Vazquez Alexei
German Aerospace Center (DLR), Institute for the Protection of Terrestrial Infrastructures, Rathausallee 12, 53757 Sankt Augustin, Germany.
Phys Rev E. 2021 Feb;103(2-1):022309. doi: 10.1103/PhysRevE.103.022309.
The spreading dynamics of infectious diseases is determined by the interplay between geography and population mixing. There is homogeneous mixing at the local level and human mobility between distant populations. Here I model spatial location as a type and the population mixing by intra- and intertype mixing patterns. Using the theory of multitype branching process, I calculate the expected number of new infections as a function of time. In one dimension the analysis is reduced to the eigenvalue problem of a tridiagonal Teoplitz matrix. In d dimensions I take advantage of the graph cartesian product to construct the eigenvalues and eigenvectors from the eigenvalue problem in 1 one dimension. Using numerical simulations I uncover a transition from linear to multitype mixing exponential growth with increasing the population size. Given that most countries are characterized by a network of cities with more than 100 000 habitants, I conclude that the multitype mixing approximation should be the prevailing scenario.
传染病的传播动态由地理因素和人群混合之间的相互作用决定。在局部层面存在均匀混合，而远距离人群之间存在人口流动。在此，我将空间位置建模为一种类型，并通过同类型和不同类型的混合模式来模拟人群混合。利用多类型分支过程理论，我计算了作为时间函数的新感染预期数量。在一维情况下，分析简化为一个三对角托普利兹矩阵的特征值问题。在d维情况下，我利用图的笛卡尔积从一维的特征值问题构建特征值和特征向量。通过数值模拟，我发现随着人口规模的增加，存在从线性混合到多类型混合指数增长的转变。鉴于大多数国家的特征是拥有超过10万居民的城市网络，我得出结论，多类型混合近似应该是主要情况。
