Relating Eulerian and Lagrangian spatial models for vector-host disease dynamics through a fundamental matrix
Relating Eulerian and Lagrangian spatial models for vector-host disease dynamics through a fundamental matrix
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DOI：
10.1007/s00285-022-01761-z
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发表时间：
2022-06-01
影响因子：
1.9
通讯作者：
Tien，Joseph Hua
中科院分区：
文献类型：
--
作者：
Bernal，Esteban Vargas;Saucedo，Omar;Tien，Joseph Hua
我们探讨了欧拉和拉格朗日方法之间的关系，用于对离散空间的媒介传播疾病的运动进行建模。在欧拉方法中，我们通过图拉普拉斯矩阵 L 捕获的移动速率明确地解释主机的移动。在拉格朗日方法中，我们仅通过混合矩阵 P 来考虑个体在外来斑块上花费的时间比例。我们根据矩阵LandP 建立了主机的欧拉模型和拉格朗日模型之间的关系。如果对于给定的矩阵P，可以选择矩阵L使得矩阵P和矩阵L的停留时间匹配，则我们说这两个建模框架是一致的。我们找到一致性的充分条件，并在一致和不一致的情况下检查疾病数量，例如最终爆发规模和基本繁殖数。在两斑块模型的特殊情况下，我们观察到即使在不一致的情况下，基本繁殖数和最终爆发规模也会出现相似的值。然而，在某些情况下，两种方法的最终大小可能会根据我们提出的关系而显着不同。
We explore the relationship between Eulerian and Lagrangian approaches for modeling movement in vector-borne diseases for discrete space. In the Eulerian approach we account for the movement of hosts explicitly through movement rates captured by a graph Laplacian matrixL. In the Lagrangian approach we only account for the proportion of time that individuals spend in foreign patches through a mixing matrixP. We establish a relationship between an Eulerian model and a Lagrangian model for the hosts in terms of the matricesLandP. We say that the two modeling frameworks are consistent if for a given matrixP, the matrixLcan be chosen so that the residence times of the matrixPand the matrixLmatch. We find a sufficient condition for consistency, and examine disease quantities such as the final outbreak size and basic reproduction number in both the consistent and inconsistent cases. In the special case of a two-patch model, we observe how similar values for the basic reproduction number and final outbreak size can occur even in the inconsistent case. However, there are scenarios where the final sizes in both approaches can significantly differ by means of the relationship we propose.