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

Petri nets are a promising modeling framework for epidemiology, including the spread of disease across populations or within an individual. In particular, the Susceptible-Infectious-Recovered (SIR) compartment model is foundational for population epidemiological modeling and has been implemented in several prior Petri net studies. However, the SIR model is generally stated as a system of ordinary differential equations (ODEs) with continuous time and variables, while Petri nets are discrete event simulations. To our knowledge, no prior study has investigated the numerical equivalence of Petri net SIR models to the classical ODE formulation. We introduce crucial numerical techniques for implementing SIR models in the GPenSim package for Petri net simulations. We show that these techniques are critical for Petri net SIR models and show a relative root mean squared error of less than 1% compared to ODE simulations for biologically relevant parameter ranges. We conclude that Petri nets provide a valid framework for modeling SIR-type dynamics using biologically relevant parameter values, provided that the other PN structures we outline are also implemented.