title: An avian-only Filippov model incorporating culling of both susceptible and infected birds in combating avian influenza.
abstract: Depopulation of birds has always been an effective method not only to control the transmission of avian influenza in bird populations but also to eliminate influenza viruses. We introduce a Filippov avian-only model with culling of susceptible and/or infected birds. For each susceptible threshold level [Formula: see text], we derive the phase portrait for the dynamical system as we vary the infected threshold level [Formula: see text], focusing on the existence of endemic states; the endemic states are represented by real equilibria, pseudoequilibria and pseudo-attractors. We show generically that all solutions of this model will approach one of the endemic states. Our results suggest that the spread of avian influenza in bird populations is tolerable if the trajectories converge to the equilibrium point that lies in the region below the threshold level [Formula: see text] or if they converge to one of the pseudoequilibria or a pseudo-attractor on the surface of discontinuity. However, we have to cull birds whenever the solution of this model converges to an equilibrium point that lies in the region above the threshold level [Formula: see text] in order to control the outbreak. Hence a good threshold policy is required to combat bird flu successfully and to prevent overkilling birds.
authors: Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Ave, Ottawa, ON, K1N 6N5, Canada.|School of Informatics and Applied Mathematics, Universiti Malaysia Terengganu, 21030, Kuala Terengganu, Malaysia.
authors: Nyuk Sian
authors: NS
authors: Chong
authors: Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Ave, Ottawa, ON, K1N 6N5, Canada.
authors: Benoit
authors: B
authors: Dionne
authors: Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Ave, Ottawa, ON, K1N 6N5, Canada. rsmith43@uottawa.ca.|Faculty of Medicine, University of Ottawa, 451 Smyth Rd, Ottawa, ON, K1H 8M5, Canada. rsmith43@uottawa.ca.
authors: Robert
authors: R
authors: Smith
mesh_terms: D000822:Animal Husbandry / Q000379:methods*; D000818:Animals; D001717:Birds; D004196:Disease Outbreaks / Q000517:prevention & control* / Q000706:statistics & numerical data; D005585:Influenza in Birds / Q000517:prevention & control* / Q000635:transmission
keywords: Avian influenza; Culling; Dynamical systems; Filippov model; Threshold policy