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3rd April

Please find a model and analysis of the current covid 19 pandemic.

The model will evolve over time as we obtain more data, and will be continually revised to match the data. Predictions are likely to change quite dramatically as the data comes in, and also as the government policies change.

NOTE: This model has been created with a fair bit of guess work, and research and with no input from others, but I would like everyone to get together and help co-create a model that can save lives and jobs. Please add your comments.

THANKS!

So to build the model, we need some assumptions:

1. The Corona virus is highly contagious
2. The virus can affect someone without them showing symptoms.
3. When a person is affected, they are a carrier, and can spread it to others.
4. Some develop symptoms, some don't.
5. Testing is not an exact science.
6. The body takes time to create an immune response.
7. Testing before this time will be ineffective.
- you might be infected, but the test says no
8. After the body has successfully dealt with the virus, there's a time lag for it to produce antibodies.
- you might be cured, but the test says you're infected.
9. Re-infection is very rare.
10. Serious cases require hospitalisation.
11. Almost all testing occurs of hospitalised patients and is therefore a big underestimation of the true infected population.
11. Once in hospital, fatality rates are high.
12. Fatality rates increase significantly with age.
13. Average time to Fatality for serious patients is short.
14. Time to recover for infected patients can be weeks.
15. We will assume that almost all fatalities occur in hospital.
16. We assume that once a patient reaches hospital, they no longer infect others.

For this analysis, these are the assumptions we make:

Now we need some actual data to build the model.

We get it from the official Government site:
Govt Corona data

Plot Virulence

We then plot the virulence, and compare the daily growth rates of the cases and of the fatalities. The more virulent it is, the higher the growth rate. We use a 7 day rolling average to smooth out the bumps, and try to provide something that we can use visually to get a feel for how the pandemic is developing:

Polulation distribution

Next, we need to know what the UK population distribution is... We use this:

Fatality by Age

So now, we have the actual case and fatality data and the population density.

We now bring in the fatality by age group, and make an assumption on impact of age in the likelihood of having the virus passed on. We assume that the older you are, the more likely you are to contract the virus.

MODEL

Now we need to come up with a model of how quickly the virus spreads, and a formula for the spread.

We use the actual fatality data as an input to this model because it's the most reliable number.

Here's the formula we use for the infection rate per person per day:

infection rate per person per day
=EXP(Infection_co_efficient)*Infectable Population/Total population*(1-The Effectiveness of social isolation)

We calibrate the virulence of the actual fatality data vs the model, and come up with Infection_co_efficient= -1.15071451817298

In plane English, this says:
- Each infected, unquarantined person can infect 0.32 people per day provided there's no social isolation.
- If everyone is 100% isolated, no infections can occur
- If Everyone is immune, no infections can occur

We see that approximately every 10 days, the fatalities increase by a factor of 7 at the start of an outbreak, so we calibrate the model to this.

Government Influence

Now, a government has control over 2 main factors in this equation.

1. The effectiveness of the social isolation.

- these range from:
- washing hands
- staying 2m away from others
- avoiding large gatherings
- banning public transport
- enforcing that non-key workers stay home
- enforcing that everyone stay home

We can only guess the effectiveness of these isolation strategies, and we can enter what we think the effectiveness is in the model.... For example, we assume that lockdown of everyone apart from key workers is about 70% effective.

2. The length of time the measures are enforced for.
- The safest from a virus perspective is for everyone to stay in their rooms until no-one in the world has the virus any more, but clearly then we'd all starve, so the government needs to make a tradeoff.

We input some assumptions on the likely social distancing rules, and then map the infection rates of the population.

How does the model perform?

We can now plot the model predictions vs the actual data, and see where we're heading:

Fatality by Age

We can also look at how the pandemic will affect the various age groups:

Key Points

Concluding... these are the main bullet points:

Caveat:
- This model is based on a number of assumptions. The reality is most probably completely different. It is presented as a basis for discussion, not as a finished product. The author has absolutely no virology experience.

Model Uses

If the model were correct, then it could be used to solve for whatever your objective is.

