An avian-only Filippov model incorporating culling of both susceptible and infected birds in combating avian influenza (Q314529)

Depopulation of birds has always been an effective method not only to control the transmission of avian influenza in bird population but also to eliminate influenza viruses. In this paper the authors propose a Filippov avian-only model with culling of susceptible and/or infected birds. For each susceptible threshold level \(S_b\) the phase portrait for the dynamical system is derived for a varied infected threshold level \(I_b\) with account for the existence of endemic states. The endemic states are represented by real equilibria, pseudo-equilibria and pseudo-attractors. It is shown generically that all solutions of this model will approach one of the endemic states.