Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 143019, 15 pages
doi:10.1155/2009/143019
Research Article
A General Discrete Time Model of Population Dynamics in the Presence of an Infection
1Department of Mathematics and Applications “R. Caccioppoli“, University of Naples “Federico II“, Via Cintia, Monte S. Angelo, 80126 Napoli, Italy
2Department of Mathematical Sciences, Waseda University, 3-4-1 Ohkubo Shinjuku-ku, Tokyo 169-8555, Japan
3Istituto per le Applicazioni del Calcolo “M. Picone”, Via P. Castellino, 111, 80131 Napoli, Italy
Received 16 January 2009; Revised 12 March 2009; Accepted 17 March 2009
Academic Editor: Leonid Berezansky
Copyright © 2009 Giuseppe Izzo 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
We present a set of difference equations which generalizes that proposed in the work of G. Izzo and A. Vecchio (2007) and represents the discrete counterpart of a larger class of continuous model concerning the dynamics of an infection in an organism or in a host population. The limiting behavior of this new discrete model is studied and a threshold parameter playing the role of the basic reproduction number is derived.