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<TITLE>CoVID 19 Growth Rate</TITLE>
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  <H1>CoVID 19 Worldwide Growth Rates</H1>
  <P>
    <font color="red">Updated: 30th March 2020, 03:33 UTC <B>All graphs have been updated, but very little of the commentary has been as my family insisted I did something other than graphs today. I have managed to add a new Central America graph covering Mexico, Panama and the Domincan Republic, and split South America into two graphs, as there appears to be two distinct clusters of behaviour. MJH</B></font>
<P>
This page presents historical SARS-CoV-2 coronavirus infection
information.  I try to present it in a way that helps inform about how
the virus is progressing throughout the main outbreaks worldwide in a
way that allows countries to be compared and perhaps lessons learned.
The underlying infection and containment processes are complicated,
and conclusions you or I may draw from these graphs are not true
predictions.  For that, you'd need much more data about what is being
done in each country, and about how the data is collected. Comments
are my interpretation only.  Nevertheless, I hope you find it useful.
</P>
<P>
  <a href="http://www.cs.ucl.ac.uk/staff/m.handley/">Mark Handley</a>, UCL.
</P>
<h2>Contents</h2><DL>
<DT><a href="#covid-eu">Graph 1:</a> <B>Cases</B>: Western Europe: Italy, Spain, France, Germany, Netherlands, UK</DT>
<DT><a href="#covid-eu-norm">Graph 2:</a> <B>Cases</B>: Western Europe: Italy, Switzerland, Spain, France, Germany, Netherlands, UK</DT>
<DT><a href="#rates">Graph 3:</a> <B>Increases</B>: Western Europe Daily Increases: Italy, Lombardy, France, USA, UK, Spain, Greece, Denmark</DT>
<DT><a href="#deaths-eu-norm">Graph 4:</a> <B>Deaths</B>: Deaths: Western Europe: Italy, Spain, France, Netherlands, Switzerland, UK, Germany</DT>
<DT><a href="#covid-eu-lom">Graph 5:</a> <B>Cases</B>: Italy, Lombardy, Switzerland, Austria</DT>
<DT><a href="#covid-eu-norm2">Graph 6:</a> <B>Cases</B>: Nordic Region: Italy, Iceland, Denmark, Norway, Sweden, Finland, South Korea</DT>
<DT><a href="#covid-eu-norm2b">Graph 7:</a> <B>Cases</B>: Nordic Region (offset curves): Denmark, Norway, Sweden, Finland</DT>
<DT><a href="#rates-nordic">Graph 8:</a> <B>Increases</B>:  Nordic Region, Daily Increases: Italy, Denmark, Sweden, Norway, Finland, Iceland, Estonia</DT>
<DT><a href="#covid-eu-norm3">Graph 9:</a> <B>Cases</B>: Italy, Belgium, Ireland, Portugal, Luxembourg</DT>
<DT><a href="#deaths-eu-norm2">Graph 10:</a> <B>Cases</B>: Deaths: Italy, France, Germany, Luxembourg</DT>
<DT><a href="#covid-eu-norm4">Graph 11:</a> <B>Cases</B>: Italy, Greece, Czech Republic, Slovenia, Slovakia, Croatia, Romania, Poland, Hungary, Bulgaria, Serbia</DT>
<DT><a href="#rates-eeu">Graph 12:</a> <B>Increases</B>: Eastern Europe, Daily Increases: Italy, Taiwan</DT>
<DT><a href="#covid-eu-norm5">Graph 13:</a> <B>Cases</B>: Italy, Estonia, Belarus, Lithuania, Latvia, Ukraine, Russia</DT>
<DT><a href="#covid-eu-linear">Graph 14:</a> <B>Cases</B>: Western Europe: Italy, France, Germany, Spain, Switzerland, UK, Netherlands, Sweden</DT>
<DT><a href="#covid-uk">Graph 15:</a> <B>Cases</B>: UK: England Regions</DT>
<DT><a href="#covid-uk-linear">Graph 16:</a> <B>Cases</B>: UK: England Regions</DT>
<DT><a href="#covid-uk-all">Graph 17:</a> <B>Cases</B>: UK: England, Scotland, Wales, Northern Ireland</DT>
<DT><a href="#covid-world">Graph 18:</a> <B>Cases</B>: World: China, Italy, Iran, France, Spain, USA, South Korea, Japan</DT>
<DT><a href="#covid-world-norm">Graph 19:</a> <B>Cases</B>: World: Italy, Iran, France, USA, Australia, South Korea, Singapore, Japan</DT>
<DT><a href="#covid-us-norm">Graph 20:</a> <B>Cases</B>: US States: Italy, Washington, New York, New Jersey, Louisiana, Michigan, Massachusetts, Illinois, Colorado, California, Florida, Texas</DT>
<DT><a href="#covid-world-norm2">Graph 21:</a> <B>Cases</B>: Italy, USA, South Korea, Canada, New Zealand</DT>
<DT><a href="#covid-world-norm3">Graph 22:</a> <B>Cases</B>: Italy, Israel, Pakistan, Turkey, South Africa, Russia, Saudi Arabia</DT>
<DT><a href="#deaths-us">Graph 23:</a> <B>Deaths</B>: Deaths: USA: Italy, France, USA, Germany</DT>
<DT><a href="#covid-world-sa2">Graph 24:</a> <B>Cases</B>: South America (Andean): Italy, Chile, Ecuador, Peru, Bolivia, Argentina</DT>
<DT><a href="#covid-world-sa3">Graph 25:</a> <B>Cases</B>: South America: Italy, Brazil, Colombia, Uruguay, Paraguay, Venezuela</DT>
<DT><a href="#covid-world-ca">Graph 26:</a> <B>Cases</B>: Central America: Italy, Panama, Dominican_republic, Mexico</DT>
<DT><a href="#covid-world-seasia">Graph 27:</a> <B>Cases</B>: South East Asia: Italy, Thailand, Taiwan, Philippines, Vietnam, Cambodia</DT>
<DT><a href="#covid-world-warm">Graph 28:</a> <B>Cases</B>: Warm Countries: Italy, France, USA, Brazil, Australia, Malaysia, Qatar, Thailand, Bahrain, Indonesia, Kuwait, Egypt, India</DT>
<DT><a href="#covid-world-warm2">Graph 29:</a> <B>Cases</B>: Warm Countries: Malaysia, Qatar, Bahrain, Egypt, India, Kuwait</DT>
<DT><a href="#covid-world-linear">Graph 30:</a> <B>Cases</B>: World: China, Italy, Iran, France, USA, South Korea, Japan</DT>
</DL>
<hr><P><h3><a name="covid-eu"></a>Western Europe: Italy, Spain, France, Germany, Netherlands, UK</h3><P>
<img src="29mar2020/covid-eu.png"><P>
<UL>
<LI>The graph shows <B>cumulative number of confirmed cases</b>, plotted on a log
scale, against time.  The country curves are shown offset by the
amounts shown. </LI>
   <LI>Italy's daily increase rate had been reducing slowly, and is
   showing signs that it may be peaking (see Graph 3).  Lombardy's
   daily increase rate results appeared to have peaked six days ago,
   though it ticked back up the last two days. If it hasn't peaked, it
   seems like it is close.
  <LI>Over the past two weeks France, Germany, the UK, the Netherlands and Spain
    all became aligned with the 22 percent daily increase curve
    that Italy followed at this point, rather than the higher 35%
    curve all the large European countries initially followed.
  <LI>France,  and the Netherlands appear now to have followed Italy in
    dropping off the 22% curve in the last five or six days, and are more
  aligned now with the 13% curve that Italy followed for about a week.
  <LI>Spain is just starting to shown signs of following the others,
  but only today's update reached 13%, which isn't long enough to
  establish a new trend.
  <LI>For nearly two weeks the UK has been on the 22% daily increase
  curve, rather than the 35% daily increase curve it was previously
  on.  However, see the UK regional graphs for the wide difference
  between London and the other regions.
</UL>
<hr><P><h3><a name="covid-eu-norm"></a>Western Europe: Italy, Switzerland, Spain, France, Germany, Netherlands, UK</h3><P>
<img src="29mar2020/covid-eu-norm.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>confirmed cases per million                                                                                       inhabitants</B>, plotted on a log scale, against time.  The
country curves are shown offset by the amounts shown.</LI>
<LI><I>Commentary updated 30th March 2020</I>
<DL>
<DT>35% daily increase corresponds to a doubling time of 2.5 days</DT>
<DT>22% daily increase corresponds to a doubling time of 3.5 days</DT>
<DT>13.5% daily increase corresponds to a doubling time of 5.5 days</DT>
</DL>

