Spatial dynamics of bar-headed geese migration in the context of H5N1

Abstract

Virulent outbreaks of highly pathogenic avian influenza (HPAI) since 2005 have raised the question about the roles of migratory and wild birds in the transmission of HPAI. Despite increased monitoring, the role of wild waterfowl as the primary source of the highly pathogenic H5N1 has not been clearly established. The impact of outbreaks of HPAI among species of wild birds which are already endangered can nevertheless have devastating consequences for the local and non-local ecology where migratory species are established. Understanding the entangled dynamics of migration and the disease dynamics will be key to prevention and control measures for humans, migratory birds and poultry. Here, we present a spatial dynamic model of seasonal migration derived from first principles and linking the local dynamics during migratory stopovers to the larger scale migratory routes. We discuss the effect of repeated epizootic at specific migratory stopovers for bar-headed geese (Anser indicus). We find that repeated deadly outbreaks of H5N1 on stopovers during the autumn migration of bar-headed geese could lead to a larger reduction in the size of the equilibrium bird population compared with that obtained after repeated outbreaks during the spring migration. However, the opposite is true during the first few years of transition to such an equilibrium. The age-maturation process of juvenile birds which are more susceptible to H5N1 reinforces this result.

Seasonal migration dynamics: periodicity, transition delay and finite-dimensional reduction

“…We follow Bourouiba et al (2010) and Gourley et al (2010) to consider a single species bird population migrating between a summer breeding patch and a winter refuge patch. We will ignore stopover patches, though mortality during the flights to these patches and at these stopover patches will be incorporated in the model parameters indirectly.…”

“…To illustrate this, we provide a numerical simulation based on parameters suggested in Bourouiba et al (2010): T 1 = 46, T 2 = 138, T 3 = 61 and T 4 = 120, the time delays are taken as t ws = 16 and t sw = 16, and all units are days. The death rates are m s = 0.00088 and m w = 0.00088.…”

The Interaction of Migratory Birds and Domestic Poultry and Its Role in Sustaining Avian Influenza

“…Apart from migratory birds, other main causes of H5N1 introduction include the trade in poultry and poultry products, and the trade in wild birds. In previous works (Gourley et al [14], Bourouiba et al [6]), we developed mathematical models of the bird migration phenomenon with the ultimate aim of understanding the role of migratory birds in spreading the highly pathogenic avian influenza (H5N1), leading to a massive outbreak in wild birds at Lake Qinghai in central China (2005). Bourouiba et al [6] particularly focused on bar-headed (Anser indicus) geese migration in the Central Asian Flyway form Mongolia to India.…”

“…In previous works (Gourley et al [14], Bourouiba et al [6]), we developed mathematical models of the bird migration phenomenon with the ultimate aim of understanding the role of migratory birds in spreading the highly pathogenic avian influenza (H5N1), leading to a massive outbreak in wild birds at Lake Qinghai in central China (2005). Bourouiba et al [6] particularly focused on bar-headed (Anser indicus) geese migration in the Central Asian Flyway form Mongolia to India. Migratory birds encounter a variety of climatic and other conditions at their breeding and wintering locations and along their flyways and resting places (stopover sites) which led us initially to consider the possibility of a partial differential equation model.…”

“…We have in our previous works allowed for the fact that migration is essentially a periodic phenomenon. In the model derivation in [14] and [6] the reaction-advection equations are eliminated and the system reduced to a system of delay differential equations for the numbers of birds on the patches, where the delays represent the flight times between patches. One of the patches is the breeding patch, and in our models births are assumed to occur only on this patch.…”