Analysis and optimal control strategies of epidemic models with nonlinear incidence rates

The H5N1 avian influenza virus has garnered global attention in recent years due to its high pathogenicity and potential threat to humans. Studies have shown that the H5N1 virus could acquire human-to-human transmissibility through specific mutations or reassortment with human influenza viruses, increasing the risk of a global pandemic. This paper develops a six-dimensional infectious disease model, incorporating nonlinear incidence rates with media reporting, providing a more accurate representation of the current H5N1 transmission dynamics. We analyze the model’s dynamical behavior, conduct a sensitivity analysis of the basic reproduction number, and confirm the existence of a transcritical bifurcation. By applying Pontryagin’s Maximum Principle, we formulate optimal control strategies that include time-dependent measures for transmission control, enhanced vaccination, and effective treatments. Numerical simulations show that combined strategies (a combination of transmission control, vaccination, and treatment) are most effective in reducing infections, though undoubtedly more resource-intensive than single strategies. While transmission control alone is the most economical, it is insufficient for long-term effective containment of the flu’s spread. A phase-specific control strategy, tailored to different stages of the pandemic, has proven to be the most effective global pandemic control measure. This study provides significant biological insights into the potential evolution of the virus and the most effective public health responses, offering valuable guidance for global health efforts in combating avian influenza and other emerging infectious diseases.