<LI> I'm now showing these countries aligned with the 13.5% curve as
all of them now appear to have left the 22% curve.  

<LI> France, Germany and (tentatively) the UK are all now tracking
along the 13.5% daily increase curve that Italy followed.

<LI> Italy has now dropped off of exponential increases and appears to have peaked.

<LI>Switzerland has a relatively small population, and so the number
    of cases per million inhabitants is much higher.  Switzerland is
    shown two days behind Italy and has followed Italy closely for the
    last two weeks.
    
  <LI> See the <a href="#deaths-eu-norm">this death rates graph</a> for why I am
    not confident in this placement for Switzerland - it appears that
    Switzerland is testing more widely than Italy, so Switzerland is
    likely to be perhaps as much as 10 days behind Italy.
    
  <LI>Spain stayed at 35% daily increases for much longer than any
    other large European country, which caused it to close on Italy,
    then followed the 22% curve for a week. Spain is now tracking
    along the 13.5% curve, although it joined this curve at roughly
    the point where Italy departed it.
</UL>
<hr><P><h3><a name="rates"></a>Western Europe Daily Increases: Italy, Lombardy, France, USA, UK, Spain, Greece, Denmark</h3><P>
<img src="29mar2020/rates.png"><P>
<UL>
<LI>The graph shows <B>daily increase in confirmed cases                                                                                   per million inhabitants</B>, plotted on a log scale, against time.
  A Holt-Winters moving average filter with constants &alpha;=0.5 and
  &beta;=0.5 has been applied to smooth the curves as differences are
  very noisy.  This is a moderate amount of smoothing and it imposes a
  about a days lag, but it does extract trends fairly well.  The
  curves are not offset, today is Day 0 for all curves.</LI>
  <LI>Generally, trends are easier to see on a cumulative plot, as changes are inherently more noisy.  However, this view is better to see whether a country has peaked or not.
  <LI>The daily increase in cases appears to have peaked in Lombardy, and perhaps in Italy as a whole.  The daily increases have decreased for five consecutive days in Lombardy.
  <LI>Spain and the US are showing no signs of nearing a peak, whereas France and the UK show slightly sub-exponential increases.
  <LI>Denmark and Greece show no clear pattern recently, but neither has peaked yet.
</UL>
<hr><P><h3><a name="deaths-eu-norm"></a>Deaths: Western Europe: Italy, Spain, France, Netherlands, Switzerland, UK, Germany</h3><P>
<img src="29mar2020/deaths-eu-norm.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>deaths per million
      inhabitants</B>, plotted on a log scale, against time.  The
      country curves are shown offset by the amounts shown.</LI>
    <LI> As different countries have different testing policies, many
      people have suggested that we should look at deaths instead.
      There are several downsides to using deaths as a metric.  First,
      if the purpose of these graphs is to provide warning of what is
      to come, or to verify whether measure are working, deaths is not
      very useful.  Death rate is too low to provide a warning signal
      in advance of there being a problem, and it is not a good early
      indicator of whether measures are working because it lags case
      data by between one and two weeks.  It can, however, provide
      some insight into what fraction of infections are being detected
      in different countries.  Generally, if a country is further
      behind in this graph than in the equivalent cases graph, then
      the country is probably catching a larger fraction of cases.
      This is particularly pronounced in the case of Germany.
    <LI>
      Death data is also problematic because deaths per day does not
      go down quickly when cases go down.  This is particularly clear
      in the Korean data, where the death rate has remained nearly
      constant for three weeks after new infections peaked.
    <LI>
      Finally, when a healthcare system gets overwhelmed, death rate
      goes up from something like 0.9% (Korea) to something like 3-4%
      (Hubei, parts of Lombardy).
    <LI>
      Generally when cases are increasing exponentially, most
      countries' death rate curves shadow the cases curve, with a lag
      of between 6 (France, UK) and 12 days (Germany).  Spain, France,
      Netherlands and the UK look very similar to how they looked using
      case data around 6 days ago.  Germany is about ten days further
      back on this graph.  The difference in
      per-capita testing rates does not seem to explain this
      difference.
</UL>
<hr><P><h3><a name="covid-eu-lom"></a>Italy, Lombardy, Switzerland, Austria</h3><P>
<img src="29mar2020/covid-eu-lom.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>confirmed cases per million                                                                                       inhabitants</B>, plotted on a log scale, against time.  The
country curves are shown offset by the amounts shown.</LI>
  <LI>I have aligned the 35% daily increase rate parts of the four
    graphs, so the points at which they diverge can be seen.  As a
    result the graph shows Lombardy as being 5.5 days ahead of Italy,
    but a more realistic value based on today's data points is seven
    days ahead.

