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Epidemic spread correlates to life expectancy

Understanding the dynamics of an epidemic progression depends on a country’s ability to identify and count contagion cases.
This ability, having an impact on the measured data, can alter the perception of the problem.
For example, a country with a low capability to detect infections could mistakenly appear, and consider itself, less affected by the epidemic than another country, perhaps less affected in absolute terms but with a better detection capacity.
We can expect that many heterogeneous factors affect the detection capability. Such factors may include: the organization and capillarity of health systems; the level of attention of the population to health-related issues; the spread of information; the ease of access to care.
It is difficult – perhaps impossible – to identify a single synthetic factor that can represent all these aspects in a synoptic way. Among the possible options, life expectancy at birth is considered here.


We tried to evaluate whether there could be any link between the number of infections in European countries, expressed as the total number of cases per million inhabitants, and the life expectancy of that country.
A preliminary analysis showed that there is actually an exponential trend: the number of infections per million inhabitants grows exponentially with life expectancy in a given country.
The fitting was repeated over several days, from 18 to 28 March 2020, verifying a monotonous growth in the determination coefficient (R^2).
The following figure shows the fitting with data related to 27 March 2020.


We found the following correlation law (R^2 = 0.66):

    \[y = 1.5208 ln (x) + 72.249\]

(1)
where y is life expectancy at birth and x is the number of infections per million inhabitants.

To evaluate the predictive capacity of this equation, we proceeded as follows.
Since each Italian region is characterized by its own regional health system and specific demographic data, including life expectancy, the relationship (1) has been used to predict the number of infections.
The following figure compares predicted and real values (official data updated on 27/03/20).

As expected, the infection rate is lower than the real one only for the northern regions, most affected by the Covid-19 epidemic; the expected value is instead an underestimation of the real value for the central-southern regions, which probably benefited from the containment measures implemented by the Italian government, that slowed down the spread of the virus.


In conclusion, it is believed that there is a non-negligible correlation between the number of infections observed in a country and life expectancy in that country.
Furthermore, the relationship found has a certain predictive power, although the data are affected by a significant dispersion.

The origin of this relationship remains to be understood. It is probable that the effort for its understanding may shed light on the deeper implications of diversity in life expectancy among various countries.

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