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The emerging threat of a human pandemic caused by the H5N1 avian influenzavirus strain magnifies the need for controlling the incidence of H5N1 infectionin domestic bird populations. Culling is one of the most widely used controlmeasures and has proved effective for isolated outbreaks. However, thesocio-economic impacts of mass culling, in the face of a disease which hasbecome endemic in many regions of the world, can affect the implementation andsuccess of culling as a control measure. We use mathematical modeling tounderstand the dynamics of avian influenza under different culling approaches.We incorporate culling into an SI model by considering the per capita cullingrates to be general functions of the number of infected birds. Complex dynamicsof the system, such as backward bifurcation and forward hysteresis, along withbi-stability, are detected and analyzed for two distinct culling scenarios. Inthese cases, employing other control measures temporarily can drasticallychange the dynamics of the solutions to a more favorable outcome for diseasecontrol.

Forward Hysteresis and Backward Bifurcation Caused by Culling in an Avian Influenza Model