  <LI>Lombardy now appears to have peaked, though I won't be sure of
  this for a few more days.  See Graph 3.  The daily increase in cases
  is today was roughly the same as ten days ago, with a peak five days
  ago.

  <LI>Switzerland tracked along the 35% curve about six days further
    than Italy did, so comparing with Italy as a whole no longer seems
    to be the right baseline. The Lombardy results provide a better
    new reference curve.  Beware though that these time estimates
    depend on both Lombardy and Switzerland detecting roughly the same
    fraction of cases.  Switzerland is only testing severe cases at
    this point, and Lombardy was clearly overloaded at the same point.
    The death rate in Lombardy at this
    point was, however, about four times higher than in Switzerland.
    It is risky to read too much into the death rates, but it might
    mean that Switzerland is counting a larger fraction of infected
    people than Lombardy did at the same point; if so, then
    Switzerland is further behind Lombardy than I have suggested.  THe
    death rate curves in the previous graph certainly suggest this may
    be the case.

  <LI>Austria has been on the 35% daily increase curve, but the last
  five days' increases have been lower. Austria now appears to be
  following the Lombardy curve about ten days behind.
</UL>
<hr><P><h3><a name="covid-eu-norm2"></a>Nordic Region: Italy, Iceland, Denmark, Norway, Sweden, Finland, South Korea</h3><P>
<img src="29mar2020/covid-eu-norm2.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>confirmed cases per million                                                                                       inhabitants</B>, plotted on a log scale, against time.  The
country curves are shown offset by the amounts shown.</LI>
      <LI>Data for most Nordic countries shows large waves of
      imported cases, with increase rates above 35%, followed by a
      slump as the imports cease. Sometimes this is followed six or so
	days later by an echo of the original surge.
      <LI>Iceland suffered a large number of imported cases relative
      to its very small population.  After that burst stopped, Iceland
      followed roughly the same curve as Italy, two days ahead.  Eight
      days ago Iceland's increase rate increased for five days, but it
      has now levelled off at a similar rate to Italy. It is possible
      that this is due to increased testing rather than a burst in new cases.
      <LI>I will discuss Sweden, Denmark, Norway and Finland on the
      next graph.  Unfortunately the data no longer looks similar to the South
      Korean curve.
</UL>
<hr><P><h3><a name="covid-eu-norm2b"></a>Nordic Region (offset curves): Denmark, Norway, Sweden, Finland</h3><P>
<img src="29mar2020/covid-eu-norm2b.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>confirmed cases per million                                                                                       inhabitants</B>, plotted on a log scale, against time.  The
country curves are shown offset by the amounts shown.</LI>
      <LI> These countries experienced a large wave of imported cases.
      However, it appears they were effective at contact tracing for
      these cases, and most of them were effectively quarantined.
      Despite this, it appears a non-negligible number of local
      infections escaped detection, and from this smaller base,
      exponential growth continued.  I have subtracted the amounts
      shown from the case counts before plotting - these represent my
      guess at the number of imported cases and their immediate
      contacts that were stopped by contact tracing.  If we subtract
      these values, the remaining cases show straight lines at the
      characteristic values of 35% or 22%.  Am I convinced by these
      offset ammounts?  No, not completely - see Norway below.  But this way of viewing
      the data makes more sense to me than the raw counts in the previous
	graphs.
      <LI>Sweden appeared to be growing exponentially at 35% per day
	from a base of about 220 active cases six days ago, but a
	sudden change to a 16% daily increase rate occurred five days
	ago.
      <LI>Finland appears to have been growing exponentially at 22%
      per day from a base of about 135 active cases nine days ago.  The last three days hint that a change to a lower increase rate similar to Sweden's 16% has occured.
      <LI>Denmark was growing exponentially for seven days at 22% per
	day from a base of about 185 active cases nine days ago.  The last four days Sweden seems to have moved to a lower increase rate similar to Sweden.
	<LI>Norway appeared to be growing exponentially at 35% per day
	from a base of about 260 active cases six days ago. Norway
	also appears to have switched to a 16% daily increase the last
	few days.
</UL>
<hr><P><h3><a name="rates-nordic"></a> Nordic Region, Daily Increases: Italy, Denmark, Sweden, Norway, Finland, Iceland, Estonia</h3><P>
<img src="29mar2020/rates-nordic.png"><P>
<UL>
<LI>The graph shows <B>daily increase in confirmed cases                                                                                   per million inhabitants</B>, plotted on a log scale, against time.
  A Holt-Winters moving average filter with constants &alpha;=0.5 and
  &beta;=0.5 has been applied to smooth the curves as differences are
  very noisy.  This is a moderate amount of smoothing and it imposes a
  about a days lag, but it does extract trends fairly well.  The
  curves are not offset, today is Day 0 for all curves.</LI>
<LI><I>Commentary updated 30 March 2020.</I>

<LI>Generally, trends are easier to see on a cumulative plot, as
changes are inherently more noisy.  However, this view is better
to see whether a country has peaked or not.

<LI>Daily increases in absolute numbers have been nearly constant for
several days in Finland and Iceland.  This is likely to an indication
that the infection rate in these countries is peaking, though we wont
be sure until it has been going down again for more than a week.
Certainly, exponential growth is no longer occurring in these
countries.

