This insight began as a March 22nd Clone of "Italian COVID 19 outbreak control"; thanks to Gabo HN for the original insight. The following links are theirs:
Initial data from:
Italian data [link] (Mar 4)
Incubation estimation [link]
Andy Long
Northern Kentucky University
August 11th, 2020
This is an update of our "final" model from May, 2020.
I thought I'd check back, as classes begin again, to see how well our SIR did. So I'm updating the data on the Italian situation. Meanwhile, I'm thinking that an agent-based model would be better for the US situation, given the wild variation in local parameters (e.g. rates of mask-use).
It looks like our model was overly pessimistic: deaths were only about 89% of what we expected; total cases were perhaps 82% of what we expected (and the situation flattened quite a bit shortly after the 60 day mark).
What follows were the notes for the previous version.
As we prepare for our final exam, I read a story in The Guardian about Italy's struggle to return to normalcy. The final paragraphs:
During the debate in the Senate on Thursday, the opposition parties
grilled Conte. Ex-prime minister Matteo Renzi, who has called for less
restraint in the reopening, remarked, “The people in Bergamo and Brescia
who are gone, those who died of the virus, if they could speak, they’d
tell us to relaunch the country for them, in their honour.”
Renzi’s controversial statement was harshly criticised by doctors who
warned that the spread of the disease, which, as of Thursday, had
killed almost 30,000 people in the country and infected more than
205,000 [ael: my emphasis], was not over and that a misstep could take the entire country
back to mid-March coronavirus levels.
“We risk a new wave of infections and outbreaks if we’re not
careful,” said Tullio Prestileo, an infectious diseases specialist at
Palermo’s Benefratelli Hospital. “If we don’t realise this, we could
easily find ourselves back where we started. In that case, we may not
have the strength to get back up again.”
I have since updated the dataset, to include total cases from February 24th to May 2nd. I went to Harvard's Covid-19 website for Italy and and then to their daily updates, available at github. I downloaded the regional csv file for May 2nd, which had regional totals (21 regions); I grabbed the column
"totale_casi" and did some processing to get the daily totals from the
24th of February to the 2nd of May.
The cases I obtained in this way matched those used by Gabo HN.
The initial data they used started on March 3rd (that's the 0 point in this Insight).
You
can get a good fit to the data through April 9th by choosing the following (and notice
that I've short-circuited the process from the Infectious to the Dead
and Recovered). I've also added the Infectious to the Total cases.
The question is: how well did we do at modeling this epidemic through May 2nd (day 60)? And how can we change the model to do a better job of capturing the outbreak from March 3rd until May 2nd?
Incubation Rate: .025
R0: 3
First Lockdown: IfThenElse(Days() == 5, 16000000, 0)
Total Lockdown: IfThenElse(Days() >= 7, 0.7,0)
(I
didn't want to assume that the "Total Lockdown" wasn't leaky! So it
gets successively tighter, but people are sloppy, so it simply goes to 0
exponentially, rather than completely all at once.)
deathrate: .01
recoveryrate: .03
"Death flow": [deathrate]*[Infectious]
"Recovery flow": [recoveryrate]*[Infectious]
Total Reported Cases: [Dead]+[Surviving / Survived]+[Infectious]
Based on my student Sean's work, I altered the death rate to introduce the notion that doctors are getting better at saving lives:
[deathrate] = 0.02/(.0022*Days()^1.8+1)
I don't agree with this model of the death rate, but it was a start motivated by his work. Thanks Sean!:)
Resources:
* Recent news: "Since the early days of the outbreak in China, scientists have known
that SARS-CoV-2 is unusually contagious — more so than influenza or a
typical cold virus. Scientific estimates of the reproduction number —
the R0, which is the number of new infections that each infected person
generates on average — have varied among different communities and
different points but have generally been between 2 and 4. That is
significantly higher than seasonal influenza."
* https://annals.org/aim/fullarticle/2762808/incubation-period-coronavirus-disease-2019-covid-19-from-publicly-reported
* https://covid19.healthdata.org/italy
