论文标题
在有效繁殖数的凸面上
On The Convexity Of The Effective Reproduction Number
论文作者
论文摘要
在这项研究中，我们通过异质网络中的SIR扩散过程分析了有效的繁殖数量$ r $的演变；表征其衰减过程可以分析研究对策对异质性下病毒进展的影响，并优化其策略。 最近的研究的一个显着结果表明，节点/个体之间的异质性（或超级膨胀）可能对扩散过程的进程产生巨大影响，这可能导致受感染个体数量的非线性减少$ r $。我们说明异质性并分析扩散过程的随机发展。我们表明，$ r $的减少实际上是在受感染的个体数量中凸出的，这种凸性来自异质性。该分析基于在差异时期建立易感人群之间的随机单调关系。 我们证明，有效繁殖数的凸行为会影响用于抵抗病毒传播的对策的表现。结果也适用于控制计算机网络中病毒和恶意软件的传播。我们从数值上检查了牛群免疫阈值（命中）对异质性水平和所选政策的敏感性。
In this study we analyze the evolution of the effective reproduction number, $R$, through a SIR spreading process in heterogeneous networks; Characterizing its decay process allows to analytically study the effects of countermeasures on the progress of the virus under heterogeneity, and to optimize their policies. A striking result of recent studies has shown that heterogeneity across nodes/individuals (or, super-spreading) may have a drastic effect on the spreading process progression, which may cause a non-linear decrease of $R$ in the number of infected individuals. We account for heterogeneity and analyze the stochastic progression of the spreading process. We show that the decrease of $R$ is, in fact, convex in the number of infected individuals, where this convexity stems from heterogeneity. The analysis is based on establishing stochastic monotonic relations between the susceptible populations in varying times of the spread. We demonstrate that the convex behavior of the effective reproduction number affects the performance of countermeasures used to fight a spread of a virus. The results are applicable to the control of virus and malware spreading in computer networks as well. We examine numerically the sensitivity of the Herd Immunity Threshold (HIT) to the heterogeneity level and to the chosen policy.
