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Negative criteria for the existence of periodic solutions in a class of delay-differential equations. (English) Zbl 1087.34542

The authors consider the class of delay-differential equations with distributed delay which can be transformed into an equivalent expanded system of ordinary differential equations (“linear chain trick”). To that system they apply the criterion of Li and Muldowney on the nonexistence of nonconstant periodic solutions for autonomous systems in \(\mathbb{R}^n\). The obtained results are applied to a SIR epidemic model.

MSC:

34K13 Periodic solutions to functional-differential equations
92D30 Epidemiology
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