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\begin{document}

\title{A theoretical description of polylactic acid biodegradation in
composting processes through mathematical modeling}



\author[1]{Yvan Baldera-Moreno}%
\author[1]{Alejandro Rojas}%
\author[1]{Rodrigo Andler}%
\affil[1]{Universidad Catolica del Maule}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\begin{abstract}
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.%
\end{abstract}%



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