<LI>Norway was growing exponentially until 26th March, but since then
has been decreasing, Three days is not long enough to have confidence
that Norway has peaked, as daily change data is always noisy, but it
hints that it might have done so, especially relatively good news from elsewhere
in the Nordic region.

<LI>Denmark and Sweden have very similar exponential increase rate
profiles for the last two weeks. In both countries there is a hint of
a slow decrease below exponential in the last two days, but it's not a
long enough trend to say anything with confidence.

<LI>Ten days ago, Estonia looked like it had peaked, but this behviour
has happened in other rountries such as Denmark, where a large number
of case are imported.  The imported cases are mostly tracked down,
leading to a dip, then growth again as transmission that was missed
grows.  The peak the last four days may be an echo of the original
imported peak - this happened in Denmark and Sweden too, though their
echoes were less pronounced.</UL>
<hr><P><h3><a name="covid-eu-norm3"></a>Italy, Belgium, Ireland, Portugal, Luxembourg</h3><P>
<img src="29mar2020/covid-eu-norm3.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>confirmed cases per million                                                                                       inhabitants</B>, plotted on a log scale, against time.  The
country curves are shown offset by the amounts shown.</LI>
      <LI>In Belgium, the inital early ramp-up appears to be mostly
      due to imported cases from Italian ski resorts. Since these
      imports stopped, Belgium seems to be on a similar 22% daily
      increase curve to that followed by Italy
      <LI>Ireland and Portugal continue to follow the Italian curve closely, about 12 days behind.
      <LI>Luxembourg has a very small population, so the curve is
      noisy.  However, the last ten days data have taken Luxembourg
      well above the point Lombardy reached at this stage of the
      infection, but the last two datapoints hint at lower increases
      around 22% in the future.  See the next graph for why I am not
      confident Switzerland really is quite so close behind Italy as
      this graph would suggest.
</UL>
<hr><P><h3><a name="deaths-eu-norm2"></a>Deaths: Italy, France, Germany, Luxembourg</h3><P>
<img src="29mar2020/deaths-eu-norm2.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>confirmed cases per million                                                                                       inhabitants</B>, plotted on a log scale, against time.  The
country curves are shown offset by the amounts shown.</LI>
<LI>Luxembourg is such an outlier in the previous graph that this
leads me to doubt that the confirmed case data is comparable with
other countries.  The number of deaths in Luxembourg is very small -
only eight - but it's just enough that we can get a very rough
cross-calibration of case data vs death data.  It seems likely that
testing in Luxembourg is much more effective than in France or Italy,
and so is identifying many more people whose symptoms would be too
mild to merit testing in France or Germany.  It is clear that there
are a large number of cases in Luxembourg, but not so many more per
million inhabitants as the previous graph shows.  It looks like deaths
lag case data by about ten days more in Luxembourg than in France.
The German data shows a similar additional lag.
</UL>
<hr><P><h3><a name="covid-eu-norm4"></a>Italy, Greece, Czech Republic, Slovenia, Slovakia, Croatia, Romania, Poland, Hungary, Bulgaria, Serbia</h3><P>
<img src="29mar2020/covid-eu-norm4.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>confirmed cases per million                                                                                       inhabitants</B>, plotted on a log scale, against time.  The
country curves are shown offset by the amounts shown.</LI>
  <LI> Most Eastern European countries have shown large downturns.  This logscale plot of cumulative confirmed cases no longer gives enough visibility into what is happened.  See the next graph for a better view.
</UL>
<hr><P><h3><a name="rates-eeu"></a>Eastern Europe, Daily Increases: Italy, Taiwan</h3><P>
<img src="29mar2020/rates-eeu.png"><P>
<UL>
<LI>The graph shows <B>daily increase in confirmed cases                                                                                   per million inhabitants</B>, plotted on a log scale, against time.
  A Holt-Winters moving average filter with constants &alpha;=0.5 and
  &beta;=0.5 has been applied to smooth the curves as differences are
  very noisy.  This is a moderate amount of smoothing and it imposes a
  about a days lag, but it does extract trends fairly well.  The
  curves are not offset, today is Day 0 for all curves.</LI>
<LI><I>Updated 29th March</I>
<LI>Generally, trends are easier to see on a cumulative plot, as
    changes are inherently more noisy.  However, this view is better
    to see whether a country has peaked or not.

<LI>I thought Slovakia had peaked a few days ago, but it appears I was
wrong.  Nevertheless, growth there is almost constant, and certainly
no longer exponential.

<LI>Greece, Bulgaria, Hungary and perhaps Poland appear to be close to
  peaking - the daily increase has been nearly constant for a number
  of days, and they no longer shows signs of exponential growth.

<LI>Slovenia and Romania are still growing exponentiall, though with a
relatiively low daily increase rate.

<LI>I have added Belarus to this graph, as the curve is intereting.
Belarus definitely seems to have peaked a week ago, though the
absolute values are so small - only 94 cases in total - that only a
small undetected outbreak could reverse this trend.</UL>
<hr><P><h3><a name="covid-eu-norm5"></a>Italy, Estonia, Belarus, Lithuania, Latvia, Ukraine, Russia</h3><P>
<img src="29mar2020/covid-eu-norm5.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>confirmed cases per million                                                                                       inhabitants</B>, plotted on a log scale, against time.  The
country curves are shown offset by the amounts shown.</LI>
  <LI>Estonia's small population and recent fast ramp up of cases
  means it now has a high number of cases per million inhabitants. The
  current dip may be due to the end of a wave of imported cases, as
  seen in the Danish data.
  <LI>Belarus and Lithuania have too few cases for the current trend
  lines to be clear.  With the exception of the most recent datapoint,
  they appear to be very roughly following the 35% curve, or a little
  higher.
  <LI>Russia is experiencing a lower daily increase rate than most
  northern countries at the equivalent stage of the infection.  I've aligned it with the 22% daily increase
  curve that many countries followed.
<LI>Latvia also appears to be roughly following the 22% daily increase curve.
</UL>
<hr><P><h3><a name="covid-eu-linear"></a>Western Europe: Italy, France, Germany, Spain, Switzerland, UK, Netherlands, Sweden</h3><P>
<img src="29mar2020/covid-eu-linear.png"><P>
<UL>
<LI>The graph shows <b>number of confirmed cases</b>, plotted on a
linear scale, against time.  The country curves are shown offset
by the amounts shown.</LI>
       <LI>I normally use a log scale on the y-axis because
     exponential growth gives a straight line on a log-linear graph.
     This allows exponential growth rates to be compared. However,
     many readers don't like log-linear graphs, so this one is for
     them.  It has to be truncated, or you cannot see any information.
     It doesn't really show anything additional over the log graphs,
     except it looks scarier.  
</UL>
<hr><P><h3><a name="covid-uk"></a>UK: England Regions</h3><P>
<img src="29mar2020/covid-uk.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>confirmed cases per million                                                                                       inhabitants</B>, plotted on a log scale, against time.  The
country curves are shown offset by the amounts shown.</LI>
<LI>All the English regions converged onto the 35% daily increase
curve that Italy followed, and appear now to be starting to transition
to the 22% daily increase curve.

