In 1995, a disease control and intervention project was initiated in Malmöhus county in southern Sweden to limit the spread of penicillin-resistant pneumococci. Since most of the carriers of pneumococci are preschool children, and since most of the spread is believed to take place in day-care, a mathematical model, in the form of a stochastic process, for the spread in a day-care group was constructed. Effects of seasonal variation and size of the day-care group were particularly considered. The model was then used for comparing results from computer simulations without and with intervention. Results indicate that intervention is highly effective in day-care groups with more than ten children during the second half of the year.