# Exercising with numbers: solution

In this article Jakob Zinsstag explains the solution for the exercise presented in the previous step.

Here you find the solution to the exercise of the previous step. If desired, you may download a completed spreadsheet.

The formulas should be:
(S_{(T+1)})= B2 + ($F$2 * (B2+C2+D2)) – ($E$2 * B2 * C2) – ($F$2 * B2)
(I_{(T+1)})= C2 + ($E$2 * B2 * C2) – ($F$2 * C2) – ($G$2 * C2)
(R_{(T+1)}) = D2 + ($G$2 * C2) – ($F$2 * D2)

The graph should look like this:
Time dependent changes in the numbers of susceptible, infectious and recovered individuals. © Jakob Zinsstag

We observe an initial epidemic peak and then an on-going low level of transmission.

The formula works with non-integer numbers. In principle, there should only be integers if we assume individuals. This problem can be overcome if we assume that we deal with large numbers, for example, a million people instead of one thousand. The model uses discrete time steps, which is a good approximation if the time steps are short (like days) but performs poorly if the time steps represent years.