Reckell Trevor, Sterner Beckett, Jevtić Petar, Davidrajuh Reggie
School of Mathematical and Statistical Sciences, Arizona State University, 901 S. Palm Walk, Tempe, AZ 85287-1804, USA.
School of Life Sciences, Arizona State University, Tempe, USA.
ArXiv. 2024 Jul 17:arXiv:2407.10019v2.
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.
Petri网是一种很有前景的流行病学建模框架，可用于研究疾病在人群中或个体内部的传播。特别是，易感-感染-康复（SIR） compartment模型是群体流行病学建模的基础，并且已经在先前的一些Petri网研究中得到应用。然而，SIR模型通常被表述为具有连续时间和变量的常微分方程（ODE）系统，而Petri网是离散事件模拟。据我们所知，之前没有研究调查过Petri网SIR模型与经典ODE公式的数值等效性。我们在用于Petri网模拟的GPenSim软件包中引入了实现SIR模型的关键数值技术。我们表明，这些技术对Petri网SIR模型至关重要，并且在生物学相关参数范围内，与ODE模拟相比，相对均方根误差小于1%。我们得出结论，只要我们概述的其他PN结构也得到实现，Petri网就为使用生物学相关参数值对SIR型动力学进行建模提供了一个有效的框架。
