VISUALISING THE REPRODUCTION NUMBER GIVES KEY INSIGHTS IN HOW A VIRUS SPREADS AMONG SO MANY
Definition (wiki): “The effective reproduction number Re is used, usually written as Rt, or the average number of new infections caused by a single infected individual at time t in the partially susceptible population.”
Considering one person infected, let’s imagine this person can infect 2 people. After one step we are going to have 2 infected people. the second step the two people infected are going to infect two people more, we end up having 4 infected.
We can calculate till 10 steps, then 1024 people are infected.
Calculating until 20 steps and the below graph will show the total number of people infected.
More than a million infected in only 20 steps! So far we have seen that every person can infect 2 other people, or the average number of new infections caused by a single infected individual is 2, or in other words Rt = 2.
Lets now consider the Rt = 1.2 and we see the graph below
At step 20 there are a bit more than 38 new infected. Rt = 1.3 instead.
We can see by the above graph how important is the value of the Rt number.
Even with small changes, after 20 steps we can have more than a million infected when the Rt is equal to 2, instead 38 when the Rt is 1.2
What is positive about this?
Let’s consider a situation where the Rt = 0.8.
After 20 steps 0.01 new people are infected! Every step we need to multiply the new infected to a number less than 1, so after 20 steps we are going to end up with a number way lower than 1, almost 0.
Let’s now consider three Rt values = 1.1, 1.2, and 1.3 (in the graph R1, R2, R3) at the same time, and let’s focus on the differences.
In order to understand the three curves we need to read the graph vertically
When Rt grown also the variation of the Rt itself become more intensive. In the left graph above we see the Rt at step 14 and on the right graph the Rt at step 16. Going from Rt 1.1 to 1.2 there is little variation, but variations of Rt from 1.2 to 1.3 are way wider.
What this can teach us?
Our behavior allows us to variate the Rt number. Each of us affects the Rt number and its variation. If we keep the number of Rt below 1 the health system won’t have any more stress and our life can go back to normal. All of us count in the fight against this pandemic.