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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 5310837, 13 pages
https://doi.org/10.1155/2017/5310837
Research Article

Discrete Models of Disease and Competition

1U.D. Matemáticas, Universidad de Alcalá, 28871 Alcalá de Henares, Spain
2Departamento de Matemática Aplicada, ETSI Industriales, Universidad Politécnica de Madrid, 28006 Madrid, Spain

Correspondence should be addressed to R. Bravo de la Parra

Received 9 June 2017; Revised 25 July 2017; Accepted 10 August 2017; Published 20 September 2017

Academic Editor: Vicenç Méndez

Copyright © 2017 R. Bravo de la Parra et al. 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

The aim of this work is to analyze the influence of the fast development of a disease on competition dynamics. To this end we present two discrete time ecoepidemic models. The first one corresponds to the case of one parasite affecting demography and intraspecific competition in a single host, whereas the second one contemplates the more complex case of competition between two different species, one of which is infected by the parasite. We carry out a complete mathematical analysis of the asymptotic behavior of the solutions of the corresponding systems of difference equations and derive interesting ecological information about the influence of a disease in competition dynamics. This includes an assessment of the impact of the disease on the equilibrium population of both species as well as some counterintuitive behaviors in which although we would expect the outbreak of the disease to negatively affect the infected species, the contrary happens.