A theoretical description of polylactic acid biodegradation in composting processes through mathematical modeling

Polylactic acid (PLA) is a bio-based plastic that is biodegradable under appropriate conditions of temperature, humidity and oxygen, which are achieved in the composting process. The objective of this work is to formulate a mathematical model that predicts the biodegradation of polylactic acid in composting processes. We performed a qualitative analysis of the reduced composting mass system, which is non-linear and non-autonomous. First, the reduced model was transformed into an autonomous system, showing that their solutions are positive, bounded and non-periodic. Furthermore, it was shown that the origin is locally and globally exponentially stable, the axial equilibrium is unstable and that a degenerate transcritical bifurcation exists at the origin. Simulations of the reduced system indicated that the PLA mass is completely biodegraded when the time tends to infinity, which was shown theoretically. In addition, numerical simulations of the complete composting system were performed considering three initial values of the carbon/nitrogen ratio. It was concluded that the initial carbon/nitrogen ratio of 32.5 reached 90% of PLA biodegradation in approximately 150 days. This work provides a mathematical tool applied to the field of biotechnology of biodegradable plastics.