• The UK urgently needs help from modellers. You must be willing to work on specified tasks and meet deadlines. Previous experience in epidemic modelling is not required.

• MIT is having a “Beat the Pandemic” hackathon online April 3-5. You can help them develop solutions that address the most pressing technical, social, and financial issues caused by the COVID-19 outbreak:

• The Real Time Epidemic datathon, which started March 30, is collective open source project for developing real-time and large-scale epidemic forecasting models:

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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?

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.

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.

What I just described just involves composition of deterministic networks. But to what is to extent is stochasticity fundamental to the evolution of a pandemic. E.g. a super-spreader went to a funeral and started a huge wave of disease in one region. To that extent, perhaps it makes sense to retain a stochastic Petri net framework. This could also on a regional basis, and the local networks composed into a global network. Or one could imagine hybrid models that use deterministic nets for the well mixed populations, but have stochastic regions as well. Certain parts of the network may be more critical and sensitive, and may deserve to be modeled at a more fine-grained, stochastic level. I’m thinking of individuals who have many connections. Whether or not a key politician practices social distancing could have a big ripple effect, due to the large number of social connections – and that a stochastic, individual consideration.

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.

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

A general underlying question here is to what extent stochastic, individual differences will actually “wash out” in the evolution of a pandemic – or whether there may still be large variances in overall development due to chance factors. To the extent that a deterministic compartmental model actually produces good predictions – then that argues that the stochastic factors do wash out.

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.

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.

Thanks for the links, John. I’ll make myself known to the Royal Society one.

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.

You can use Markdown or HTML in your comments. You can also use LaTeX, like this: $latex E = m c^2 $. The word 'latex' comes right after the first dollar sign, with a space after it. Cancel reply

You need the word 'latex' right after the first dollar sign, and it needs a space after it. Double dollar signs don't work, and other limitations apply, some described here. You can't preview comments here, but I'm happy to fix errors.

Good explanation of the course of infection

U.S. Postal Workers Quarantined

Eat more rhubarb?

Enhanced isolation of SARS-CoV-2 by TMPRSS2-expressing cells

Explanation of estimated vs. measured as opposed to actual death-rates

Italy: they 3D-printed ventilator parts they could not get. Manufacturer sues them.

Typhoid Mary – Asymptomatic Carriers

The Andromeda Strain – BSL-4 gasket-eating microbes Plastic-eating microbes

8 Amazon Warehouses Test Positive For Coronavirus

Coronavirus Was Not Bioengineered

Does using ACE-inhibitors or ARBs increase your Coronavirus risk?

Antimicrobials

DIY Face masks (use hot glue?)

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?

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.

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

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.

What I just described just involves composition of deterministic networks. But to what is to extent is stochasticity fundamental to the evolution of a pandemic. E.g. a super-spreader went to a funeral and started a huge wave of disease in one region. To that extent, perhaps it makes sense to retain a stochastic Petri net framework. This could also on a regional basis, and the local networks composed into a global network. Or one could imagine hybrid models that use deterministic nets for the well mixed populations, but have stochastic regions as well. Certain parts of the network may be more critical and sensitive, and may deserve to be modeled at a more fine-grained, stochastic level. I’m thinking of individuals who have many connections. Whether or not a key politician practices social distancing could have a big ripple effect, due to the large number of social connections – and that a stochastic, individual consideration.

David wrote:

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.

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?

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

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!

A general underlying question here is to what extent stochastic, individual differences will actually “wash out” in the evolution of a pandemic – or whether there may still be large variances in overall development due to chance factors. To the extent that a deterministic compartmental model actually produces good predictions – then that argues that the stochastic factors do wash out.

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.

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.

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

Thanks for the links, John. I’ll make myself known to the Royal Society one.

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