  The emerging threat of a human pandemic caused by the H5N1 avian influenza
virus strain magnifies the need for controlling the incidence of H5N1 infection
in domestic bird populations. Culling is one of the most widely used control
measures and has proved effective for isolated outbreaks. However, the
socio-economic impacts of mass culling, in the face of a disease which has
become endemic in many regions of the world, can affect the implementation and
success of culling as a control measure. We use mathematical modeling to
understand the dynamics of avian influenza under different culling approaches.
We incorporate culling into an SI model by considering the per capita culling
rates to be general functions of the number of infected birds. Complex dynamics
of the system, such as backward bifurcation and forward hysteresis, along with
bi-stability, are detected and analyzed for two distinct culling scenarios. In
these cases, employing other control measures temporarily can drastically
change the dynamics of the solutions to a more favorable outcome for disease
control.
