A note on the existence of positive bounded solutions for an epidemic model

In this short note, we establish an existence and uniqueness theorem about a positive bounded solution for a nonlinear infinite delay integral equation, which arises in some epidemic problems. As one can see, our main result can deal with some cases, to which many previous results cannot be applied. In addition, we show that our main result can also be applied to a Lasota–Wazewska model.