Respiratory protective devices (RPDs) are critical for reducing the spread of infection via inhalable droplets. In determining the type of RPD to deploy, it is important to know the reduction in the infection rate that the RPD enables for the given pathogen and population. This paper extends a previously developed susceptible-infected-recovered (SIR) epidemic model to analyse the effect of a protection strategy. An approximate solution to the modified SIR equations, which compares well with a full numerical solution to the equations, was used to derive a simple threshold equation for predicting when growth of the infected population will occur for a given protection strategy. The threshold equation is cast in terms of a generalized reproduction number, which contains the characteristics of the RPDs deployed by the susceptible and infected populations, as well as the degree of compliance in wearing the equipment by both populations. An example calculation showed that with 50% of the susceptible population deploying RPDs that transmit 15% of pathogens, and an unprotected infected population, an otherwise growing infection rate can be converted to one that decays. When the infected population deploys RPDs, the transmission rate for the RPDs worn by the susceptible population can be higher.

中文翻译：

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一种数学模型，用于评估防护设备在减少可吸入飞沫感染风险方面的有效性。

呼吸防护装置（RPD）对于减少可吸入小滴传播的感染至关重要。在确定要部署的RPD的类型时，重要的是要知道RPD可以降低给定病原体和种群的感染率。本文扩展了先前开发的易感感染恢复（SIR）流行病模型，以分析保护策略的效果。修改后的SIR方程的近似解可以与方程的完整数值解很好地比较，用于得出简单的阈值方程，以预测在给定的保护策略下何时会出现感染人口的增长。阈值方程式是根据广义再现数进行转换的，其中包含易感人群和感染人群部署的RPD的特征，以及这两个人群在佩戴设备时的依从程度。一个示例计算表明，在50％的易感人群中部署了传播15％病原体的RPD，以及未受保护的感染人群，原本正在增长的感染率可以转化为衰落率。当感染人群部署RPD时，易感人群佩戴的RPD的传播率会更高。否则，感染率的增长可以转化为衰败率。当感染人群部署RPD时，易感人群佩戴的RPD的传播率会更高。否则感染率的增长可以转化为衰减率。当感染人群部署RPD时，易感人群佩戴的RPD的传播率会更高。