<LI>London is running around a week ahead of the UK, and is tracking
along the curve that Lombardy followed.  Unlike France and Germany,
the UK government was slow to impose stringent isolation measures;
indeed they are still not as strict as elsewhere in Europe.
</UL>
<hr><P><h3><a name="covid-uk-linear"></a>UK: England Regions</h3><P>
<img src="29mar2020/covid-uk-linear.png"><P>
<UL>
<LI>The graph shows <b>number of confirmed cases</b>, plotted on a
linear scale, against time.  The country curves are shown offset
by the amounts shown.</LI>
<LI>The main reason to include this graph is that it shows much much
further London has to go if it follows Lombardy.
</UL>
<hr><P><h3><a name="covid-uk-all"></a>UK: England, Scotland, Wales, Northern Ireland</h3><P>
<img src="29mar2020/covid-uk-all.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>confirmed cases per million                                                                                       inhabitants</B>, plotted on a log scale, against time.  The
country curves are shown offset by the amounts shown.</LI>
<LI>England (excluding London), Scotland, Wales and Northern Island
are all experiencing daily increase rates close to or below the 22%
curve that Italy followed.
</UL>
<hr><P><h3><a name="covid-world"></a>World: China, Italy, Iran, France, Spain, USA, South Korea, Japan</h3><P>
<img src="29mar2020/covid-world.png"><P>
<UL>
<LI>The graph shows <B>cumulative number of confirmed cases</b>, plotted on a log
scale, against time.  The country curves are shown offset by the
amounts shown. </LI>
     <LI> The early part of the China curve is shown for
     comparison. I'm not sure how accurate the numbers are in the
     early stage because they didn't initially know what to look for,
     and the way of measuring changed part way through this period.
     The initial increase rate is fairly consistent with the 35% daily growth seen in
     Europe.
     <LI>Other than China, South Korea is the only country to have had a
     high sustained increase rate, and then bring the virus under
     control.
     <LI>The USA had been tracking very closely along the 35% growth
     line, and has done so for much longer than any other
     country. Testing in the US was initially very limited, but
     recently it seems testing has been catching up somewhat. In the
     last few days the US has shown the first signs of dropping off of
     the 35% daily increase curve.
     <LI>Cases in the US are concentrated in a few states, in a
     similar way to how cases in Italy are concentrated in
     Lombardy.
     <LI>Iran tracked a little above a 35% increase rate until three
     weeks ago.  Since then, Iran had experienced ten days of
     consistent 11.5% exponential growth, with the last ten days
     showing further decline.  For many days the daily increase in
     cases had been roughly constant at around 1100-1200 new cases per
     day, but it has now started to increase again.  It is possible
     this was due to limitations in testing.
     <LI>Japan is an enigma.  The testing rate there is low, so cases
     may be being underreported.  However consistently missing the
     same fraction of cases would not affect the exponential growth
     doubling time, which had been extremely consistent at 8.5% per
     day for many weeks, until the last week when it has declined
     further.  It seems more likely that early measures taken there
     are being effective at reducing the increase rate, but are not
     sufficient to avoid exponential growth altogether. It looks like
     the combination of early school closure, plus ubiquitous face
     masks and regular Japanese good hygene may be responsible for
     Japan's unique track. No-one really knows,
     but <a href="https://www.japantimes.co.jp/opinion/2020/03/21/commentary/japan-commentary/japan-still-coronavirus-outlier/#.XnZH06FRUlQ">many
     are speculating.</a>
</UL>
<hr><P><h3><a name="covid-world-norm"></a>World: Italy, Iran, France, USA, Australia, South Korea, Singapore, Japan</h3><P>
<img src="29mar2020/covid-world-norm.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>confirmed cases per million                                                                                       inhabitants</B>, plotted on a log scale, against time.  The
country curves are shown offset by the amounts shown.</LI>
  <LI> Showing cases per million inhabitants does not greatly change
  the overall picture compared to the previous graph.
  <LI>In this view, the US moves a few days further behind Italy.  This
  is probably deceptive, and it might be better to show data for
  New York State, for example, on this graph.
  <LI>I've added a curve for Singapore, which contained the initial
  imported cases very well.  The graph shows a worrying slow but
  steady super-exponential growth recently though, perhaps indicating
  that current measures are starting to not be effective, or that more
  cases are being imported again.  I've been told that most of the new
  cases are imports; it makes sense that if Singapore's quarantining
  of visitors and contact tracing is mostly keeping on top of local
  spread, then as the pandemic ranges worldwide, Singapore will see an
  equivalent rise in imported cases.  The number of untraced cases remains small at this time.
</UL>
<hr><P><h3><a name="covid-us-norm"></a>US States: Italy, Washington, New York, New Jersey, Louisiana, Michigan, Massachusetts, Illinois, Colorado, California, Florida, Texas</h3><P>
<img src="29mar2020/covid-us-norm.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>confirmed cases per million                                                                                       inhabitants</B>, plotted on a log scale, against time.  The
country curves are shown offset by the amounts shown.</LI>
  <LI>I am now pulling data for this graph from
    the <a href="https://github.com/nytimes/covid-19-data">NYT
    dataset</a>, which is much less noisy than the JHU dataset I was
    previously using.
  <LI>Most US states are a long way behind European countries, but
    several now have comparable rates per million inhabitants and New
    York is ahead. I have plotted the states with most confirmed
    cases.
  <LI>European countries moved from a 35% daily increase curve to a
    22% daily increase curve; Washington is one of the few US states
    to have clearly made a similar transition, and in the last few
    days the daily increase rate has declined further.  Washington is
    the only US state with a large number of cases to start to turn
    the tide significantly.
  <LI>New York was growing at close to the 35% daily increase rate
    seen in Europe, but then had very large increases over a week.
    This usually happens when cases have been spreading undetected,
    and suddenly testing starts catching up. The last few days, cases
    in NY have been growing exponentially at around 22% per day.  This
    is the same growth curve most European countries followed once
    people started to get concerned about COVID19.  I have placed New
    York so as to align it with the 22% curve.  This places it 4 days
    offset from Italy, but today's datapoint would place New York
    above Italy.  As Italy seems to have peaked and New York has more
    cases per head of population than Italy, it makes no sense saying
    where New York is on Italy's track: New York is forming its own
    track.
  <LI>Illinois and California are the other two states that are now
    following the 22% curve.  California has followed the curve for
    some time, but Illinois has only recently come out of fast growth
    (presumably due to testing catching up somewhat) so we will have
    to wait and see it it stabilizes along this curve.
  <LI>New Jersey, Louisiana, Michigan, Colorado, Florida, and Texas
    have been increasing recently at close to the 35% daily increase
    rate seen in Europe, so I've placed then on that curve, though
    this gives misleading time delays relative to Italy.  Based on the
    most recent data point, New Jersey is 12 days behind Italy.
</UL>
<hr><P><h3><a name="covid-world-norm2"></a>Italy, USA, South Korea, Canada, New Zealand</h3><P>
<img src="29mar2020/covid-world-norm2.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>confirmed cases per million                                                                                       inhabitants</B>, plotted on a log scale, against time.  The
country curves are shown offset by the amounts shown.</LI>
<LI>Canada has been tracking along the 35% daily increase curve that
most other countries have followed before social isolation measures
were introduced, started on a downturn, then had a big step increase.
I'm told this is likely to be due to a large number of people
returning from spring break in the US.

