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Simon Anthony: Migration of Infection

This is a guest post by Simon Anthony, a one-time theoretical physicist.


One of the complications in trying to understand the behaviour of Covid-19 is that data is, for obvious reasons, almost invariably associated with countries.  Viruses don’t necessarily respect arbitrary boundaries so it can be helpful to look at the data in a way which may be more relevant to its geographical rather than national distribution.

An obvious variable which may affect C-19’s behaviour is latitude.  While there seems to be little known with certainty about exactly how weather affects viruses (several mechanisms have been suggested; all sound plausible but none seems to have been properly investigated), flu pandemics are strongly seasonal and it’s reasonable to assess whether C-19 might also be influenced.

In an earlier post I looked at the overall mortality rate attributed to C-19 as a function of latitude and found a peak at ~50 degrees north, with the rate falling close to zero outside a range between ~30 and ~60 degrees (the latter perhaps because of the almost complete absence of human habitation that far north).

I thought it would be interesting to look at how the infection has varied with latitude over the couple of months since it began to spread.  I estimated the mortality rate for each latitude from the number of deaths for each day and the populations of countries at that latitude.  I found the latitude with the daily peak mortality rate and also the daily average latitude (weighted by mortality) from when the outbreak began to move beyond China, up to 25th April. (I averaged mortality data over a week so as to partially counter “weekend effects” and other reporting distortions).

As might be expected, both charts show the “locus of infection” moving fairly monotonically northwards.  Over approximately 10 weeks the peak has moved north by about 20 degrees and the average by about 16 degrees.  During the same period the sun’s declination (angle between the equatorial plane and a line joining the centres of the Earth and sun) has moved ~28 degrees north.

If the sun didn’t influence, directly or indirectly, the pandemic’s progress there’d be no reason to expect a correlation between its position and the areas affected by C-19.  In practice, it turns out that both sun and C-19 have been moving in the same direction, albeit with the sun moving faster.

As every fule kno, correlation doesn’t imply causation but causation does require correlation.  In six months or so, it will become clear whether there’s actually a significant seasonal component to C-19’s behaviour; so far the evidence is in favour (or, at any rate, not contradictory).

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12 thoughts on “Simon Anthony: Migration of Infection

  1. I think it is interesting to compare the overall spread of infections in England in this map:

    with the reported infections in the recent fortnight:

    It is clear that in London the infections are increasingly abating, while in some outlying areas the epidemic is only much more recently peaking. Also of note is that the SW has remained much freer of infection, while the North seems to have suffered, particularly of late.

  2. As every physicist knows, a data point should always be accompanied by an uncertainty band. It would be interesting to try to estimate uncertainty bands for the data points used to support the postulated link between C-19 mortality rate and latitude. However, that is very difficult because (1) the data is politicized, and (2) even without politics, there are major differences in the way different jurisdictions report data.

    On the qualitative level, there is an interesting feature. Wuhan, the asserted source of C-19, sits almost on North 30 latitude — at the southern boundary of the apparent 30 – 60 North range.

    Most of the “advanced” countries lie north of Wuhan — Europe, North America, Russia, Korea, Japan. I.e., wealthy places where bureaucrats can focus resources on C-19.

    There are very large population countries south of Wuhan — India, Pakistan, Indonesia. Population densities and standards of living in those countries are such that it would not be surprising if they were badly affected by a lethal virus — but that does not show up in the graph of peak latitude versus date.

    Perhaps the countries south of Wuhan have not put comparable resources into tracking C-19 as countries north of Wuhan? Or perhaps the younger age distribution in the southern countries is a much more important factor than latitude? With inadequate politicized data, the real uncertainty bands could probably accommodate many different hypotheses.

  3. You could probably find a +ve correlation with per capita red meat consumption and a -ve correlation with per capita fish consumption. Or with shouty indoor events of say 100+. Or having stalinist healthcare. I just don’t get where these observations over latitude are heading.
    What I really want to know is if soft restrictions work better than hard lock-downs, on the totality of well-being?
    We might know in 2 years time, when the next mutation of this thing has ripped through. It will feel like 12 years by the time we get there.

  4. Bongo

    From what you say, I should have explained the significance of latitude more carefully.

    Latitude is a proxy for weather. If weather significantly affects C-19 – as it does flu – it may have a major impact on how governments deal with it in future, particularly on whether lockdown measures may be imposed throughout the year or only for some part of it.

    The flu virus is highly seasonal in both northern and southern hemispheres. Various reasons have been suggested to account for this: people spend more time indoors in winter rather than summer possibly leading to higher infection rate in winter; dryer mucus particles in winter staying airborne for longer; the virus survives longer at colder temperatures with low relative humidity; vitamin D levels may affect the immune system’s response to the virus.

