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- Title
A mathematical model for assessing the effectiveness of protective devices in reducing risk of infection by inhalable droplets.
- Authors
MYERS, MATTHEW R.; HARIHARAN, PRASANNA; GUHA, SUVAJYOTI; YAN, JING
- 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.
- Subjects
RISK assessment -- Mathematical models; BREATHING apparatus; COMMUNICABLE diseases; PREVENTION of infectious disease transmission; PATHOGENIC microorganisms; SAFETY
- Publication
Mathematical Medicine & Biology: A Journal of the IMA, 2018, Vol 35, Issue 1, p1
- ISSN
1477-8599
- Publication type
Article
- DOI
10.1093/imammb/dqw018