<LI>New Zealand is proceeding along the 35% daily increase curve with
remarkable accuracy, and has just passed the point where the increase rate started to reduce in Italy.
</UL>
<hr><P><h3><a name="covid-world-norm3"></a>Italy, Israel, Pakistan, Turkey, South Africa, Russia, Saudi Arabia</h3><P>
<img src="29mar2020/covid-world-norm3.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>confirmed cases per million                                                                                       inhabitants</B>, plotted on a log scale, against time.  The
country curves are shown offset by the amounts shown.</LI>
  <LI>Canada has been tracking along the 35% daily increase curve that most other countries have followed before social isolation measures were introduced, but is showing a lower increase rate the last four days.
  <LI>Israel's lower increase a week ago turned out to be a false hope, as they moved back to tracking just below the 35% curve afterwards.
  <LI>Chile and New Zealand appear to be roughly following the 35% daily increase curve.
  <LI>Pakistan has seen very rapid rises, but is now converging on the 35% daily increase curve about 28 days behind Italy.
</UL>
<hr><P><h3><a name="deaths-us"></a>Deaths: USA: Italy, France, USA, Germany</h3><P>
<img src="29mar2020/deaths-us.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>deaths per million
      inhabitants</B>, plotted on a log scale, against time.  The
      country curves are shown offset by the amounts shown.</LI>
<LI>Confirmed cases in the US have been growing very fast recently.
The US testing procedures were very slow to get started, but are
reported to have scaled up quickly.  How much of the rapid increase in
case data is due to this scale-up?  This graph shows the US death
rate, with Italy and France for comparison.  When looking at confirmed
cases, the US is roughly 15 days behind Italy, whereas when looking at
death rates, the US is roughly 19 days behind Italy.  This probably
indicates that a small part of the recent increases is indeed due to
improved testing, but the difference is nowhere near as large as
Germany or Luxembourg, so the underlying infection rate must also be
high.  If this gap widens in the future, then this would be evidence
  that testing is getting ahead of the epidemic.
  <LI> To put this in perspective if Italy is identifying just the ~10% of infections that need ICU care, the US is probably identifying very roughly ~30% of infections. (1.35 ^ 4 ~= 3)
</UL>
<hr><P><h3><a name="covid-world-sa2"></a>South America (Andean): Italy, Chile, Ecuador, Peru, Bolivia, Argentina</h3><P>
<img src="29mar2020/covid-world-sa2.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>confirmed cases per million                                                                                       inhabitants</B>, plotted on a log scale, against time.  The
country curves are shown offset by the amounts shown.</LI>
<LI>Data on this graph comes directly from the <a
href="https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data">JHU
dataset</a>, or from the Wikipedia dataset which is often better
quality.  I have not double-checked the data, and it may lag by up to
a day.

<LI>South American countries seem to be clustered into two: Andean
states except for Columbia have recently been tracking roughly along
the 22% daily increase curve, roughly following the track taken by
Italy.

<LI>Cases in Ecuador were increasing significantly faster than 35% per
day until a week ago.  This usually indicates that the epidemic has
spread without being detected, and testing is now catching up.  For
the last week, increase rates declined significantly, to less than
15%.
</UL>
<hr><P><h3><a name="covid-world-sa3"></a>South America: Italy, Brazil, Colombia, Uruguay, Paraguay, Venezuela</h3><P>
<img src="29mar2020/covid-world-sa3.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>confirmed cases per million                                                                                       inhabitants</B>, plotted on a log scale, against time.  The
country curves are shown offset by the amounts shown.</LI>
<LI>Data on this graph comes directly from the <a
href="https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data">JHU
dataset</a>, or from the Wikipedia dataset which is often better
quality.  I have not double-checked the data, and it may lag by up to
a day.