That could be:

- Minimum of Max deaths per day
- Minimum period of Isolation to allow deaths under X
- Minimum of Max patients arriving in hospital per day
- Minimum total deaths
- Minimum End date of pandemic

Some observations:

1. Most people have mild or no symptoms (We only see the tip of the iceberg in hospital)
2. We don’t want the isolation to be too effective
- A 100% effective lockdown simply delays the deaths, it doesn’t reduce them materially
3. The overall death rate is much lower than is being touted by media (creating unnecessary panic)
- we can argue it’s as low as 0.14% of the population
4. Without social isolation, the peak would be towards the end of April, and fatalities per day would be around 6,000
5. We don’t know anything about is how effective the NHS can be in saving lives if they are not overwhelmed… Happy to model that in...

Can you help?

WhatsApp me: 00447846607383

Many thanks
Nick

I WILL BE ADDING TO THIS BLOG BASED ON FEEDBACK
... the next things to add will be what policy decisions to make to optimise based on the various criteria.

Volunteered modeling help here:
https://epcced.github.io/ramp/

4th April

Sitting looking at Trump claiming that it will all be over in a few weeks for the US based on decreasing fatality rate in Spain / Italy.

It could be argued that the decreasing fatality rate is solely due to the dramatic social isolation tactics that have been implemented, and that once the politicians declare triumph and reduce the social isolation, the cases will accelerate again.

We see this to be a very bumpy chart... It will bounce all over the place due to the various lags and factors in play.

The key points are:
- when the daily numbers go down, it doesn't mean success at this stage.
- Social Isolation isn't decreasing the total fatalities significantly, it just postpones them.
- The solution is an immune population

5th April - SWEDEN

The Swedes have gone out on a limb, and decided to keep the economy going and not limit social interaction too much. This may be because they are a few weeks behind the rest of the world and the pandemic isn't an issue yet. It could also be because the population of Sweden is very spread out and doesn't interact much.

However, it raises an interesting question:
- Does social isolation work?
- Surely the only solution is either an immune population OR a vaccine. The vaccine appears a way away.

Let's look at what happens if there is no social isolation at all.

With No social isolation:

Observation:

- with no social distancing, the pandemic is over far quicker, the total fatalities are not hugely different, and there's almost no economic impact
- We must consider whether Sweden has gotten this right. Is the cost of lockdown greater than the benefit?
- Most countries don't think it works for them.
- There is no attempt to model in the effectiveness of the health service in saving lives, and also with this level of hospitalisations the health service would only be able to cope with a fraction of the ill patients. The result would be catastrophic for anyone becoming ill at the height of the pandemic
- The capacity of the health service is not fixed, and buying time by locking down can allow the health service to increase capacity.

6th April - Schools reopen?

The latest UK data show a reduction in daily cases. This is expected due to the closing of schools on 22 March.

Recalibrating the model, we can solve for the effectiveness of the school closures. It's estimated that this is about 64% effective at preventing the spread.

From here we expect between 400 and 800 daily fatalities between now and end May.

Policy makers might be tempted to reopen the schools at the end of summer half term... If they do so, we'd expect a 2nd peak in early July.

7th April - Data quality

The bane of any modeller's life is data quality. Models are built with the assumptions that the data is collected consistently, in a timely manner and is correct.

What we see here is that there appears to be a lag receiving the data after the weekend.

What this means is that the model needs to adjust for this in order to have improved predictive powers. With bumpy data, more data points need to be collected and larger data sets need to be fed into the model.

Yesterday's conclusion around the effectiveness of the social distancing now needs a review. Based on today's jump in fatalities, the effectiveness of social distancing appears less.

Our thoughts are with Boris wishing him a speedy and full recovery.

8th April - It's All Over Date

Yesterday's realisation that the data isn't measured consistently turns out to be good news for those hoping that the pandemic will be over quickly. To match the new data, we reduce the effectiveness of the social distancing to 50%, and look at the new projections.

If we define "It's all over" as <1000 new cases per day, we come up with 3rd June.
- This will change based on government response to social isolation
- If the trajectory is similar to what we see in the graph below, expect possibility of increased social isolation.... Things like banning exercise outside.

Please note.. all these conclusions are based on guess work and an effort to model data which may or may not be correct.

10th April - STAY AT HOME, STAY AT HOME, STAY AT HOME

Why is it so important to stay at home right now?
Simply put: If we stop the social distancing now, many more people will die

Maintain Social distancing

If we all go out now

so STAY AT HOME!

11th April - Opening up scenarios

Assuming the model is correct (which it almost certainly isn't), we can take a look at some scenarios.

