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首页> 外文期刊>Mathematical Biosciences: An International Journal >Qualitative dynamics of lowly- and highly-pathogenic avian influenza strains
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Qualitative dynamics of lowly- and highly-pathogenic avian influenza strains

机译：低致病性和高致病性禽流感毒株的定性动力学

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摘要

A new deterministic model for the transmission dynamics of the lowly- and highly-pathogenic avian influenza (LPAI and HPAI) strains is designed and rigorously analyzed. The model exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium whenever the associated reproduction number is less than unity. It is shown that the re-infection of birds infected with the LPAI strain causes the backward bifurcation phenomenon. In the absence of such re-infection, the disease-free equilibrium of the model is globally-asymptotically stable when the associated reproduction number is less than unity. Using non-linear Lyapunov functions of Goh-Volterra type, the LPAI-only and HPAI-only boundary equilibria of the model are shown to be globally-asymptotically stable when they exist. A special case of the model is shown to have a continuum of co-existence equilibria whenever the associated reproduction numbers of the two strains are equal and exceed unity. Furthermore, numerical simulations of the model suggest that co-existence or competitive exclusion of the two strains can occur when the respective reproduction numbers of the two strains exceed unity.
机译：设计并严格分析了低致病性高致病性禽流感（LPAI和HPAI）菌株传播动态的新确定性模型。该模型表现出向后分叉的现象，每当相关的繁殖数小于1时，稳定的无病平衡与稳定的地方性平衡并存。结果表明，感染LPAI株的禽类再次感染会导致反向分叉现象。在没有这种再次感染的情况下，当相关的繁殖数小于1时，模型的无病平衡是全局渐近稳定的。使用Goh-Volterra类型的非线性Lyapunov函数，模型的仅LPAI和仅HPAI的边界平衡在存在时显示为全局渐近稳定的。每当两个菌株的相关繁殖数相等且超过1时，该模型的特例显示具有连续的共存平衡。此外，该模型的数值模拟表明，当两种菌株的各自繁殖数超过1时，可以发生两种菌株的共存或竞争排斥。

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