<LI>South American countries seem to be clustered into two: Andean
states except for Columbia have recently been tracking roughly along
the 22% daily increase curve, roughly following the track taken by
Italy.  The rest of South America seems to be fairing considerably better, with lower overall numbers of cases and lower increase rates.  Growth is still exponential though.
</UL>
<hr><P><h3><a name="covid-world-ca"></a>Central America: Italy, Panama, Dominican_republic, Mexico</h3><P>
<img src="29mar2020/covid-world-ca.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>confirmed cases per million                                                                                       inhabitants</B>, plotted on a log scale, against time.  The
country curves are shown offset by the amounts shown.</LI>
<LI>Data on this graph comes directly from the <a
href="https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data">JHU
dataset</a>, or from the Wikipedia dataset which is often better
quality.  I have not double-checked the data, and it may lag by up to
a day.

<LI>Panama, Mexico and the Domincan Republic all seem to be following
the track paved by Italy, though they are at different stages along
this track.

<LI>In part, the reason Mexico is further behind is simply because it
has a larger population; as the outbreak is not evenly distributed,
this may underplay the severity in the outbreak clusters.</UL>
<hr><P><h3><a name="covid-world-seasia"></a>South East Asia: Italy, Thailand, Taiwan, Philippines, Vietnam, Cambodia</h3><P>
<img src="29mar2020/covid-world-seasia.png"><P>
<UL>
<LI>The graph shows cumulative number of <B>confirmed cases per million                                                                                       inhabitants</B>, plotted on a log scale, against time.  The
country curves are shown offset by the amounts shown.</LI>
  <LI>Data on this graph comes directly from the <a href="https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data">JHU dataset</a>.  I have not double-checked the data, and it may lag by up to a day.
  <LI>I have included a graph for Vietnam, Cambodia, Taiwan and the Philippines, not because the situation there is bad (they all have a few weeks lead time to prepare), but because the trend for each has recently started to look worrying.  
</UL>
<hr><P><h3><a name="covid-world-warm"></a>Warm Countries: Italy, France, USA, Brazil, Australia, Malaysia, Qatar, Thailand, Bahrain, Indonesia, Kuwait, Egypt, India</h3><P>
<img src="29mar2020/covid-world-warm.png"><P>
<UL>
<LI>The graph shows <B>cumulative number of confirmed cases</b>, plotted on a log
scale, against time.  The country curves are shown offset by the
amounts shown. </LI>
  <LI>Very few warm countries have enough cases to establish a clear
  increase rate trend.  The graph shows number of confirmed case for
  some typical "cool" countries and some "warm" ones.  During the
  timescale shown, Spain had experienced cool weather.
  <LI>Malaysia, India, Bahrain, Kuwait and Egypt are all warm countries and have all been experiencing
    roughly 14% daily growth.
  <LI>Australia used to be on the 14% curve, but ten days ago it
  switched to the 22% curve.  The results from ten days ago correspond
  to infections from roughly 17-20 days ago.  The mean daytime
  temperature in Sydney for the five days before March 3rd (17 days
  ago) was 28.6C, whereas for the five days after March 3rd it was
  23.8C.  More analysis is needed to know if this is significant.
  <LI>Malaysia had a large increase four days ago, but since seems to be tracking close to 14%.
  <LI>Brazil seems to be tracking roughly along the 35% line, which seems to run counter to warm weather inhibiting the spread of the virus.
  <LI> Both Qatar and Bahrain have very low recent increase
  levels. This may indicate that most cases were imports, and that
  local spread has been effectivel contained.
  <LI>Although Singapore has a warm climate, I have ommited it from
  this graph, because strong contact tracing there dwarfs any
    climate-dependent effect we might observe.
  <LI> In general, it does appear that COVID19 may spread more slowly in warm climates, but the evidence is inconclusive, with Brazil being the main counterexample.
</UL>
<hr><P><h3><a name="covid-world-warm2"></a>Warm Countries: Malaysia, Qatar, Bahrain, Egypt, India, Kuwait</h3><P>
<img src="29mar2020/covid-world-warm2.png"><P>
<UL>
<LI>The graph shows <B>cumulative number of confirmed cases</b>, plotted on a log
scale, against time.  The country curves are shown offset by the
amounts shown. </LI>
  <LI> The graph shows number of confirmed cases per million
  inhabitants, plotted on a log scale, against time.  The country
    curves are shown offset by the amounts shown.
  <LI>This graph shows the same warm countries as the previous graph.
  <LI>Australia had been tracking along the 14% curve, but the last few day this has increased to 25% daily increase per day.  Australia has been cooler recent as it moves into Autumn.
  <LI>In general, all the warm country data is quite noisy.  Partly this is due to there being few cases in each country.  All these countries are showing a lower average increase rate to that see in Europe or the US.
</UL>
<hr><P><h3><a name="covid-world-linear"></a>World: China, Italy, Iran, France, USA, South Korea, Japan</h3><P>
<img src="29mar2020/covid-world-linear.png"><P>
<UL>
<LI>The graph shows <b>number of confirmed cases</b>, plotted on a
linear scale, against time.  The country curves are shown offset
by the amounts shown.</LI>

