Dynamics Analysis and Optimal Control for an Avian Influenza Model Among Multi-Populations (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, a compartment model is formulated to study thetransmission dynamics of avian influenza virus among birds, poultry and human population. Due to the strong coupling of the system caused by the transmission route, there are some mathematical challenges to obtain the existenceof the endemic equilibrium and its global asymptotic stability. Firstly, we givethe well-posedness of the model and then discuss the threshold dynamics forthree sub-models. Next, we give the threshold dynamics for the whole system:the disease-free equilibrium is locally asymptotically stable with $R_01.$ Furthermore, the sensitivity analysis and an optimal control problemare discussed. Finally, some numerical simulations are carried out to illustrateour theoretical results and visualize the impact of various parameters on modeldynamics, which suggest that decreasing the recruitment rate and increasingthe death rate of poultry, can only control the disease by simultaneously cutting off the transmission from birds to poultry and humans even if the ultimatescale of the disease can be effectively controlled. In addition, enhancing publicawareness of prevention to reduce the transmission from birds and poultry tohumans is also effective in controlling the final scale of disease.