A Two--Strain Avian--Human Influenza Model with Environmental Transmission: Stability Analysis and Optimal Control Strategies

Abstract

On the basis of the WHO legitimated fear that there will be an avian influenza virus strain capable of mutating once it reachesthe human population and sustains human-to-human transmissions, we formulate an "hypothetical" mathematical modelwhich accounts for the mutation of an avian influenza virus having the ability to spill over into the human population and become ahighly pathogenic strain. We compute the basic reproduction number of the model and use it to study the existence andstability of equilibrium points. We derive conditions for the global asymptotic stability of any of the three equilibrium.The model is extended to incorporate six relevant time-dependent controls, and use the Pontryagin's maximum principle toderive the necessary conditions for optimal disease control. Finally, the optimal control problem is solved numerically to showthe effect of each control parameter and their combination. The incremental cost-effectiveness ratios are calculatedto investigate the cost-effectiveness of all possible combinations of the control strategies. This study suggests that quarantineinfected humans might be the most cost-effective strategy to control avian influenza transmissionswith the virus mutation.

Keywords: Avian influenza, Mutation, Environment transmission, Cost-effectiveness.