Forward Hysteresis and Backward Bifurcation Caused by Culling in an Avian Influenza Model

TL;DR

This paper uses mathematical modeling to analyze how culling strategies affect avian influenza dynamics, revealing complex behaviors like bifurcations and hysteresis that influence disease control outcomes.

Contribution

It introduces a novel SI model with general culling functions, uncovering complex dynamics such as backward bifurcation and hysteresis in avian influenza control.

Findings

Complex dynamics like backward bifurcation are identified.

Culling strategies can lead to bi-stability and hysteresis.

Temporary additional control measures can improve disease management.

Abstract

The emerging threat of a human pandemic caused by the H5N1 avian influenza virus strain magnifies the need for controlling the incidence of H5N1 infection in domestic bird populations. Culling is one of the most widely used control measures and has proved effective for isolated outbreaks. However, the socio-economic impacts of mass culling, in the face of a disease which has become endemic in many regions of the world, can affect the implementation and success of culling as a control measure. We use mathematical modeling to understand the dynamics of avian influenza under different culling approaches. We incorporate culling into an SI model by considering the per capita culling rates to be general functions of the number of infected birds. Complex dynamics of the system, such as backward bifurcation and forward hysteresis, along with bi-stability, are detected and analyzed for two distinct culling scenarios. In these cases, employing other control measures temporarily can drastically change the dynamics of the solutions to a more favorable outcome for disease control.