David said:

> "True the page I referred you to talks about the deterministic interpretation of the Petri net SI model. Yet this occurs in the broader context of the stochastic interpretation of Petri nets - which is very much a discrete popcorn-like process - and that is what I meant to be talking about."

I generally agree with your argument as that is basically what is involved when developing a state diagram that represents probability flow -- for example when Markov modeling a system for stochastic reliability analysis, c.f. top citations https://scholar.google.com/scholar?q=Markov+modeling+for+reliability+analysis

![](https://imagizer.imageshack.com/img921/7210/swnhu1.png)

The mean value flow in this case is describing the probability of a fault-tolerant system existing in a particular state, with the Petri net providing a more concise representation than the expanded state diagram, due to the extra logic in the bar symbols. See this paper for how to create rewrite rules for transforming between Petri net and pure Markov state diagram representations:

> Pukite, P. (1995). Intelligent reliability analysis tool for fault-tolerant system design. In 10th Computing in Aerospace Conference https://www.researchgate.net/publication/269227210_Intelligent_reliability_analysis_tool_for_fault-tolerant_system_design/figures

So the point is that there is a distinction between how one understands the system under study versus the preferred vocabulary used by the practitioners. I certainly wouldn't have a problem calling these stochastic models, but that isn't the standard practice in epidemiology where it defines a larger spread in the model's parameterization via noise or variability.

I am not sure where this started but since you mentioned the mass-action law of chemistry, consider that a typical reaction is so well mixed and uniform that the fluctuations are not considered that important compared to the mean-value of the the reagent constituents. Consider also that in solid-state electronics where the law of mass action for electrons and holes is \\(n p = n_i ^2\\). For modeling semiconductors, the stochastic variability is not typically required unless one is interested in modeling shot noise or other carrier fluctuations. Another situation where an extra level of stochastic variability would be applied, is in the analysis of amorphous materials where for example the photovoltaic characteristics show fat tails indicating that the material has a significant spread in electrical properties. I have written about this here:

https://agupubs.onlinelibrary.wiley.com/doi/10.1002/9781119434351.ch18

This discussion is in the weeds but important when placed in context. For a reliability analyst, the stochastic part is *everything* but for a chemist or semiconductor designer, it's a secondary aspect of their models. For epidemiology, both the mean value determinism and stochastic fluctuations are apparently important.

> "True the page I referred you to talks about the deterministic interpretation of the Petri net SI model. Yet this occurs in the broader context of the stochastic interpretation of Petri nets - which is very much a discrete popcorn-like process - and that is what I meant to be talking about."

I generally agree with your argument as that is basically what is involved when developing a state diagram that represents probability flow -- for example when Markov modeling a system for stochastic reliability analysis, c.f. top citations https://scholar.google.com/scholar?q=Markov+modeling+for+reliability+analysis

![](https://imagizer.imageshack.com/img921/7210/swnhu1.png)

The mean value flow in this case is describing the probability of a fault-tolerant system existing in a particular state, with the Petri net providing a more concise representation than the expanded state diagram, due to the extra logic in the bar symbols. See this paper for how to create rewrite rules for transforming between Petri net and pure Markov state diagram representations:

> Pukite, P. (1995). Intelligent reliability analysis tool for fault-tolerant system design. In 10th Computing in Aerospace Conference https://www.researchgate.net/publication/269227210_Intelligent_reliability_analysis_tool_for_fault-tolerant_system_design/figures

So the point is that there is a distinction between how one understands the system under study versus the preferred vocabulary used by the practitioners. I certainly wouldn't have a problem calling these stochastic models, but that isn't the standard practice in epidemiology where it defines a larger spread in the model's parameterization via noise or variability.

I am not sure where this started but since you mentioned the mass-action law of chemistry, consider that a typical reaction is so well mixed and uniform that the fluctuations are not considered that important compared to the mean-value of the the reagent constituents. Consider also that in solid-state electronics where the law of mass action for electrons and holes is \\(n p = n_i ^2\\). For modeling semiconductors, the stochastic variability is not typically required unless one is interested in modeling shot noise or other carrier fluctuations. Another situation where an extra level of stochastic variability would be applied, is in the analysis of amorphous materials where for example the photovoltaic characteristics show fat tails indicating that the material has a significant spread in electrical properties. I have written about this here:

https://agupubs.onlinelibrary.wiley.com/doi/10.1002/9781119434351.ch18

This discussion is in the weeds but important when placed in context. For a reliability analyst, the stochastic part is *everything* but for a chemist or semiconductor designer, it's a secondary aspect of their models. For epidemiology, both the mean value determinism and stochastic fluctuations are apparently important.