German Aerospace Center (DLR), Institute for the Protection of Terrestrial Infrastructures, Rathausallee 12, 53757 Sankt Augustin, Germany.
Phys Rev E. 2021 Mar;103(3):L030301. doi: 10.1103/PhysRevE.103.L030301.
The heterogeneity of human populations is a challenge to mathematical descriptions of epidemic outbreaks. Numerical simulations are deployed to account for the many factors influencing the spreading dynamics. Yet, the results from numerical simulations are often as complicated as the reality, leaving us with a sense of confusion about how the different factors account for the simulation results. Here, using a multitype branching together with a graph tensor product approach, I derive a single equation for the effective reproductive number of an infectious disease outbreak. Using this equation I deconvolute the impact of crowd management, targeted testing, contact heterogeneity, stratified vaccination, mask use, and smartphone tracing app use. This equation can be used to gain a basic understanding of infectious disease outbreaks and their simulations.
人口的异质性给传染病暴发的数学描述带来了挑战。数值模拟被用来考虑影响传播动力学的许多因素。然而，数值模拟的结果往往和现实一样复杂，使得我们对于不同因素如何影响模拟结果感到困惑。在这里，我使用多类型分支和图张量积方法，为传染病暴发的有效繁殖数推导出一个单一方程。利用这个方程，我可以分解人群管理、有针对性的检测、接触异质性、分层接种、口罩使用和智能手机追踪应用程序使用对传染病暴发的影响。这个方程可以用来帮助我们基本理解传染病暴发及其模拟。
