Coronavirus 2: Graphical representation of covid19 spread in different countries                           

Coronavirus 1: A 5-min read that can hopefully save some lives



Graphical representation of coronavirus spread in different countries  


                                            Florence, Mar 9, 2020

A very good graphical representation of what I was trying to convey in words in my previous post. This is what it looks like when the epidemiological curves of different countries are aligned in time.

Graphical representation of coronavirus spread in different countries

(Source: Jean-Baptiste Mouret, INRIA, France; his original Facebook post;
Data from

First note the acceleration of the spread in all these curves (it's getting steeper and steeper with time).

Note also that there are some differences between the curves. It's probably too early to speculate about the underlying reasons but influencing factors could include variances in

- Demographics (e.g. more or less elder people)
- Population density, connectivity within the population (typical housing situation, average social life etc.)

- Number of tests administered (Accuracy of the data)

- Resources and efficiency within the health system
- Time to prepare for the epidemic (!)
- Measures taken and their effectiveness (!)

The countries where the virus arrived later had more time to prepare. And for them the future course of the curve is still to be decided. So let's not waste this opportunity. Taking and adhering to measures that prevent the spread can make all the difference!!!



A 5-min read that hopefully can save some lives. Please share!              


                                            Florence, Mar 5, 2020

Short summary:
Please all remain calm. No need to worry too much. But also: Please worry just enough so that you take all the necessary precautions against the coronavirus. If you are not overly concerned for yourself because you're young and healthy, that's good. However, please do not forget those with pre-existing conditions, the sick and the elderly, since they are the ones that are most at risk. This includes some children but maybe also your parents or your grandparents. For them the extra years that they may or may not get to live make all the difference in the world.     
The following post on the coronavirus and its spread was written from the perspective of someone living in Florence, Italy, on March 5, 2020. However, given the current situation and outlook everywhere many of the underlying ideas should be quite generalisable to other places and times. I just posted this on the local Facebook page “Foreigners in Florence”, mostly in reply to local people (understandably) urging people to not give up on visiting Italy (in particular Tuscany):
As a scientist with some knowledge about the spread of epidemics I would like to offer some explanations and thoughts about the current situation regarding the Coronavirus. In particular I would like to explain the reasoning behind some of the measures being taken right now and even more to encourage everyone to follow them as much as possible.
In order to bring my points across I need to be a bit alarmist now and then but I really think this is necessary (“better safe than sorry”). I tried to be as understandable as possible, but if you have questions or comments I would be happy to either address them myself (if I can) or refer you to someone who can (a website or a person). Also please feel free to share this. I would be even happier if someone could translate this to Italian. I do speak the language but it would be much clearer if a native speaker could do the translation. The more people start to act the better for all of us.
Epidemics tend to spread exponentially and this is currently true for the coronavirus as well. What this means is that for now every person who has the coronavirus infects on average between 2 and 3 other persons. The current best estimate for this number is 2.2 but for simplicity let’s assume it is 2. This means the first sick person in Italy infected 2 persons, these 2 infected 4, those 8, then 16 and so on.
One can see where this leads, both the number of new cases and the overall number of cases increase with bigger and bigger jumps, so there is not only further and further spread but the spread actually accelerates. That’s exactly what is happening now all over the world. For example, it took Italy about two weeks to go from the first case to 1500 cases but it took just three days to go from 1500 cases to 3000 cases.

For now unfortunately this acceleration will continue. We are clearly on the rising part of the curve (“it will first get worse before it will get better”). In order for the epidemic to die out as quickly as possible we need to press this number mentioned above from 2.2 to below one (which would mean that over time both the number of new cases and the overall number of cases would fade away).
There are various ways to do that, for example large-scale vaccination. This would decrease the number of susceptible people in the population until at some point the virus can’t find any new hosts and slowly fades away. Unfortunately, current estimates expect the availability of a corona-vaccine to be about a year away (first the development itself, then many tests for side effects etc.).
So the next best thing and at the moment our only viable solution is to slow down the spread. For this people need to finally take the epidemic seriously and behave accordingly (i.e. follow medical and governmental advice, avoid large crowds, wash hands etc., basically do everything possible to prevent a further spread of the virus). The earlier and the more we do that, the less likely are new infections, and the faster we reach that magic number of less than 1 new infection for each existing infection.
What makes the whole situation slightly worse is that the numbers we hear are the number of identified cases and for this there are two things to consider: the quite long incubation period (there is a delay of about 5 but up to 14 days from getting the disease to showing first symptoms) and the fact that even after the incubation period 80% of cases are quite mild. Both of this implies that a lot of sick people are not getting tested and thus do not show up in the statistics.

So at each point in time there are many more unidentified than identified cases in the population. For the current situation this means that unfortunately there are already a large number of infected people walking around Tuscany and inadvertently spreading the virus. This again should emphasise the urgency of the situation. So please start to act now and do not wait until we reach the numbers of Lombardy and other similarly affected regions. The only difference between them and us is that the virus got there earlier than here.

As mentioned above, the often repeated argument that for about 80% of cases the Coronavirus is basically like a regular flu is true. But there are two replies to this: First, for the other 20% it is not like the common flu at all and unfortunately it can get really bad. And, second and more importantly: if you're young and healthy and do not have a lot to fear, good for you! But please have the basic human decency to consider also the fate of those not as fortunate as you, in particular people with pre-existing conditions (and this can include children) and the sick and the elderly who are most at risk. For them the extra years that they might or might not enjoy make all the difference in the world. So maybe think of your parents and grandparents first.
Even if the epidemic can not be stopped anymore (and indeed for Italy, and probably the planet as a whole, this point seems to have passed) slowing it down is absolutely essential because it means more time for the health services to react and thus better chances of appropriate treatment for everyone that will be affected. So again, the earlier people react the better.