    All of these factors (and others) depend on the weather, which depends on the seasons, which depend on latitude and time of year. So it seems as though a factor associated with latitude strongly affects flu. If it didn’t, flu might be equally dangerous throughout the year, killing perhaps 2 to 3 times as many people as it currently does as well as causing widespread year-round illness.

    Currently, AFAIK, no one knows for sure whether C-19 is seasonal like flu or in some other way. Seeing how its behaviour currently varies with latitude is a way to find out because weather varies with latitude.

    From what you say, you’re concerned about lockdowns. Suppose that C-19 infections vanish in the northern hemisphere in the next month. An important question, for measures in both the southern hemisphere in the coming months and for the northern hemisphere next winter, would be whether the virus went into abeyance because of lockdowns or merely because summer’s come and it would have receded anyway. Or suppose that no C-19 vaccine becomes available and governments feel it necessary to impose some form of lock-down whenever C-19 threatens. If it’s seasonal like flu, that might be 4-5 months of the year. Otherwise it might be for the entire year.

    I hope that helps to explain why it’s worth looking at C-19’s dependence on latitude.

  5. With lockdown in the UK happening at exactly the same time for each region, but the with differing levels of C19 penetration, we should have an indication if we were late in introducing the lockdown (eg London) or if the timing made no discernible difference. And therefore if it was needed at all.

  6. “… weather varies with latitude.”

    Daylight hours vary with latitude. Weather varies with a lot more than latitude. The deserts of Libya and the swamps of Louisiana are on more-or-less the same latitude. The idea of seeing if there was a link between death rates and latitude was worth looking at, but the data is too crude and undependable to allow meaningful analysis.

    “suppose … governments feel it necessary to impose some form of lock-down whenever C-19 threatens. If it’s seasonal like flu, that might be 4-5 months of the year. Otherwise it might be for the entire year.”

    Judging by the rising tide of contempt for politicians and the plummeting esteem for academics & media types, the probability is that “lockdown” will be thrown down the memory hole as soon as politicians can find a way to escape from the corner they have painted themselves into.

    Fortunately, C-19 has turned out to be rather mild, with very low rates of serious sickness or death. The important question is what should we do if (when) there is a real pandemic, an actual plague?

  7. Gavin

    “Daylight hours vary with latitude”

    Thanks for the reminder which of course emphasises the importance of latitude. I’d wrongly assumed that people would know that “latitude” was a stand-in for the factors which directly affect C-19 and neglected the details.

    “the data is too crude and undependable to allow meaningful analysis”

    Could be but, to repeat a response I previously made to similar qualms:

    “I agree with those people who’ve expressed doubts about the reliability of C-19 data. But I think the evidence shows that the conclusion I came to – that it seems likely that weather will play an important role in limiting/encouraging C-19’s spread – is still probably true.

    I say this for two reasons: first, mortality rates are so overwhelmingly higher in N hemisphere countries than SH that, for the weather to have had no effect, would require about 99% of C-19 deaths throughout the SH to go unrecorded.

    Second, reliability of SH data may range from very doubtful, through so-so to just as reliable as NH (Australia and NZ). For the claimed mortality rates in these different countries to be badly understated would need all of the widely varying regimes to be similarly careless in allocating C-19 deaths.

    While it’s not impossible that both these arguments are wrong, it seems highly improbable that they’re wrong enough to invalidate the conclusion.”

    “Weather varies with a lot more than latitude”

    I’m sure those other factors will be investigated as more data becomes available. In the meantime, weather – particularly temperature – varies very reliably with latitude.

  8. Simon,
    Unsure of your thesis–Wouldn’t 90% of the world’s population living in the Northern Hemisphere, with concomitant overcrowding in cities, care homes etc. have more bearing on numbers than weather? I’m pretty useless when it comes to demographics versus mathematics and fail to grasp much of anything when it comes to it!

  9. There’s a parameter called photoperiod- hours per day of daylight- which varies with latitude and date. I’m wondering if maybe repeating your analysis with photoperiod instead of latitude might help.

    I’m also struck by the two jumps in your first graph. Do you know what causes those?

    And finally… what happens if you plot those graphs without the Chinese figures? I’d regard the Chinese data as unreliable, because politicised; and unrepresentative, because it seems COVID19 was there long before anywhere else.

    With so many factors acting as confounding variables; and with latitude being such an indirect proxy for things that actually affect disease spread, I think it’ll be hard to draw much in the way of conclusions from this sort of analyis. The signal-to-noise ratio will never be good. But I think it’s still worth doing, as it will give us some sort of clue.

  10. If you want to take a look at it in more detail I produced several scatter charts of case rates, death rates and test rates where you can see the data for each point by mousing over it. I found it quite striking that data for continents tends to be grouped together, and when you look at continents that span tropics and more temperate zones, the hotter ones tend to be less affected. Try this one for example:

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