Dynamics of Low and High Pathogenic Avian Influenza in Wild and Domestic Bird Populations

Abstract

Avian influenza H5N1 is at present the most dangerous zoonotic disease infecting wild and domestic birds. Should the virus mutate and become efficiently human-to-human transmittable, a pandemic will occur with high mortality. Avian influenza H5N1 exists in two forms: Low pathogenic (LPAI) and high pathogenic (HPAI). In this talk we build a model of LPAI and HPAI in wild and domestic birds. Birds, wild and domestic, who have been priorly infected with LPAI are partially protected against HPAI. We compute the relevant reproduction numbers and invasion reproduction numbers. We find that the systems has a disease-free equilibrium, LPAI-only equilibrium, HPAI-only equilibrium and at least one coexistence equilibrium. Furthermore, the LPAI-only equilibrium and HPAI-only equilibrium are locally asymptotically stable under appropriate conditions on the reproduction numbers. In contrast, the coexistence equilibrium can lose stability and oscillations are possible. We show that the oscillations are caused by the cross-immunity and can exist in the wild bird system, separate from the domestic bird system. For a pathogen circulating in a multi-species system, species A is called a sink (source), if the pathogen cannot (can) sustain itself in species A without the inflow of infectives from other species. We investigate the sink/source status of LPAI and HPAI in wild and domestic birds.