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.
Matched MeSH terms: Influenza in Birds/transmission
Avian influenza, an infectious disease of birds, is caused by type A strain of the influenza virus. The disease, which was first identified in Italy more than 100 years ago, occurs worldwide. Avian influenza viruses are mainly distributed by migratory birds. Various animals like birds, pigs, horses, sea mammals and, finally, humans are susceptible to influenza A viruses. The high possibility of genomic changes like gene shift and drift are caused by the segmented RNA genome.
Matched MeSH terms: Influenza in Birds/transmission*
Avian influenza viruses are highly infectious micro-organisms that primarily affect birds. Nevertheless, they have also been isolated from a number of mammals, including humans. Avian influenza virus can cause large economic losses to the poultry industry because of its high mortality. Although there are pathogenic variants with a low virulence and which generally cause only mild, if any, clinical symptoms, the subtypes H5 and H7 can mutate from a low to a highly virulent (pathogenic) virus and should be taken into consideration in eradication strategies. The primary source of infection for commercial poultry is direct and indirect contact with wild birds, with waterfowl forming a natural reservoir of the virus. Live-poultry markets, exotic birds, and ostriches also play a significant role in the epidemiology of avian influenza. The secondary transmission (i.e., between poultry farms) of avian influenza virus is attributed primarily to fomites and people. Airborne transmission is also important, and the virus can be spread by aerosol in humans. Diagnostic tests detect viral proteins and genes. Virus-specific antibodies can be traced by serological tests, with virus isolation and identification being complementary procedures. The number of outbreaks of avian influenza seems to be increasing - over the last 5 years outbreaks have been reported in Italy, Hong Kong, Chile, the Netherlands, South Korea, Vietnam, Japan, Thailand, Cambodia, Indonesia, Laos, China, Pakistan, United States of America, Canada, South Africa, and Malaysia. Moreover, a growing number of human cases of avian influenza, in some cases fatal, have paralleled the outbreaks in commercial poultry. There is great concern about the possibility that a new virus subtype with pandemic potential could emerge from these outbreaks. From the perspective of human health, it is essential to eradicate the virus from poultry; however, the large number of small-holdings with poultry, the lack of control experience and resources, and the international scale of transmission and infection make rapid control and long-term prevention of recurrence extremely difficult. In the Western world, the renewed interest in free-range housing carries a threat for future outbreaks. The growing ethical objections to the largescale culling of birds require a different approach to the eradication of avian influenza.
Matched MeSH terms: Influenza in Birds/transmission