Modeling and evaluating targeted interventions to curb avian influenza spread among humans and domestic birds

Abstract

Avian influenza, caused by influenza A viruses, has drawn substantial attention globally due to increased deaths from time to time. This study examines control interventions for avian influenza transmission in humans and domestic birds using a deterministic mathematical model. The model incorporates three time-dependent interventions: vaccinating susceptible birds, maintaining proper hygiene practice, and culling infected birds. The next-generation matrix method is used to determine the effective reproduction number. Optimal control theory is applied by incorporating: vaccination, proper human hygiene practices, and culling of infected birds. To determine the necessary conditions for the existence of optimal controls, the Pontryagin’s Maximum Principle is employed. The optimal control problem is then solved using the forward-backward sweep method based on the fourth-order Runge-Kutta algorithm, implemented in MATLAB. Results from the optimal control analysis show that the strategy combining all interventions is the most effective approach for controlling the disease. Furthermore, the Incremental Cost-Effectiveness Ratio (ICER) is used to identify the most cost-effective strategy for disease control. The findings show that Strategy VII has a negative ICER, indicating that it is less costly and averts more infections. Therefore, to eliminate the disease, we recommend the implementation of all the aforementioned control measures.