In this worst case of a largely undiminished spreading what should happen eventually is that more and more people will get the virus at some point or another and either recover (the vast majority of us) or pass away (about 0.5-2% *).

In the positive case that recovery would provide immunity (which unfortunately for Corona can not yet be confirmed) this would actually be very similar to the vaccination scenario described above. In fact, vaccinations are nothing else than deliberate inductions of very mild cases of the disease. But the difference to the vaccination scenario would of course be that in this worst case many people would have died, so we should really try to do everything in our power to not let it come to that.
A lot of us are in some way negatively affected by this epidemics. The sudden drop in people visiting Tuscany has devastating consequences since many jobs and incomes depend on tourism. This is obviously very unfortunate and we should do everything possible to alleviate the situation.

But as I try to explain in this post, the solution should not be just to ignore what is happening around us with the virus and to insist on going on as before. For sure we are already at the point where any unnecessary travel should be discouraged. It just contributes to a faster spreading of the virus.

So instead, better try to find other ways to help each other: Support businesses in Florence and Tuscany in general (in particular buy locally, don’t use Amazon), look out for people in need. If you want to go even further, please spend a week in a nice spa hotel in Florence or visit an agriturismo in the beautiful countryside nearby, hire a local guide etc., in short try to replace the missing tourists from far away.

If everyone everywhere would do that, we would have more winners or at least not that many losers from this situation and without any of the grave consequences of excessive travel. If the worst happens, seek help, self-isolate or help people that self-isolate (someone healthy needs to do their shopping etc.).
Currently Tuscany is about two weeks behind Lombardy on the curve. This statement actually means that inviting people to come to Tuscany in two weeks is the same as sending them to Lombardy now. Would one really want to do that?

Or think about China. What is happening there right now could also happen here in the future (hopefully not but how can we be sure?). In fact, the relative numbers of cases are already higher in Italy (Italy 6.4 cases, China 5.6 cases per 100.000 people **).

But since now we’re talking about the future, it’s still in our hands. The one thing to prevent us from reaching the high numbers of Lombardy pretty soon (or of China in the more distant future) is to start acting now so that the epidemic curve in Tuscany has a milder (less steep) course than those ones. We actually have the advantage that we have been warned, so we should not ignore these warnings.
Finally, I would like to stress that there's no need to panic (and in particular don’t take this text as an appeal to buy masks, deplete supermarkets or act in a xenophobic manner towards anyone). Life goes on and hopefully people still can enjoy many of its brighter sides (

However, it's completely reasonable to worry and take precautions. Extraordinary situations require extraordinary measures, at least temporarily. The point about closing the schools (which seems to anger many of my friends and colleagues) is that the risk of children bringing the virus home from school is right now just getting so big that we shouldn't take that risk anymore.

The children would almost certainly be fine but they would endanger their older relatives. That would be especially true here in Italy (particularly the south) where many grandparents live in the same household as their grandchildren.

In epidemics like this one, instead of doing nothing it is certainly better to prepare for the worst and be pleasantly surprised if things turn out better. And there certainly is still hope for some more optimistic outcomes. But it really depends on how each of us deals with the situation. The earlier and the better we react now, the sooner we can all get back to normal.
* According to current estimates the mortality rate is about 2% for all but around 15% for people 80 and older (both numbers should decrease considerably when also more mild cases are taken into account, current estimates for the final number are close to 0.5%).

** Italy: 6.4 cases per 100.000 people     (as of March 5:        3858 / 60.4 million)
    China: 5.6 cases per 100.000 people  (as of March 5:      80430 / 1.435 billion)

Some references for further information:

This is where I tracked the number of cases in Italy, where I got the “80% of all cases are mild” number, the estimate for the incubation period and also the mortality estimate of 2% (for comparison, for the common flu this value is 1.3). The estimate for the expected final value of 0.5% is from a calculation of Prof. Craig Feyed, a well-known epidemiologist who used the “Diamond Princess” cruise ship in Japan as starting point.  
This is where I found the number 2.2 for the estimated number of new infections per infected person.
This is an understandable description of a basic epidemiological model. The green curve in the graph shows a typical behaviour for the number of infections in an epidemic in which catching the disease and recovering provides immunity. As mentioned above it is not yet clear if this is the case for Corona (also for the flu immunity only lasts a certain time and then you can catch it again). So no one can know exactly how the Corona curve will develop in the future but it is probably safe to say that currently we are still rather at the beginning of the rising part.
Three disclaimers:

1. I am not a medical doctor so I cannot give any medical advice, please look elsewhere for this, for example here:

In case of (suspected) infection, of course better speak to a doctor as soon as possible (preferably first by telephone, do not just go to the hospital).
2. The whole text is written after quite extensive research and to the best of my (current) knowledge. But please refer to official sites for more in-depth knowledge and the latest updates.
3. I’m aware that this is a controversial debate and many people speak about hysterics, fear-mongering and spreading panic but this should not prevent us from a reasonable discussion based on facts and careful extrapolations. If someone has evidence-based counter-arguments to some of my thoughts I am very open to listen and would potentially acknowledge that you have convinced me of a different point of view. Then this would be my new recommendation based on my then best knowledge. This is how science works, recommendations get updated based on new data and information coming in.