Exponential coronavirus growth

In these days of emergency for Covid-19 we are bombarded with conflicting news: alarmist messages on the one hand, hymns to normality on the other.

Coronaviruses are a large family of respiratory viruses that can cause mild to moderate illnesses, from the common cold to respiratory syndromes. The virus responsible for the current pandemic is a new strain of coronavirus never previously identified in humans. The contagiousness of this virus can be described through a statistical factor called R0.

The R0 value, or the "basic reproduction number", indicates the average number of infections directly caused by each infected individual since the beginning of the epidemic.  If R0 is 2 it means that on average each infected person will infect two people, so the higher the R0 value, the higher the risk of spreading the virus. If R0 is less than 1 (ie each infected infects less than one person), it means that the infection will tend to extinguish naturally because the number of infected will progressively decrease.

Initially, the spread of the virus could be described by an exponential function.

Exponential growth occurs when the growth rate of a mathematical function is proportional to the present value of the function. It appears initially characterized by a rather slow trend which then undergoes a sudden acceleration.

However, the type of growth previously illustrated do not accurately describe the trend of the situation as they are far from a realistic model.  A logistic function describes a curve whose growth is initially almost exponential, then slows down, becoming logarithmic, to reach an asymptotic position where there is no more growth.  Through this type of function it is in fact possible to observe how, in the case of an epidemic, the presence of healed and deaths decreases the R0, contributing to the slowdown, stabilization and resizing of the phenomenon analyzed.

In concrete terms, it is the behaviors that determine the changes. If lockdowns and restrictive measures had not been implemented, the peak of infections and the number of deaths would have been higher.

The graphs have helped to raise awareness of the extent of the phenomenon and also highlight the progress made by the company over the past few months.