This study proposes and analyzes a mathematical model of the transmission dynamics of H5N1 between avian and human populations, explicitly incorporating environmental contamination as an indirect transmission pathway. The model captures direct transmission through bird-to-bird spread within avian populations, bird-to-human transmission, and human-to-human transmission, together with indirect transmission arising from environmental viral persistence, using a compartmental modeling framework. A qualitative analysis of the model is performed to determine the disease-free and endemic equilibria, the stability of the disease-free equilibrium, and the threshold conditions governing disease outbreaks. A forward sensitivity analysis is also conducted to assess the influence of model parameters on the basic reproduction number. The study further investigates optimal control strategies, including treatment, vaccination, disinfection, and public health interventions, to reduce disease prevalence while minimizing implementation costs. A cost-effectiveness analysis is performed to compare alternative intervention scenarios. Numerical simulations demonstrate that combined strategies targeting both direct transmission and environmental contamination are the most effective in controlling H5N1 outbreaks, highlighting the importance of integrating environmental management into disease-control policies. Overall, the findings underscore the importance of integrated, evidence-based strategies that combine poultry management, human protection, environmental sanitation, and vaccination to effectively reduce H5N1 transmission, mitigate outbreak severity, and enhance preparedness for future outbreaks. To support the modeling results, the study conducts a case study based on H5N1 incidence data from Asia. The model is fitted to the observed data in the absence of control measures, and the resulting dynamics are compared with scenarios incorporating all control interventions and human vaccination. The results indicate that the combined control strategy achieves the greatest reduction in H5N1 infections. Nevertheless, vaccination alone also provides substantial benefits when other interventions are unavailable or impractical to implement.