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

Abstract

We formulate a mathematical model which accounts for the mutation of an avian influenza virus which is able to spill over into the human population and become a highly pathogenic strain. We compute the basic reproduction number of the model and use it to study the existence and stability of equilibrium points. We derive conditions for the global asymptotic stability of any of the three equilibrium. The model is extended to incorporate five relevant time-dependent controls, and use the Pontryagin’s maximum principle to derive the necessary conditions for optimal disease control. Finally, the optimal control problem is solved numerically to show the effect of each control parameter and their combination. The incremental cost-effectiveness ratios are calculated to investigate the cost-effectiveness of all possible combinations of the control strategies. This study suggests that the combination of vaccination of poultry, treatment of infected humans, and education campaigns for humans in contact with the poultry environment might be the most cost-effective way to control avian influenza transmission.

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