Avian influenza dynamics in wild birds with bird mobility and spatial heterogeneous environment

Naveen K. Vaidya; Feng-Bin Wang; Xingfu Zou

doi:10.3934/dcdsb.2012.17.2829

Article Contents

2012, Volume 17, Issue 8: 2829-2848. Doi: 10.3934/dcdsb.2012.17.2829

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Avian influenza dynamics in wild birds with bird mobility and spatial heterogeneous environment

1.
Department of Applied Mathematics, University of Western Ontario, London, Ontario, N6A 5B7
2.
Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7

Received: April 2011

Revised: August 2011

Published: November 2012

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Abstract

In this paper, we propose a mathematical model to describe the avian influenza dynamics in wild birds with bird mobility and heterogeneous environment incorporated. In addition to establishing the basic properties of solutions to the model, we also prove the threshold dynamics which can be expressed either by the basic reproductive number or by the principal eigenvalue of the linearization at the disease free equilibrium. When the environment factor in the model becomes a constant (homogeneous environment), we are able to find explicit formulas for the basic reproductive number and the principal eigenvalue. We also perform numerical simulation to explore the impact of the heterogeneous environment on the disease dynamics. Our analytical and numerical results reveal that the avian influenza dynamics in wild birds is highly affected by both bird mobility and environmental heterogeneity.

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Mathematics Subject Classification: 35K57, 37N25, 92D30.

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