• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.843-856
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• 2022

In this article, we analyze the first order delay dynamic equations with several nonmonotone arguments. Also, we present new oscillation conditions involving lim sup and lim inf for the solutions of these equations. Finally, we give an example to demonstrate the results.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.779-793
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• 2009

This paper deals with a delayed SEIRS epidemic model with pulse vaccination and crowded incidence rate. Moreover, the case of vertical and horizontal transmission is considered. By using the discrete dynamical system determined by the stroboscopic map, the exact infection-free periodic solution of the SEIRS model is obtained. Further, by employing the comparison arguments, we prove that under the condition that $R_*$ < 1 the infection-free periodic solution is globally attractive, and that under the condition that $R^*$ > 1 the disease is uniformly persistent, which means that after some period of time the disease will become endemic.