We could try and add up all these values to work out the expected outbreak size. But fortunately there’s an easier option. In the nineteenth century, mathematicians proved that there’s an elegant rule we can apply to sequences like the one above. If R is between 0 and 1, the following equation is true: 1 + R + R2 + R3 + … = 1/(1–R) In other words, as long as the reproduction number is below 1, the expected outbreak size is equal to 1/(1–R).
