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Cuchulainn
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Re: Models for Covid-19

March 23rd, 2020, 4:46 pm

Perhaps use SARS (with caution) as a similar case and make adjustments?

Also able to produce individual models using the cruise ships, China as longest duration study and includes a tight lockdown, and Washington state as a case where it enters into a frail, elderly population in institutional setting almost immediately upon arrival (traveller).
I think the first two can be modelled by MSEIR (no births/death on cruise ship, so SIR?).
For Washington, need to model by the demographic model (age variable)?
 
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Trickster
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Joined: August 28th, 2008, 4:59 pm

Re: Models for Covid-19

March 23rd, 2020, 4:52 pm

Perhaps use SARS (with caution) as a similar case and make adjustments?

Also able to produce individual models using the cruise ships, China as longest duration study and includes a tight lockdown, and Washington state as a case where it enters into a frail, elderly population in institutional setting almost immediately upon arrival (traveller).
I think the first two can be modelled by MSEIR (no births/death on cruise ship, so SIR?).
For Washington, need to model by the demographic model (age variable)?
For Washington , cases by county, deaths by age, other data - just keep scrolling down.

Note that King Country, with highest cases at 1,040, is where the nursing facility (Lifecare Center of Kirkland is).

On that DOH grid, you can click through to each county's reports on individual county websites and get further details on the cases and ages etc.
Time consuming, but useful.

https://www.doh.wa.gov/Emergencies/Coronavirus

See e.g. Case updates at the end of this King County page: https://www.kingcounty.gov/depts/health ... covid.aspx

If you do find this to be valuable, let me know and I can gather data today.  Excel spreadsheet OK?  ; )

If so, I would do: WA, CA, FL, NY, at least to start.

WA - as stated - hit elderly first
CA - they are not listening to government recommendations - flocking to beaches, gathering outside, etc - 
FL - also high level of elderly population may be part of it - and beaches (and students on spring break?)
NY - this is maybe the best test case of dense area, diverse age groups and health care system that is going to get hammered badly

**

For international comparisons:

https://www.worldometers.info/coronavir ... try/italy/
https://www.worldometers.info/coronavir ... try/spain/
https://www.worldometers.info/coronavir ... y/germany/
https://www.worldometers.info/coronavir ... ry/france/
...

https://www.worldometers.info/coronavirus/country/uk/
https://www.worldometers.info/coronavir ... therlands/

Choose others as you see fit here:

https://www.worldometers.info/coronavirus/#countries

This provides good augmentation to info on the Johns Hopkins site. Not sure how good the sources are for the worldometers across then board, but can cross check against more official sites and other research.
Last edited by Trickster on March 23rd, 2020, 6:03 pm, edited 6 times in total.
 
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Cuchulainn
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Re: Models for Covid-19

March 23rd, 2020, 4:54 pm

Is that the model?
Essentially, yes. Corona is less verbose. I'll write it up soon. But I am using MSEIR from Hethcore, SIAM Review 2000.
We have 4 dependent variables [$]{m, e, i, r}[$]  [$] (s = 1 - m - e - r )[$]
 4 is a nice number.

So, essentially we are benchmarking the Imperial model.
 
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Cuchulainn
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Re: Models for Covid-19

March 23rd, 2020, 5:00 pm

OK then, I am now setting up the MSEIR ODE model in C++ as here, I hope to get back in a few days. Since I am not a epidemologist, I will need your support to tell  what the ODE parameters are and their values (e.g. for chickenpox, the infectious period [$]1/\gamma[$] is 6 months, etc.) 
From the How should we threading OT - a paper I posted last week - noticed you have mentioned Cascella here earlier - he is also a coauthor on this one:

Here is a recent paper on the NCBI website:

Features, Evaluation and Treatment Coronavirus (COVID-19) Marco Cascella et al. - update March 8 2020

Current view (at least here) is that Ris 2.2 - which is in the range cited elsewhere over the past few weeks - 2.0 - 2.5 from what I have seen.

"Based on data from the first cases in Wuhan and investigations conducted by the China CDC and local CDCs, the incubation time could be generally within 3 to 7 days and up to 2 weeks as the longest time from infection to symptoms was 12.5 days (95% CI, 9.2 to 18).[5] This data also showed that this novel epidemic doubled about every seven days, whereas the basic reproduction number (R0 - R naught) is 2.2. In other words, on average, each patient transmits the infection to an additional 2.2 individuals. Of note, estimations of the R0 of the SARS-CoV epidemic in 2002-2003 were approximately 3.[6] "

I have also read papers that stated it could continue to be contagious even after the person has "recovered" - still showing some positives about two weeks later. Clearly a problem if so, with the recovered folks getting back to their normal lives. 


