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Petri nets at Azimuth, in the new context

edited May 17 in Drafts

I suggest we revive this classical Azimuth topic at the Forum -- Petri nets / reaction networks -- in light of the present day context. On the theoretical side, things have changed due to advances in the application of category theory to Petri nets. And in practice they have changed due to the pandemic, which brings matters of epidemiological modeling to a higher level of prominence on the social radar. Compartmental models are of signal importance to this subject. And the mathematics of Petri nets provides the stochastic and deterministic foundations for these models. This is math that matters for the social planet -- Azimuth math.

The subject of Petri nets is rich and expansive.

Comments

  • 1.

    I recently started on this fishing expedition, with a couple of comments to this post by John on the blog:

    Comment 1:

    Modeling each country separately leaves holes in the overall model for a pandemic. E.g. if the curve goes down, travel restrictions are lifted, and then it goes back up due to what’s happening in other countries. Compartmental models use ODEs and assume a well-mixed population. What about a multi-level approach, where each country or well-mixed region has a compartmental model with its own parameters. Then there could be transitions between the compartments in different countries, reflecting flows due to travel. This looks like a potential application of composition of open networks. Perhaps a good composition rule could produce an aggregated, abstracted compartmental model for the whole globe. Or help us in other ways to understand the dynamics of the whole. What do you think?

    Comment Source:I recently started on this fishing expedition, with a couple of comments to this post by John on the blog: * [How scientists can help fight Covid-19](https://johncarlosbaez.wordpress.com/2020/03/31/how-scientists-can-help-fight-covid-19/), Azimuth blog, March 31. Comment 1: > Modeling each country separately leaves holes in the overall model for a pandemic. E.g. if the curve goes down, travel restrictions are lifted, and then it goes back up due to what’s happening in other countries. Compartmental models use ODEs and assume a well-mixed population. What about a multi-level approach, where each country or well-mixed region has a compartmental model with its own parameters. Then there could be transitions between the compartments in different countries, reflecting flows due to travel. This looks like a potential application of composition of open networks. Perhaps a good composition rule could produce an aggregated, abstracted compartmental model for the whole globe. Or help us in other ways to understand the dynamics of the whole. What do you think?
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