How to analyze if a specific event caused an increase in coronavirus cases? I'm going to post a question related to the current events and I think it could be very interesting.
In the midst of the crisis with the coronavirus, Croatian capital of Zagreb was hit by a strong earthquake on March 22. Since a lot of people escaped their homes in panic, there were fears that the earthquake would cause an increase in the cases of coronavirus since people didn't obey the rules of social distancing when they escaped outside due to the earthquake.
The Director of the Croatian Institute for Public Health, Krunoslav Capak, said that they conducted some preliminary analyses that suggest that the earthquake didn't cause an increase in the number of COVID-19 cases. The analyses are preliminary becuase the incubation period of the virus is known to be as long as 14 days, so it's possible that the effect is not visible yet.
Regardless of the incubation period length, I was confused by Capak's statement because I cannot think of a statistical method I would use to make that inference. Does anyone know what analyses was Capak referring to? What statistical analyses would be appropriate to determine if there was an increase in the number of COVID-19 cases in Croatia due to the earthquake?
The number of coronavirus cases in Croatia can be found here: https://github.com/viborccom/data/blob/master/covid-19/croatia/time-series.csv?fbclid=IwAR2ekRN44WnKwlTQJAgpfYyJTz01GedrqJupB28d-g_KoGBnroIGWt8Jb58
 A: You might wonder whether an increased infection rate during a short period could be observed in the figures of reports on infected cases or the death rate.
However, this is not feasible with the data available


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*The effect get's diluted The effect is likely to be very small in the observations (unless the infection rate is very large). 


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*If there is an increase in transmission then this will occur only in a small group, which gets diluted by the larger total number of Zagreb and the surroundings. 

*Also the time of the event is only very short and the contact between people is very local. Social distancing is 'the way to go', but it matters with which persons and how long you have contact. 
Complete strangers in a supermarket are much more a risk than your neighbors (if your neighbors got the virus than you are already at high risk to get the virus as well, being outside is not gonna change this a lot). There is a large multitude of ways how the virus can spread. If we are traveling a lot, moving around over long distances, then the virus is moving a large distance quickly and will infect a lot of people quickly. The local transmission is of less concern (in terms of speed of transmission, and flattening the curve, the local transmission is eventually determining how many people get sick. The long range transmission is determining how fast people get sick*).


*Ad hoc ergo propter hoc Even if there is a change in the trend/growth in the number of infections or the number of death cases, then it will be very difficult to connect this observation to a specific event. There are too many variables that are changing such that it is not possible to draw strong conclusions about causal relationships based on correlations.
The current cases in Zagreb and Croatia are very small. So the number will be expected to rise, already without an earthquake. This rise will occur with lots of uncertainty**. The information and background information is so noisy that it is not possible to make a lot of sensible predictions.
See the past reports on the cases below. The curve is not a nice straight line and is varying in growth rate and bumpy. It is very difficult to make a specific relation between specific events and this curve. That is because the time between infection, start of symptoms, and start of registration/confirmation occurs with an unknown delay.


*Time delay Also, there is a delay in reporting of the numbers. This makes the above effects count stronger. It will take two weeks before the effect of increased transmission is measurable. But at that time many more events have happened which may cause an effect as well. And also the time delay is a random value. What happens now in a single day, will not create a sudden peak of a single day two weeks later, but instead it gets spread out over multiple days and becomes less noticeable (and then there are also large high noise levels in the measurements which might be a fourth point). 
denominator. Furthermore, there is always a few weeks of delay in death registration and reporting. Hence, the EuroMOMO mortality figures for the most recent weeks must be interpreted with some caution.

*A simple model that shows how the reduction in the long-range transmission is having a strong effect and going on the streets and have local community spread is slightly less worrisome. I used the code from this answer which made used of a $R_0$ for short distance transmission and a $R_1$ for long distance transmission. I did two computations, one with $R_1 = 0.25 , R_0 = 2.25$ and one with one with $R_1 = 0 , R_0 = 2.5$. The total reproduction rate, $2.5$, is the same, but the models deviate quickly once the infection reaches the edges of the neighborhood.
**In the Netherlands the officials were counting on a very specific rise of cases in the Intensive Care. Now... they are surprised that it did not turn out to be that specific number and it is a larger number than predicted (they were expecting 1600 people in the Intensive Care at some date, and not this is gonna happen a week earlier than expected)
Me... I am surprised that they are surprised about the number turning out to be different. These sort of predictions should have been made with a very wide confidence interval indicating that there is very little certainty about the forecasts.
