结核病在异质性复合人群中的传播分析
Analysis of the spread of tuberculosis in heterogeneous complex metapopulations
摘要：
本文描述和分析了结核病在复杂集合种群上的空间传播，该集合种群是由迁移流连接的种群网络，其结构用节点（斑块）的连通性分布和具有相同度的节点类之间的连通性的条件概率来描述。迁移和迁移过程是同时进行的。对于不相关网络，在标准发病率传播的假设下，计算了无病平衡点和基本再生数，并证明了无病平衡点是局部渐近稳定的.对于不相关网络，在简单质量作用传递的假设下，给出了无病平衡点不稳定的充要条件。还讨论了地方病平衡的存在性。最后，结核病感染的患病率作为路径连通性的函数的集合种群进行了研究，使用数值模拟。
英文摘要：
his paper describes and analyzes the spatial spread of tuberculosis (TB) on complex metapopulation, that is, networks of populations connected by migratory flows whose configurations are described in terms of connectivity distribution of nodes (patches) and the conditional probabilities of connections among classes of nodes sharing the same degree. The migration and transmission processes occur simultaneously. For uncorrelated networks under the assumption of standard incidence transmission, we compute the disease-free equilibrium and the basic reproduction number, and show that the disease-free equilibrium is locally asymptotically stable. Moreover, for uncorrelated networks and under assumption of simple mass action transmission, we give a necessary and sufficient conditions for the instability of the disease-free equilibrium. The existence of endemic equilibria is also discussed. Finally, the prevalence of the TB infection across the metapopulation as a function of the path connectivity is studied using numerical simulations.
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