| Abstract: |
| An approach to modelling bird migration is proposed, in which there is a region where birds do not move but spend time breeding. Birds leave this breeding region and enter a migration flyway which is effectively a one-way corridor starting and ending at the breeding location. Mathematically, the flyway is a curve parametrised by arc-length. Flight speed depends on position along the flyway, to take account of factors such as wind and the pausing of birds at various locations for wintering or stopovers. Per-capita mortality along the flyway is both position and age-dependent, allowing for increased risks at stopover locations due to predation, and increased risks to immature birds. We also model indirect transmission, via contact with viruses, of avian influenza in migratory and nonmigratory birds, taking into account age structure. Sufficient conditions are obtained for the local stability of the disease-free equilibrium (for a species without migration) and for the disease-free periodic solution (for a migratory species). |
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