论文标题
反馈先生（FSIR）模型强调了依赖感染的缓解策略的优势和局限性
A feedback SIR (fSIR) model highlights advantages and limitations of infection-dependent mitigation strategies
论文作者
论文摘要
流行病暴发的传播率可能会随着时间的流逝而变化，具体取决于社会反应。非药理缓解策略，例如社会距离和采用保护设备，旨在通过降低传染性接触来降低传输速率。为了研究缓解策略对流行病演变的影响，受感染，死亡或恢复水平影响的非线性传播速率已包括在经典SIR模型的许多变体中。这类模型尤其与Covid-19的流行病特别相关，其中人口行为受到前所未有的丰富性和通过在线平台的全球感染和死亡数据的快速分布的影响。该手稿重新审视了SIR模型，其中降低传输速率是由于感染的知识。通过一种假设个体在混合溶液中表现得像分子的平均野外方法，人们通过负反馈术语得出了一个随时间变化的繁殖数，该繁殖数量依赖于感染信息，而这些反馈术语等同于生态学中的II型功能，而Michaelis-Menteren在化学和分子生物学中的功能。提供了模型的逐步推导，并概述了其定性分析的方法，表明负反馈在结构上降低了感染的峰值。同时，反馈可能会大大延长流行病的持续时间。计算模拟与分析预测一致，并进一步表明，即使在存在信息延迟的情况下，感染峰值降低也存在。如果缓解策略与感染成正比成正比，则将单个参数添加到SIR模型中，从而有助于说明感染依赖性社会距离的影响。
Transmission rates in epidemic outbreaks may vary over time depending on the societal response. Non-pharmacological mitigation strategies such as social distancing and the adoption of protective equipment aim precisely at reducing transmission rates by reducing infectious contacts. To investigate the effects of mitigation strategies on the evolution of epidemics, nonlinear transmission rates that are influenced by the levels of infections, deaths or recoveries have been included in many variants of the classical SIR model. This class of models is particularly relevant to the COVID-19 epidemic, in which the population behavior has been affected by the unprecedented abundance and rapid distribution of global infection and death data through online platforms. This manuscript revisits a SIR model in which the reduction of transmission rate is due to knowledge of infections. Through a mean field approach that assumes individuals behave like molecules in a well-mixed solution, one derives a time-varying reproduction number that depends on infection information through a negative feedback term that is equivalent to Holling type II functions in ecology and Michaelis-Menten functions in chemistry and molecular biology. A step-by-step derivation of the model is provided, together with an overview of methods for its qualitative analysis, showing that negative feedback structurally reduces the peak of infections. At the same time, feedback may substantially extend the duration of an epidemic. Computational simulations agree with the analytical predictions, and further suggest that infection peak reduction persists even in the presence of information delays. If the mitigation strategy is linearly proportional to infections, a single parameter is added to the SIR model, making it useful to illustrate the effects of infection-dependent social distancing.
