Dcm ngm primer

[dinacmistry]

No description provided.

[dinacmistry]

No where even close to done, just making it a draft right now so I can use PR tools.

[dinacmistry]

Also, there will be so many commits on this as I figure my way through how I want to write about this in a way that's hopefully clear and useful to others. I'll plan to squash as many commits as I think reasonable closer to when a draft is complete.

[dinacmistry]

This feels like a fairly comprehensive review of NGMs.

Fwiw, the formulation in the approach doc, $R_{ij} = \frac{\beta_{ij}S_i}{\gamma N}$ is not accurate though it functionally still works. If we're going to be formal about definitions, we should replace $S_i$ with $N_i$. This is because we linearize the system around that DFE, so that $S_i \approx N_i$ and then we can define the NGM. I think it's an important difference since $N_i$ is a constant, while $S_i$ isn't.

[dinacmistry]

This is helpful! There are a number of minor math formatting issues in Github as already noted.

I like the list of assumptions - can we make it more of a compact list rather than subsections?

Do you think it could be helpful to write some sort of glossary explaining the main terms used here (spectral radius, eigenvalues, eigenvectors, transition matrix, transmission matrix, DFE) and how they relate to disease models?

I think if the audience is Andy and me before this project, I could have used a more concrete example showing an example NGM itself, the way you get R0 and infection distribution (which means we need a bit about the eigenvector of the NGM) and the way you think about adding in vaccination by factoring rows by the proportion susceptible remaining. The example now is a bit confusing, since it references K&R but only in that it arrives at the NGM of beta/gamma * N_i / N. I guess the helpful thing from K&R for me was validating that we understood what exactly was the NGM, and corresponding R0 and infection distribution. Without numbers, I think the example now still could have been a bit mystifying for me a month ago.

Thanks @paigemiller! Made a few changes to address yourfeedback:

• made the conditions and limitations section into a bulleted list
• new issue for glossary since I think this is out of scope for a first draft of the primer
• new issue for explicit example with vaccination, which is probably going to be just cannibalizing what's in the approach doc

[swo]

@dinacmistry I think this is mature enough that we should just merge it?

We can revisit in #91 , to see how this will work with other docs

[dinacmistry]

@dinacmistry I think this is mature enough that we should just merge it?

We can revisit in #91 , to see how this will work with other docs

Re-requested your review - need approval for the merge. Thanks!

[dinacmistry]

Just a heads up: there were a lot of great points brought up in this PR. Some were out of scope so I made issues for them either in this repo or in the recipes repo if it required more math details/explanations. I think we should merge this now.

[paigemiller]

This looks good to me! just suggested a few small edits to improve readability

[dinacmistry]

This looks good to me! just suggested a few small edits to improve readability

Got it, will make those edits and then merge. Thanks Paige!