The highly pathogenic avian influenza (HPAI) subtype H5N1 is a severe viral disease which continues to pose a significant threat to public health and a rigorous understanding of its transmission dynamics across its major pathways is essential for developing effective control strategies. Phylogenetic analysis suggests that H5N1 spillover occurs primarily between wild and domestic birds. However, increasing contact between these species and humans increases the risk of zoonotic transmission. In this work, we develop a mathematical model to examine the transmission dynamics of H5N1 and evaluate the effectiveness of proposed control measures. The model employs a compartmental framework that includes human, domestic, and wild bird populations. We then use this model to estimate the basic reproduction number for each population group and perform a sensitivity analysis to assess the contribution of the parameters to the spread of the disease. Numerical simulations are also conducted to evaluate the impact of inter-species interactions on H5N1 infection in humans and to determine the effectiveness of different control measures. The results suggest that a vaccination strategy with high vaccine efficacy, combined with a vaccination rate above 50%, significantly reduces transmission. In addition, decreasing cross-species interactions leads to a substantial reduction in disease transmission within the human population. Moreover, an optimal control analysis indicates that a combined approach involving environmental sanitation, vaccination, and targeted culling of confirmed infected poultry is an effective strategy to control the outbreak, reducing the likelihood of spillover to humans.