TY - JOUR
T1 - Dynamics Analysis and Optimal Control for an Avian Influenza Model Among Multi-Populations
AU - Luo , Yantao
AU - Huang , Jianhua
AU - Wang , Xiao
AU - Zheng , Tingting
AU - Teng , Zhidong
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 890
EP - 918
PY - 2024
DA - 2024/12
SN - 6
DO - http://doi.org/10.12150/jnma.2024.890
UR - https://global-sci.org/intro/article_detail/jnma/23662.html
KW - Avian influenza, bird-poultry, coexistence equilibrium, existence
and stability.
AB - <p style="text-align: justify;">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 $R_0&lt;1,$ and
the other conditions are required for the global asymptotic stability of the
disease-free equilibrium. The endemic-equilibrium is globally attractive when $R_0&gt;1.$ 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.</p>