Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Age-dependent population dynamics diffusive systems

Pages: 1233 - 1247, Volume 4, Issue 4, November 2004      doi:10.3934/dcdsb.2004.4.1233

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Bedr'Eddine Ainseba - Mathématiques Appliquées de Bordeaux, UMR CNRS 5466, case 26, Université Victor Segalen Bordeaux 2, 33076, Bordeaux Cedex, France (email)

Abstract: A nonlinear and nonlocal reaction-diffusion system of population growth is investigated which allows for consideration of both age-size and spatial effects. The mortality and fertility processes of the population are assumed to be linear to simplify the exposition. Local existence, continuation property, positivity, and global existence are obtained. This theory is applied to some specific reaction-diffusion epidemic model including the SI system, the SIS system with vertical transmission, and the SIR system.

Keywords:  Age structure, reaction-diffusion, population dynamics, global existence.
Mathematics Subject Classification:  35L60, 35K57, 92D25 , 35A05.

Published: August 2004.