Existence and uniqueness results for a smooth model of periodic infectious diseases. (English) Zbl 1470.45006

Summary: We prove the existence of a curve (with respect to the scalar delay) of periodic positive solutions for a smooth model of Cooke-Kaplan’s integral equation by using the implicit function theorem under suitable conditions. We also show a situation in which any bounded solution with a sufficiently small delay is isolated, clearing an asymptotic stability result of Cooke and Kaplan.


45G10 Other nonlinear integral equations
92D30 Epidemiology
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