Dang Yan-Xia, Li Xue-Zhi, Martcheva Maia
a Department of Public Education , Zhumadian Vocational and Technical College , Zhumadian , People's Republic of China.
b Department of Mathematics and Physics , Anyang Institute of Technology , Anyang , People's Republic of China.
J Biol Dyn. 2016 Dec;10(1):416-56. doi: 10.1080/17513758.2016.1217355.
In this paper, a multi-strain model that links immunological and epidemiological dynamics across scales is formulated. On the within-host scale, the n strains eliminate each other with the strain having the largest immunological reproduction number persisting. However, on the population scale, we extend the competitive exclusion principle to a multi-strain model of SI-type for the dynamics of highly pathogenic flu in poultry that incorporates both the infection age of infectious individuals and biological age of pathogen in the environment. The two models are linked through the age-since-infection structure of the epidemiological variables. In addition the between-host transmission rate, the shedding rate of individuals infected by strain j and the disease-induced death rate depend on the within-host viral load. The immunological reproduction numbers [Formula: see text] and the epidemiological reproduction numbers [Formula: see text] are computed. By constructing a suitable Lyapunov function, the global stability of the infection-free equilibrium in the system is obtained if all reproduction numbers are smaller or equal to one. If [Formula: see text], the reproduction number of strain j is larger than one, then a single-strain equilibrium, corresponding to strain j exists. This single-strain equilibrium is globally stable whenever [Formula: see text] and [Formula: see text] is the unique maximal reproduction number and all of the reproduction numbers are distinct. That is, the strain with the maximal basic reproduction number competitively excludes all other strains.
本文构建了一个跨尺度连接免疫动力学和流行病学动力学的多毒株模型。在宿主内尺度上，n个毒株相互竞争，具有最大免疫繁殖数的毒株持续存在。然而，在种群尺度上，我们将竞争排斥原理扩展到一个针对家禽高致病性流感动力学的SI型多毒株模型，该模型纳入了感染个体的感染年龄和环境中病原体的生物学年龄。这两个模型通过流行病学变量的感染后年龄结构相联系。此外，宿主间传播率、j毒株感染个体的排毒率和疾病诱导死亡率取决于宿主体内病毒载量。计算了免疫繁殖数[公式：见原文]和流行病学繁殖数[公式：见原文]。通过构造一个合适的李雅普诺夫函数，如果所有繁殖数小于或等于1，则系统中无感染平衡点是全局稳定的。如果[公式：见原文]，即j毒株的繁殖数大于1，则存在对应于j毒株的单毒株平衡点。只要[公式：见原文]且[公式：见原文]是唯一的最大繁殖数且所有繁殖数都不同，这个单毒株平衡点就是全局稳定的。也就是说，具有最大基本繁殖数的毒株竞争性地排斥所有其他毒株。
