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

A mathematical model for the propagation of a hantavirus in structured populations

Pages: 1065 - 1089, Volume 4, Issue 4, November 2004      doi:10.3934/dcdsb.2004.4.1065

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Cédric Wolf - UMR CNRS 5466, Mathématiques Appliquées de Bordeaux, UFR Sciences et Modélisation, Case 26, Université Victor Segalen Bordeaux 2, 146, rue Léo Saignat, 33076 Bordeaux Cedex, France (email)

Abstract: We analysed a mathematical model for the propagation of Puumala hantavirus (PUU), within a population of bank voles (Clethrionomys glareolus). This model includes the chronological age of individuals and the time elapsed since an individual is infected. The hantavirus propagates via direct transmission (contacts between individuals) and indirect transmission (through the environment). Demographic parameters are population density dependent and the maturation rate is adult density dependent. This leads to a weakly coupled system of hyperbolic equations featuring nonlocal nonlinearities. We give a global existence and uniqueness result.

Keywords:  Global existence, nonlocal hyperbolic system, SI structured system.
Mathematics Subject Classification:  35B60, 35L45, 92D30.

Received: March 2003;      Revised: February 2004;      Published: August 2004.