 <LI>In the other graphs I use a log scale on the y-axis because
    exponential growth gives a straight line on a log-linear graph, and this makes changes in the growth rates visible and allows exponential growth rates to be compared. However, many
    readers have told me they don't like log-linear graphs, so this one is for them.  It
    has to be truncated, or you cannot see any information.  It
    doesn't really show anything additional over the log graphs,
    except it looks scarier and shows how much worse things are set to get if effective measures are not taken.
    <LI>I have shown the China curve until the daily increase rate
    drops below 0.1%.  The glitch in the center of this curve is a
    change in measurement methodology.  If Italy followed a similar
    curve, this wave of the epidemic may have abated in 30 days time,
    but this prediction should be tempered by the fact that Italy has
    not quite reached the logistics curve inflection point, though it
    appears to be close.  On this basis, because deaths lag infections
      by 1-2 weeks, the worst is yet to come for many Italian hospitals.
   <LI>One thing this view shows well is how much of an outlier the US
   is - the faster increase rate of the US
   curve is self-evident.  The US exceeded both China and Italy's
   case counts today.
<LI>This view also makes clearer the recent restart of exponential
  growth in Iran.  It is unclear to me whether exponential growth
  actually had previously stopped in Iran, or whether the increase
  rate was simply limited by their testing capacity.  If it was the
  latter, then something about their process for confirming cases has
  changed.
</UL>
<hr>
<h3>Thoughts</h3>
<P>
    While you're sitting pondering your mortality, think how astounding it is that one single viral particle from a bat can replicate so far, so fast, and cause so much trouble!  Biology is truly amazing!
</P>    
<h3>FAQ</h3>
<P><B>Q: Where does the data come from?</B>
<P>Where possible, the data comes from the relevant national
authorities, as they tend to be more up to date.  In some cases I'm
using
the <a href="https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports">WHO
daily briefing</a>, but they lag the national authorities somewhat.
The <a href="https://en.wikipedia.org/wiki/2019%E2%80%9320_coronavirus_pandemic">wikipedia
pages</a> contain links to the national authorities.  Some are
  <a href="https://thl.fi/en/web/infectious-diseases/what-s-new/coronavirus-covid-19-latest-updates">Finland</a>,
  <a href="https://www.santepubliquefrance.fr/maladies-et-traumatismes/maladies-et-infections-respiratoires/infection-a-coronavirus/articles/infection-au-nouveau-coronavirus-sars-cov-2-covid-19-france-et-monde">France</a>,
  <a href="https://www.rki.de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/Fallzahlen.html">Germany</a>,
  <a href="https://www.gov.ie/en/news/7e0924-latest-updates-on-covid-19-coronavirus/">Ireland</a>,
  <a href="https://www.fhi.no/sv/smittsomme-sykdommer/corona/dags--og-ukerapporter/dags--og-ukerapporter-om-koronavirus/">Norway</a>
  <a href="https://www.moph.gov.qa/english/Pages/Coronavirus2019.aspx">Qatar</a>,
  <a href="https://www.gov.si/teme/koronavirus/">Slovenia</a>,
  <a href="https://www.cdc.go.kr/board/board.es?mid=a30402000000&bid=0030">South Korea</a>,
  <a href="https://www.mscbs.gob.es/profesionales/saludPublica/ccayes/alertasActual/nCov-China/situacionActual.htm">Spain</a>,
  <a href="https://www.bag.admin.ch/bag/en/home/krankheiten/ausbrueche-epidemien-pandemien/aktuelle-ausbrueche-epidemien/novel-cov.html">Switzerland</a>,
  <a href="https://www.gov.uk/guidance/coronavirus-covid-19-information-for-the-public">UK</a>,

<P><B>Q: Can I have your data?</B>
  <P>My data is <a href="https://github.com/mhandley/COVID19/">on github</a>..
  <P>A more complete dataset is the <a href="https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data/csse_covid_19_time_series">Johns Hopkins</a> one. It tends to lag the national data sources and the WHO, but it is complete and machine readable.

  <P><B>Q: Can I use your graphs?</B>
  <P>
    Yes, they're under a CC0 "No rights reserved" license.  You can
    use them for any purpose.  I'd prefer you link back here though,
    as the explanations add important context.

  <P><B>Q: Different countries are testing at different rates.  How can you compare the data?</B>
    <P>So long as the fraction of actual cases being detected does
    not change, this does not affect any inference we can make about
    the growth rate.  35% growth is still 35% growth, whether we
    measure 100% of the cases or 50%.
    <P>If, for example, Italy is detecting 50% of the cases and the
    US is detecting 25% of cases, this affects any predictions of how
    far the US is behind Italy At 35% growth, cases double every 2.5
    days, so this undersampling would show the US 2.5 days further
    behind than it really is.
    <P>Likely no-one except Korea and Singapore are getting close to
    100% of cases.  Probably everyone is detecting at least 20% of
    cases, because those require medical attention.  We don't really
    know what fraction of cases are missed, but the difference in
    sampling between countries might skew the delays by a few days in
      either direction.

  <P><B>Q: Comparing with Italy as a whole is flawed. Shouldn't you be comparing with Lombardy?</B>
    <P>Perhaps.  Certainly cases in Italy are concentrated in the
    North at the moment.  Lombardy is running about seven days ahead
    of the rest of the country, as measured by cases per million
    inhabitants. I've shown this in <a href="#g3">graph 3</a>. The
    problem is that cases in some other countries, notably France,
    Spain and the USA, are also concentrated, so comparing these
    entire countries with Lombardy is biased in the other direction.
    These graphs give a crude indication, but they're never going to
    be able to track problems down to the local level, where an
    individual town is overwhelmed by cases before this becomes
    commonplace in a country.  Just remember, to compare with
    Lombardy, a rough approximation is to move the Italy curve seven days
    to the right.
    <P><B>Q: Shouldn't you break out China by province?</B>
    <P> At the moment I'm only showing China on the graphs that show
    absolute counts, not counts per million inhabitants.  As the vast
    majority of Chinese cases were in Hubei, there's not a great deal
    of difference on these graphs between showing Hubei and showing
    all of China.  The population of Hubei provice is around 57
    million, which is roughly the same as Italy.  Thus the data for
    China is reasonably comparable with the data for Italy.
<P>
   The Chinese data is somewhat suspect in the early days, so it's not
   very good for comparison until the epidemic gets a fair way along.
   Mostly I'm using Italy to provide a model for how other places
   might progress, as it's a better fit.  But as of March 16th, I've
   changed the last (linear) graph to use the Chinese data to show one
   possible direction that Italy might folliow.
<P>
   Elsewhere in China, cases that arose were stamped on quickly, and
   pretty much all of China shut down until that was complete.  In
   Europe we failed to learn from that model, so we're all much
   further along than Beijing, Shanghai, or similar provinces ever
   got.
      
  <P><B>Q: Why didn't you show my country?</B>
    <P>A1. Until the number of cases reaches around 100, the data
    tends to be too noisy to draw conclusions
    <P>A2. The graphs are pretty cluttered as it is.  
    <P>A3. I'll add more as I find time.

  <P><B>Q: You aren't an epidemiologist. Why should I listen to you?</B>
    <P>You probably shouldn't.  I'm a computer scientist and I've
    spend decades analysing data, but you should talk to a real
    epidemiologist if you want to understand the underlying causes.
    Computer scientists do know a lot about exponential growth though.
  <P><B>Q: I'm a journalist.  Will you appear on my TV show?</B>
    <P>No. You should have a real epidemiologist on your TV show.
  </DT>
</DL>
<P>
  Mark Handley, UCL.
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