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Abstract and Applied Analysis
Volume 2016 (2016), Article ID 1708527, 4 pages
http://dx.doi.org/10.1155/2016/1708527
Research Article

Existence and Uniqueness Results for a Smooth Model of Periodic Infectious Diseases

1International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
2Institut de Mathématiques et de Sciences Physiques (IMSP), 01 BP 613 Porto-Novo, Benin

Received 14 July 2016; Accepted 18 August 2016

Academic Editor: Mohsen Alimohammady

Copyright © 2016 Guy Degla. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.