标题： 基于SEIARD流行病学模型的传染病保险精算分析 显示英文标题

标题： Actuarial Analysis of an Infectious Disease Insurance based on an SEIARD Epidemiological Model

摘要： 不断增长的传染病爆发数量，如由SARS-CoV-2病毒引起的爆发，突显了能够适应流行病驱动风险的精算模型的必要性。 传统的寿险框架通常依赖于静态的死亡率假设，这些假设无法捕捉疾病传播的时间和行为复杂性。 在本文中，我们提出了一种基于SEIARD流行病学模型的综合精算框架。 该框架能够对潜伏期和疾病导致的死亡率进行明确建模。 我们根据SEIARD动态推导了关键的精算量，包括年金福利的现值、支付流和净保费。 我们制定了一个前瞻性准备金函数，并分析其在整个流行病过程中的演变。 此外，我们研究了感染力、死亡率和移除率，以评估它们对流行病调整后的生存概率的影响。 通过非标准有限差分（NSFD）方案实现的数值模拟展示了该模型在各种参数设置和保险政策假设下的适用性。 显示英文摘要

摘要： The growing number of infectious disease outbreaks, like the one caused by the SARS-CoV-2 virus, underscores the necessity of actuarial models that can adapt to epidemic-driven risks. Traditional life insurance frameworks often rely on static mortality assumptions that fail to capture the temporal and behavioral complexity of disease transmission. In this paper, we propose an integrated actuarial framework based on the SEIARD epidemiological model. This framework enables the explicit modeling of incubation periods and disease-induced mortality. We derive key actuarial quantities, including the present value of annuity benefits, payment streams, and net premiums, based on SEIARD dynamics. We formulate a prospective reserve function and analyze its evolution throughout the course of an epidemic. Additionally, we examine the forces of infection, mortality, and removal to assess their impact on epidemic-adjusted survival probabilities. Numerical simulations implemented via a nonstandard finite difference (NSFD) scheme illustrate the model's applicability under various parameter settings and insurance policy assumptions.