Bivariate collocation for computing R0 in epidemic models with two structures
Bivariate collocation for computing R0 in epidemic models with two structures
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DOI：
10.1016/j.camwa.2021.10.026
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发表时间：
2021-09
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影响因子：
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通讯作者：
D. Breda;Simone De Reggi;F. Scarabel;R. Vermiglio;Jianhong Wu
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作者：
D. Breda;Simone De Reggi;F. Scarabel;R. Vermiglio;Jianhong Wu
结构化流行病模型可以用一阶双曲偏微分方程表示，其中“空间”变量代表个体特征，称为结构。对于具有两个结构的模型，我们提出了一种数值技术来近似R 0，它测量传染病的传播性，严格地说，被定义为下一代算子的主导特征值。通过二元配置和张量网格上的体积，后者是近似的有限维矩阵，使其主导特征值可以很容易地计算与标准技术。我们使用测试的例子，实验研究的行为的近似：收敛顺序似乎是无限的，当相应的本征函数是光滑的，有限的不规则的本征函数。为了证明该技术的有效性，更现实的应用，我们提出了一个新的流行病模型结构的人口年龄和免疫力，并研究了近似R 0在一些特殊情况下的利益。
Structured epidemic models can be formulated as first-order hyperbolic PDEs, where the “spatial” variables represent individual traits, called structures. For models with two structures, we propose a numerical technique to approximate R 0, which measures the transmissibility of an infectious disease and, rigorously, is defined as the dominant eigenvalue of a next generation operator. Via bivariate collocation and cubature on tensor grids, the latter is approximated with a finite-dimensional matrix, so that its dominant eigenvalue can easily be computed with standard techniques. We use test examples to investigate experimentally the behavior of the approximation: the convergence order appears to be infinite when the corresponding eigenfunction is smooth, and finite for less regular eigenfunctions. To demonstrate the effectiveness of the technique for more realistic applications, we present a new epidemic model structured by demographic age and immunity, and study the approximation of R 0 in some particular cases of interest.