Is that part of the 1-2 punch?

Even so, these self quarantines and shut downs should help if they can last 2 weeks or "ideally" a month, perhaps.


/end quote

NY at 16,916 now, change is +44% from Saturday

Italy at 46,638, change is +9% from Saturday
Yes, Casella uses SIR with a bit of  discussion on control (not clear). I would have more fiducia in Lyapunov theory (only a hunch).
https://arxiv.org/abs/1812.10676
Last edited by Cuchulainn on March 23rd, 2020, 5:06 pm, edited 1 time in total.
 
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Paul
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Re: Models for Covid-19

March 23rd, 2020, 5:04 pm

Is that the model?
Essentially, yes. Corona is less verbose. I'll write it up soon. But I am using MSEIR from Hethcore, SIAM Review 2000.
We have 4 dependent variables [$]{m, e, i, r}[$]  [$] (s = 1 - m - e - r )[$]
 4 is a nice number.

So, essentially we are benchmarking the Imperial model.
Why pick that model? There are many models in this field! Either use the one they are using, or the best or the worst, for checking and comparison!
 
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Cuchulainn
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Re: Models for Covid-19

March 23rd, 2020, 5:09 pm

I have to start somewhere. I can always extend/scope it.
Besides, it looks close to (or is) the IC model.

Please feel free to suggest alternatives. I'll need feedback for sure. Once MEIR is in place, it is then possible to compare it with reduced models like SEIR, SIR, SIRS etc.(I suppose..)
Last edited by Cuchulainn on March 23rd, 2020, 5:19 pm, edited 2 times in total.
 
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Herd
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Re: Models for Covid-19

March 23rd, 2020, 7:47 pm

What is the list of inputs?
 
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Paul
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Re: Models for Covid-19

March 23rd, 2020, 7:52 pm

Every applied mathematician, numerical analyst and programmer is about to jump on Ferguson's neck!
 
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Cuchulainn
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Re: Models for Covid-19

March 23rd, 2020, 8:02 pm

What is the list of inputs?
I will post them in the next few days.
 
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Cuchulainn
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Re: Models for Covid-19

March 23rd, 2020, 8:05 pm

Every applied mathematician, numerical analyst and programmer is about to jump on Ferguson's neck!
It's not personal. It feels more like an episode of Columbo.
It beats prediction using an S curve.

Should we wait on the physicists?

Seriously, a model that has hit the headlines and no on knows how it works! It must have been one helluva sales pitch.
Last edited by Cuchulainn on March 23rd, 2020, 8:28 pm, edited 4 times in total.
 
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Paul
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Re: Models for Covid-19

March 23rd, 2020, 8:20 pm

All of these models gives S curves. (Some asymptote to extinction!) The question is which is the right S curve!
 
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Herd
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Re: Models for Covid-19

March 23rd, 2020, 9:15 pm

What is the list of inputs?
I will post them in the next few days.
Thank you.

It seems there is massive uncertainty on some of them. Mortality rate is super low in Germany, people with symptoms staying at home are not counted, how many people have it with no symptoms....?
 
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Herd
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Re: Models for Covid-19

March 23rd, 2020, 9:24 pm

Every applied mathematician, numerical analyst and programmer is about to jump on Ferguson's neck!
Haha!
My understanding is that his simulations were important in these social distancing decisions. But it seems strange that such decisions would be based on simulations of one single team?
 
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Paul
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Re: Models for Covid-19

March 23rd, 2020, 9:38 pm

Yes, worrying.

I am hoping that Germany is doing a good job of counting the infected. (And obviously that they are good at helping people, although I wish they’d tell us how!)

Not sure that “Doing what Italy is doing is the best approach”!
 
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Cuchulainn
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Re: Models for Covid-19

March 23rd, 2020, 9:53 pm

All of these models gives S curves. (Some asymptote to extinction!) The question is which is the right S curve!
That's what I want to show. 

BTW do you want to compare the corresponding dependent variables [$]m,s,e,i,r[$] of models A and B or just within a single model? Please clarify.
Some curves will go up to a maximum before they taper off, e.g. [$]i(t)[$].