(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, a compartment model is formulated to study the transmission 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 existence of the endemic equilibrium and its global asymptotic stability. Firstly, we give the well-posedness of the model and then discuss the threshold dynamics for three 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 problem are discussed. Finally, some numerical simulations are carried out to illustrate our theoretical results and visualize the impact of various parameters on model dynamics, which suggest that decreasing the recruitment rate and increasing the death rate of poultry, can only control the disease by simultaneously cutting off the transmission from birds to poultry and humans even if the ultimate scale of the disease can be effectively controlled. In addition, enhancing public awareness of prevention to reduce the transmission from birds and poultry to humans is also effective in controlling the final scale of disease.