Nice talk, thanks! And I see there’s followup on Zulip…

]]>My “stochastic mechanics” is pretty different, at least in intent, from Ed Nelson’s “stochastic quantum mechanics”. It’s just my name for Markov processes, viewed as analogous to quantum mechanics, but featuring probabilities instead of amplitudes. I needed to complete the analogy

quantum mechanics:amplitudes::

????????? mechanics: probabilities.

By the way, Nelson and I had the same thesis advisor!

]]>In epidemiology ‘compartmental models’ refers to things like the SIR model where the compartments are Susceptible, Infected, Removed. Epidemiologists do use well-connected groups of organisms, with fewer connections between the groups, but they are called hosts or demes. In the foot-and-mouth outbreak, farms were used as demes; in the Ebola outbreak chiefdoms were used.

]]>Just for the record, meant to say: Sure, but that analysis is based on some assumptions about “random collisions” within a homogeneous population…

]]>“and one given by the master equation, which describes stochastic dynamics”

Is this also the stochastic quantum mechanics described by Edward Nelson?

https://en.wikipedia.org/wiki/Stochastic_quantum_mechanics

also describing the Wiener process and using Ito calculus?

]]>Sure, but that analysis is based on some assumptions about “random collisions” within a heterogeneous population. In actuality we could be dealing with a connectivity graph that is far from uniform, possibly with smaller “hub” or “command” zones in which local stochastic effects could play out to produce large variances on a global scale. For a schematic example, suppose there were four countries, each modeled with its own parameters based on local policies and behavior. And that there is a world council consisting of one representative from each country, and a coordinator. The council meets periodically, with the coordinator at the center of a circle. That part of the graph is a critical hub zone consisting of four nodes. Starting from a state where only some of the countries have infected individuals, this is a model where the representatives may become super-spreaders on their return home from meetings. The council consists of a critical hub of 5 nodes, with an even more critical central node. Here local stochastic effects within the hub, such as the personal social distancing practices of the representatives, could play out to produce large variances on the overall evolution of the pandemic.

]]>The question you raise here has been studied in mathematical chemistry. As you’d expect from ideas like the ‘law of large numbers’, a stochastic treatment becomes more important when the numbers of infected patients are small.

]]>David wrote:

What I just described just involves composition of deterministic networks.

Note that open Petri nets with rates don’t commit you to a choice of deterministic or stochastic dynamics. Open Petri nets with rates are a choice of ‘syntax’, while choosing a dynamics is a choice of ‘semantics’. (If that jargon doesn’t help you, ignore it.) That is, there should be two functors out of the category with open Petri nets with rates: one given by the rate equation, which describes deterministic dynamics, and one given by the master equation, which describes stochastic dynamics. The first functor was worked out in A compositional framework for reaction networks; the second has not been studied yet.

]]>I think this is a good idea. By the way, my online talk today will allude to this idea: composition of open compartmental models, which can be open Petri nets with rates. However, I doubt I’ll be anything to do anything really useful and new with this idea at the speed required for this pandemic.

]]>I realised a few weeks ago that my expertise in phylogenetic analysis was relevant, and have been trying to figure out if and how I could be useful. The intersection of phylogenetics and epidemiology is called phylodynamics. I started a project at researchgate. So far, there are 10 collaborators.

Goal: Investigating methods which use a combination of genetic and epidemiological data to make inferences about the way that SARS-CoV-2 spreads and evolves. This could include statistical inference based on mathematical models of evolution and/or machine learning approaches. The project is exploratory, aimed at bringing together researchers with different areas of expertise, and figuring out what the ‘real’ projects should be.

https://www.researchgate.net/project/Phylodynamic-methods-for-SARS-CoV-2

Some links of my own:

Half-hour talk on the mathematics of the Corona outbreak by Tom Britton. Only needs school maths.

For programmers. Biohackathons. ‘COVID-19 Biohackathon April 5-11 2020’

https://github.com/virtual-biohackathons/covid-19-bh20“>

For programmers. Kaggle. ‘Help us better understand COVID-19’

https://www.kaggle.com

If you prefer to let your computer take the strain, you could be folding virtual proteins at home:

https://foldingathome.org/2020/03/15/coronavirus-what-were-doing-and-how-you-can-help-in-simple-terms