Option 1 - Maintain status quo for a week, then gradually loosen the lockdown week by week up to 16th May.

- here we see a second peak at the peak... no-one would want that, so if the model is right, we are unlikely to see a loosening of lockdown in the next week.

Option 2- Start loosening 26 April, and steadily loosen each week by 10% from then until 23 May.

- here, we see second peaks after the first peak, but not surpassing the previous peak

Option 3 - Full lockdown until 1 may, then completely open.

- here we see a large second peak, but not as big as the first peak. This is unlikely to happen as the government probably won't want to take the political risk
- this option does have the advantage that the second peak is not quite as big as the first

Option 4 - Likely scenario - Opening up 8th May

- the likely scenario is that the loosening will occur when the peak has been confirmed... Peak around 3rd May, and a few days to confirm it. It could be argued that the country completely reopens at this point on the basis that any further recurring peaks will not be anywhere near the peak that has passed. What actually happens might be a gradual reopening.

.... what actually happens will be a function of what the next 2 weeks data looks like.

13th April - Brand new model - We are at the peak

We have made some major changes to the model.

1. The shape of the fatalities curve was not matching the model, and it appeared as if the peak were being reached too early. We originally had 21st Jan as the start date for the pandemic. We dramatically change this to 4th Jan.

2. We then take logs of the daily fatalities and recalibrate the model to minimise the sum of the differences of the significant early data (where there's no impact from social distancing.)

3. We back out the Initial infection rate per person per day to be 0.33... Assuming people remain infectious on average for 8 days, we see that each person infects 2.63 people.

4. We note various reports saying that fatalities are sometimes being reported in a daily number that come from weeks before. We assume this doesn't impact the modelling.

5. We note that the model predicted vastly more hospitalisations than were being reported by the government. We change the model to reflect the official data from the 7th April.

6. We can work out a key piece of data by looking at the shape of the daily growths chart. To smooth the data, we plot the 7 day moving average of the growth in cases and fatalities. We see Exactly the same shape of chart, which allows us to conclude that it takes around 12 days from case being identified to fatality. We find that 10 days in the model matches the data, so we use that.

Putting all this together, the new model says we are at or within days from the peak NOW.

Notes:
1. Although we now appear to be at the peak of the daily infections (assuming we maintain the social distancing rules), we are not half way through the pandemic. The fatalities rise very quickly, and fall slower.

2. The Daily data coming from the government is still bumpy, so one needs more of it to make solid conclusions.

Here are some charts and data:

Key points that everyone wants to know:

Here we see the revised daily fatalities chart... It appears we are at the peak.

Here's the impact on the population over the next few months:

Past and present stats and key numbers:

17th April - Not happy with my model? Make your own with this template

DOWNLOAD MODEL

22nd April - Expect more high fatalities

2 Changes to the model

1. Included ability to add fatalities that are not included in the official figures... eg. care homes.
2. Model changed to fit latest data

Today's note: there was a dramatic fall in fatalities in the last few days. This is very out of line with the predictions so expect a few large numbers to come in in the following few days.

24th April - END UK LOCKDOWN NOW!

The increase in fatalities didn't happen which is incredibly good news. It suggests that we can END THE LOCKDOWN TODAY with no second peak.

28th April - Sweden and Italy

One thing that seems a surprise to everyone is why the various countries differ so much.
I believe a lot of it is to do with the distribution of the population. Evidence suggests that the virus is possibly 150 times more dangerous for the 80+ than is it for the 0-20, so this can have a massive effect on the overall fatality numbers, and arguably on the transmission.

Attempting to model Sweden who went alone, we see the following:

Notes:
1. The Daily fatalities in Sweden are all over the place... huge one day, then tiny the next.
2. There is evidence of social distancing effectiveness of around 24%
3. On the face of it there doesn't seem to be evidence that Sweden is underreporting the fatalities, but this might not be correct.
4. Peak for Sweden around 5th May, and no second peak... Total fatalities around 8,000.

Lets have a look at Italy

Locked down:

With no lockdown!!!

Notes:
1. It appears that Italy was facing a catastrophic eruption of cases that would have peaked at around 4,500 per day.
2. Italy's lockdown appears to have been highly effective at around 50%.
3. If releasing lockdown measures today, Italy would face a second peak, although it would not be as big as the first.

