamic closed (CDC) model that reflects the plastic life cycle to predict the volume of annual plastic production and plastic waste generation. The CDC model was formulated using a time-dependent linear system of ordinary differential equations; and the solution methodology was based on the Laplace transform technique. A programme was written using excel implementation codes to compute the models’ parameters and predict the values of global annual plastic production and waste generation; while implementation codes in R were applied to predict and forecast with the models. A global data on plastic waste management was used; it was sourced from the annual reports of the Plastic Europe (the Association of Europe Plastic Manufacturers), the Plastic Europe marketing Research Group, and research publications on plastics. The results revealed that the long-run equilibrium solutions of the models are zeros, which also have a practical implication under the context of a closed model. The performances of the models were investigated via the criterion of the mean absolute percentage error (MAPE), which measures the predictive power of the models. MAPE values of approximately 13% and 18% were obtained, respectively, for the global annual plastic production and plastic waste generation models. These values indicate that on average, the model for global annual plastic production can predict with an accuracy rate of 87%; while that for the global annual plastic waste generation can predict with an 82% accuracy rate. The outperformance of the CDC model was established by comparing with the best performing solid waste model developed in 2017. The model was used to forecast from 2022 to 2050. The models have significant policy implications for waste managers and all stakeholders.