A Numerical Comparison of Petri Net and Ordinary Differential Equation SIR Component Models

Area of Science:

• Computational Biology
• Epidemiological Modeling
• Discrete Event Systems

Background:

• Petri nets offer a discrete event simulation framework for disease spread modeling.
• The Susceptible-Infectious-Recovered (SIR) model is a cornerstone of epidemiological studies, often using Ordinary Differential Equations (ODEs).
• Existing Petri net implementations of SIR models lack systematic numerical convergence analysis against ODE counterparts.

Purpose of the Study:

• To systematically investigate the numerical convergence of two distinct Petri net implementations of the SIRS compartment model against the standard ODE formulation.
• To introduce novel deterministic and stochastic Petri net models for the SIRS dynamics.
• To identify critical numerical procedures for accurate simulation outcomes.

Main Methods:

• Developed a novel deterministic Petri net implementation of the SIRS model using variable transition weights in GPenSIM.
• Created stochastic Petri net models for the SIRS model using Spike.
• Applied specific rescaling and rounding procedures to Petri net simulations.
• Compared simulation results against established ODE-based SIRS models.

Main Results:

• Achieved a relative root mean squared error of less than 1% when comparing Petri net models to ODE simulations.
• Demonstrated the critical role of rescaling and rounding in achieving numerical convergence.
• Validated both deterministic and stochastic discrete time Petri net models for SIR-type dynamics.

Conclusions:

• Petri nets, with appropriate numerical procedures, are valid tools for modeling SIR-type epidemiological dynamics.
• This work establishes a foundation for employing Petri nets in more complex, large-scale disease spread simulations.
• The findings support the integration of discrete event simulation approaches in computational epidemiology.