# Evolution of R0 in Germany, France, Spain, UK and USA

In analysing epidemics, the so-called R0 parameter is of crucial importance. Specialists in the sector also address  it as the basic reproduction number, since it indicates the number of  infections directly generated by each case in a given population. The reason for its interest lies in the fact that the value of R0 indicates the trend of the epidemic and determines whether it is decreasing, increasing in its intensity, or still around its peak.

But how is R0 calculated, exactly?

To understand this, we should take a step back to understand, first, the fundamentals of how an SIR model works.

The simple SIR is one of the most used models in epidemiology and it is based on the prediction of 3 numbers: S, I, and R. For a given population, S is the number of susceptible individuals, meaning all the people who haven’t contracted the virus yet; I is the current number of infected, while R stands for “removed” and is the amount of people who have developed immunity (are healed) or deceased.

In the SIR model the predictions for these 3 counters rely on 2 parameters: and . The first defines how fast susceptible individuals become infected and the second is the speed of their removal (i.e., how fast they heal or die). In a population where the number of infected is one or more orders of magnitude less than the total, the number R0 can be easily approximated by the ratio of these 2 numbers:

Luckily, this is the case of every country considered so far. This remains true even if a large fraction of asymptomatic people is present, since the number of infected (detected) people is small compared to the population, in all of the countries that have been considered.

From this simple definition we understand that R0 can provide us with information on the intensity with which the epidemic is spreading. If R0 is greater than 1, the epidemic is spreading and, the higher the value, the faster it is. When R0 is less than 1, it means that the speed of infection is less than the speed of removal, indicating that the disease is in a phase where it is containable.

In the CoVstat_IT project, we decided to stress particularly the parameter R0 and its evolution. We have analysed its trend for 5 different countries besides Italy: Germany, Spain, France, UK, and USA within the timeframe between the last week of February and April 16th, using the data collected by the World Health Organization. Generally speaking, we have noticed that the behavior is quite similar in different countries. As a general trend, they all appear to decrease and, for Germany and Spain, R0 is reaching the value 1, or even less, just in these days. In particular, the most positive scenario is the one of Germany where in some days R0 is becoming lower than 1. At the beginning of the epidemic, R0 reaches values from 5 to 10, depending on the country considered. Then, R0 decreases with the start of the containment. We have noticed that, empirically, R0 decays exponentially in most of the cases, with a time scale of 3 weeks or more (meaning that after 3 weeks R0 becomes R0/2.7).

In the next few days, we will continue monitoring the data as they become available and update our calculations.

Author Details
PhD Student , UnivAQ
Mi sono laureata in Fisica delle Particelle e ora sono all’ultimo anno di dottorato presso l’Università dell’Aquila. Nella mia ricerca mi occupo di fisica delle alte energie in ambito fenomenologico, studiando in particolare neutrini e raggi gamma di natura astrofisica. Grazie al mio lavoro mi sono interessata alla programmazione per l’analisi dati, di cui sto attualmente approfondendo lo studio. Il resto del tempo lo dedico alla mia altra grande passione: viaggiare.
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PhD Student , UnivAQ
Mi sono laureata in Fisica delle Particelle e ora sono all’ultimo anno di dottorato presso l’Università dell’Aquila. Nella mia ricerca mi occupo di fisica delle alte energie in ambito fenomenologico, studiando in particolare neutrini e raggi gamma di natura astrofisica. Grazie al mio lavoro mi sono interessata alla programmazione per l’analisi dati, di cui sto attualmente approfondendo lo studio. Il resto del tempo lo dedico alla mia altra grande passione: viaggiare.
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