Spread Pattern Formation of H5N1-Avian Influenza and its Implications for Control Strategies

Abstract

Abstract. Mechanisms contributing to the spread of avian influenza seem to be well identified, but how their interplay led to the current worldwide spread pattern of H5N1 influenza is still unknown due to the lack of effective global surveillance and relevant data. Here we develop some deterministic models based on the transmission cycle and modes of H5N1 and focusing on the interaction among poultry, wild birds and environment. Some of the model parameters are obtained from existing literatures, and others are allowed to vary in order to assess the effectiveness of various control strategies involving bird migration, agro-ecological environments, live and dead poultry trading, smuggling of wild birds, mechanical movement of infected materials and specific farming practices. Our simulations are carried out for a set of parameters that leads to the basic reproduction number 3.3. We show that by reducing 95% of the initial susceptible poultry population or by killing all infected poultry birds within one day, one may control the disease outbreak in a local setting. Our simulation shows that cleaning the environment is also a feasible and useful control measure, but culling wild birds and destroying their habitat are ineffective control measures. We use a one dimensional PDE model to examine the contribution to the spatial spread rate by the size of the susceptible poultry birds, the diffusion rates of the wild birds and the virus. We notice the diffusion rate of the wild birds with high mortality has very little impact on the spread speed. But for the wild birds who can survive the infection, depending on the direction of convection, their diffusion rate can substantially increase the spread rate, indicating a significant role of the migration of these type of wild birds in the spread of the disease.

Epidemics spreading in predator–prey systems

“…The reason for *Corresponding author. Email: ezio.venturino@unito.it investigating such issues relies on the recent epidemics that have received wide interest in the media, such as avian influenza [13], severe acute respiratory syndrome (SARS) and the Swine flu epidemic that has originated in Mexico. A disease that certainly crosses the species barrier in predator-prey situations is represented by rabies.…”

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

“…Although environmental transmission rates are hundreds of times lower than direct transmission rates, it is known that the virions can persist in the environment for a long time. Indeed, environmental transmission apparently provides a possible persistence mechanism in situations where an epidemic would not be sustained by direct transmission alone [7,22]. The model setting in our study here does not incorporate the environmental contamination and thus may underestimate the likelihood of an outbreak for a given set of parameter values.…”

Study on Bird Flu Infection Process within a Poultry Farm with Effects of Spatial Diffusion

“…One stationary point is C(c, 0, 0), and the other stationary point is D(m/ω, ωc − m/ωr, 0). A heteroclinic connection from the stationary point D to the stationary point C gives rise to a traveling wave solution of (4). Existence of such a heteroclinic orbit in a singular limit was established under the condition ωc−m > 0 in a previous study [10].…”

“…A mathematical model to interpret the spread Avian Influenza from the bird world to the human world with autonomous ordinary differential equations was analyzed [3,7] and the stability analysis is carried out. The transmission dynamics and spatial spread rate by the size of the susceptible poultry birds were studied [4]. A disease transmission model with diffusive terms to investigate spatial spread of Avian Influenza among flock and human were studied [9].…”