Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 143019, 15 pages
doi:10.1155/2009/143019
A general discrete time model of population dynamics in the presence of an infection
Giuseppe Izzo1
, Yoshiaki Muroya2
and Antonia Vecchio3
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
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.