This paper considers a deterministic model in the theory of contagious disease. The major assumption made is that all infected individuals remain in the population to spread the disease. For this particular case an exact solution can be obtained for the differential equation arising from the mathematical model. However, a more generally useful numerical method using the Runge ‐‐ Kutta ‐‐ Fehlberg algorithm is applied and is found to give highly accurate results. This work could well form the basis of useful mathematical modelling projects in the classroom.