Subsidies are used to further control the propagation of epidemic security risks as they offer users incentives to practice security investment behaviors. However, previously proposed subsidy policies have typically been studied without insurance, and it is still challenging to build effective subsidy strategies when users can transfer some of the infection loss to the insurer by purchasing insurance, because these external incentives may alter users' decisions to purchase insurance. To this end, we designed three subsidy policies in a scenario where purchasing insurance is one of the available strategies to users: under and , the subsidies are used as the insurance funds and the risk precaution aspect of the insurance funds, respectively, and under , a fraction of the subsidies are used to support some free-riding users with high node importance in their purchase of insurance, and the remaining subsidies are used as the precaution aspect of the insurance funds. The subsidy policies are studied with a formulated security investment game model on scale-free networks from the perspectives of the public and insurer. The results show that can always work effectively and outperforms others in limiting the extent of an epidemic outbreak with similar or lower social costs, and without a reduction in profit for the insurer. More importantly, an interesting phenomenon emerges in the scenario: under specific insurance parameters, the increase in subsidy funding has a negative impact on preventing the risk spread, leading to larger final epidemic sizes. In addition, the effectiveness of on scale-free networks with larger average degree or network size and random networks are also studied. We anticipate this work can provide useful insights for policy makers with respect to design and implementation of optimal subsidy policies related to the control of epidemic security risks under an insurance scenario.

中文翻译：

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保险补贴政策对控制网络疫情安全风险传播的影响


补贴是为了进一步控制疫情安全风险的传播，激励用户践行安全投资行为。然而，之前提出的补贴政策通常是在没有保险的情况下进行研究的，当用户可以通过购买保险将部分感染损失转移给保险公司时，建立有效的补贴策略仍然具有挑战性，因为这些外部激励可能会改变用户的购买决定保险。为此，我们在购买保险作为用户可用策略之一的场景下设计了三种补贴政策：在 和 下，补贴分别用作保险资金和保险资金的风险防范方面， 和 下，其中一部分补贴用于支持部分节点重要性较高的搭便车用户购买保险，其余补贴用于保险资金的预防方面。从公众和保险公司的角度，在无标度网络上制定了安全投资博弈模型，研究了补贴政策。结果表明，在限制流行病爆发的范围方面，它总是能够有效地发挥作用，并且在社会成本相似或更低的情况下优于其他方法，并且不会减少保险公司的利润。更重要的是，场景中出现了一个有趣的现象：在特定的保险参数下，补贴资金的增加对防止风险扩散产生了负面影响，导致最终的疫情规模更大。此外，还研究了平均度或网络规模较大的无标度网络和随机网络的有效性。 我们预计这项工作可以为政策制定者在保险场景下设计和实施与控制疫情安全风险相关的最优补贴政策提供有用的见解。