#CoViD19: A #coronavirus #modelling update

It has been a few days since the Chinese authorities changed their definition of “confirmed case” in describing the #coronavirus outbreak. In a previous post I checked whether my model needed modification, which seemed only minor. Now with a few days more of ‘new’ data, let’s see what we find.

Mortality shifts

There is a lot of discussion in the media about the mortality-rate of this corona virus. Different groups of researchers produce wildly different estimates, some say less than 1% others claim well above 15%. They can’t be both right! Very often in such cases these differences arise form the different assumptions researchers make when modelling these things. A lot of fancy mathematics sometimes obstructs the view on those assumptions.

So let me take a simplistic point of view. Suppose we are a year down the line and we know how many people were infected and how many people died. Then it is a simply matter of just dividing the latter by the former to get the fraction that describes the observed mortality-rate. In a year from now, that will be the number that everyone agrees on. So if we calculate that exactly same number now then we might be getting it wrong because it could be that in an early phase in particular many elderly or people with poor health attract and die of the infection whereas at later time the people infected are more representative of the population and more young and healthy people survive. Similarly, it will take patient time to fully develop the infection and, perhaps, die of it. So there will always be a lag between the number of infections and the number of deaths while the outbreak is still ongoing. So if we plot the number of reported infections against the number reported deaths we should slowly see the mortality-rate (the steepness of the line through the data) change towards the final outcome we will all agree on next year. Here is the graph so far.

wuhan10

The number of confirmed cases prior to the change in case-definition are increased by 28% as this reflects roughly the under-counting relative to the new definition. The number of confirmed cases after the change in case-definition is given here simply as reported. The gap in the graph separates the last report before the definition change and the first report after. As we concluded last time, the gap itself did not do much to change the mortality estimate.

But note that just before the ‘gap’ there was an increase in mortality. In the past 5 days that increase has persisted. The line drawn through the dots is a ‘best-fit’ and corresponds to a mortality rate of 2.3%, up from the 2.1% we used to see last week. So the data indeed suggest that the mortality is above 2% albeit that anything above 10% still seems a very wild guess. Currently the mortality-rate that we see seems to increase with something like 0.04% a day. Even if that were to persist, it would need to do so for almost 200 days before we get anywhere near 10%. That does not seem reasonable because it would imply people that die take a very, very long time to do so. As far as I can find the longest clinical cases that led to death took about 3 weeks. That would suggest that the mortality could not grow much further than 3%. Still bad, though.

Leaky quarantine

If we know look at how my model

Wuhan-model5

describes the data in the 3 different scenarios discussed in earlier posts here, here ,here and here then we find the following graph

wuhan12

I only needed to make one modification of the parameters estimated in this model. The parameter a which is the number of people ‘leaking’ into the quarantine population each day had to be shifted upwards by 200 to between 1600 and 2000. That is in principle bad news if it means that the quarantine is losing effectiveness. But it is also not unexpected as no quarantine can be help up indefinitely … people simply ‘don’t work that way’. The experiences aboard the various cruise-ships stuck in ports or at sea with possible or confirmed cases on-board gives further reason to doubt the sustainability of quarantine even in controlled and confined quarters such as on a ship.

Look ahead

So let me end with another look ahead: where will we be in about 50 days from now if this model were correct? The graph below shows the result of the simulation

wuhan11

In about a month from now we would be exceeding the 100,000 cases of confirmed infections and a month later it would top 150,000. Most of this is due to the leaky quarantine and testament how infectious this virus is. If those numbers come true then we would be taking about between 3,000 and 4,500 deaths.

Now some online argue this #coronavirus is no worse than #justtheflue. They couldn’t be more wrong. If a typical global seasonal flue outbreak in terms of patient numbers would be matched by the Corona virus outbreak the numbers of deaths will go into the millions. I personally hope that my model is too pessimistic and that in the next days we will see the reported data drop below the projected curves. That would be an update I would love to write … so till then!

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