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A possible control strategy against the spread of an infectious disease is the treatment with antimicrobials that are given prophylactically to those that had con- tact with an infective person. The treatment continues until recovery or until it becomes obvious that there was no infection in the flrst place. The model consid- ers susceptible, treated uninfected exposed, treated infected, (untreated) infectious, and recovered individuals. The overly optimistic assumptions are made that treated uninfected individuals are not susceptible and treated infected individuals are not infectious. Since treatment lengths are considered that have an arbitrary distribu- tion, the model system consists of ordinary difierential and integral equations. We study the impact of the treatment length distribution on the large-time behavior of the model solutions, namely whether the solutions converge to an equilibrium or whether they are driven into undamped oscillations.

An Epidemic Model With Post-Contact Prophylaxis of Distributed Length II. Stability and Oscillations if Treatment is Fully Effective