If you want to know what flattening the curve looks like, Italy is a great example:

29th April - No second peak in UK

Anyone who has connections to the government, please can they ask for this graph, because as far as I can see, there's no second peak... Only a blip, and the harm from lockdown is way more damaging.

Models need to continually adjust to the actual data. When they don't things like the last financial crisis happen. The smartest people in the world modelled credit derivatives, and they got it wrong.

Modeller A at bank A came up with a valuation of 1 million in Bank A's favour.
Modeller B at bank B came up with a valuation of 1 million in Bank B's favour.

They traded, both "made" lots of money, and got paid big bonues... only the models were wrong.

How do I know this? Well, I sat next to them on the trading floor..

5th May - Second Peak For Italy

2 updates...

1. New model - Added all countries and am busy analysing them
- please see attached. (CoronaAnalysis 29 Apr World.xlsm)

2. Italy today has released lockdown... I hope it's wrong, but the model predicts a second peak in mid June.

23th May - Second infections, reopen schools in London, other countries, modelling, Lockdown in the UK

Second Infections: Should we worry?

One concern from various people is this:
- They are worried about getting the virus twice, and what will happen.

Suppose there's a population of 100. There's a deadly virus that kills the most vulnerable 10% (which is what this corona virus does). People are not immune, and it comes back round.

What's the best guess of how many people it will kill the second time round?

My argument would be that the best guess of fatality rate for the second time round is ZERO. Why? Because it killed all the vulnerable people in the first wave!

Secondly, epidemiologists argue that when a new deadly virus mutates, it mutates into a less deadly form as it's not in the interests of a parasite to kill it's host.

Reopen Schools in London - Risky?

Back of envelope calculation:
- London: Hospital daily cases 15 May: 24. Halving every 3.5 days
- by 1 jun, that’s 1.5 Hospital cases a day
- fatalities from those cases: 0.5
- fatalities for the under 60s: (teaching And pupil age): 0.05
- fatalities for healthy under 60s: 0.005
.... that’s for all Londoners.
- over a 5 week period, that’s 0.03 fatalities

- additional fatality risk caused by reopening schools has to be far less than the risk of travelling to and from school, and substantially less risky than at end March.

If people are isolating with vulnerable groups, they may have concerns.

Other countries - How are they faring?

There are huge differences between various countries.
- Slovenia for example now has no fatalities and has declared the pandemic over.
- Brazil looks set for an explosion
- Italy looks like it will see a second peak

Modelling

Why is modelling the virus so difficult?
- there are various types of models

1. Models where you estimate various inputs (how many people a virus infects a day, how many of those does it kill)

You then input them into someones else's model, and come up with total garbage like this which predicts 10,000,000 fatalities in the US:
https://medium.com/@tomaspueyo/coronavirus-the-hammer-and-the-dance-be93...

2. Models that give "confidence intervals" like this one:
https://covid19.healthdata.org/
- Again, garbage... All this is doing is taking today's value and using a random walk to guess where it might be in the future... Fine for predicting outcomes where's there's no government intervention, but when there is, it's just wrong. Introducing lockdowns slows the spread, and releasing them causes second peaks. "confidence intervals" are just not applicable here.

3. Models that are just plain wrong like this article:
https://www.nytimes.com/2020/04/14/opinion/covid-social-distancing.html

"The estimated number of deaths falls sharply with earlier interventions, using calculations based on a model by the Institute for Health Metrics and Evaluation. Ranges reflect uncertainty in the model’s estimates."

Lockdowns do not give you immunity, they postpone the fatalities.
- one thing they do appear to do is to reduce the level at which herd immunity causes the virus to die out thus reducing the total fatalities... but not by a huge percentage.

- Modelling relies on data. The data is often collected late, is wrong, is incomplete, sometimes missing, or is manipulated.. Really understanding the data is next to impossible so you can only make your best guess. The fatality numbers predicted can double on a tiny change in the slope of the curve so it's really tough to get accurate predictions.

The UK government was told there would be 510,000 fatalities with no action taken, but this was completely wrong, and it's time to admit this.

The Headlines in a few months will be:
- UK lockdown prevented 10,000 fatalities at a cost of £30,000,000 each
- Also, costing millions of jobs, livelihoods and 20,000 extra fatalities because people were too scared to go to hospital.
- Locking down healthy people who won't die from a Covid infection must be a mistake as it's preventing herd immunity

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