Every time a person becomes sick the number of Susceptible persons decreases by one. So the rate of change of the Susceptible population is the negative of the transmission rate.
S' = - a* S * I
The rate of change of the Infected population is affected by the transmission rate as well as the recovery rate. Every time a person becomes sick the Infected population increases by 1. On the other hand every time a person recovers the Infected population decreases by 1. So the total rate of change of the Infected population is the sum of the transmission rate plus the negative of the recovery rate.
I' = a S * I - b I
To complete the model we need to specify the numbers of people in each of the 3 groups initially. Let's consider the model to be at the beginning of an epidemic so that the number of recovered people is 0. In this case we only need one parameter to describe the situation, namely the number of people who are initially infected. The number of susceptible will then be the total number in the population minus the number of people who are initially infected.
In the following applet the above described model is graphed. You can change the 3 parameters discussed above, the transmission rate, the recovery rate, and the initial infected population number. You will notice that radically different curves can be produced.