title: A mathematical model for assessing the effectiveness of protective devices in reducing risk of infection by inhalable droplets.
abstract: 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.
authors: Division of Applied Mechanics, Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, Food and Drug Administration, Silver Spring, MD, USA.
authors: Matthew R
authors: MR
authors: Myers
authors: Division of Applied Mechanics, Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, Food and Drug Administration, Silver Spring, MD, USA.
authors: Prasanna
authors: P
authors: Hariharan
authors: Division of Applied Mechanics, Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, Food and Drug Administration, Silver Spring, MD, USA.
authors: Suvajyoti
authors: S
authors: Guha
authors: Division of Applied Mechanics, Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, Food and Drug Administration, Silver Spring, MD, USA.|Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, MD, USA.
authors: Jing
authors: J
authors: Yan
mesh_terms: D058872:Epidemics; D006801:Humans; D001239:Inhalation; D008962:Models, Theoretical; D011482:Protective Devices; D012141:Respiratory Tract Infections / Q000517:prevention & control*; D012306:Risk