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| Dynamics Analysis and Optimal Control for an Avian Influenza Model among Multi-populations |
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| KeyWord:Avian influenza, bird-poultry, coexistence equilibrium, existence and stability |
| Author Name | Affiliation | | Yantao Luo | College of Science, National University of Defense Technology, Changsha, 410073, China
College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China | | Jianhua Huang | College of Science, National University of Defense Technology, Changsha, 410073, China | | Xiao Wang | College of Science, National University of Defense Technology, Changsha, 410073, China | | Tingting Zheng | College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830017, China | | Zhidong Teng | College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China |
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| Abstract: |
| 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 $R_0<1$, and the other conditions are required for the global asymptotic stability of the disease-free equilibrium. The endemic-equilibrium is globally attractive when $R_0>1$. 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. |
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