Commentary on Ferguson, et al., \u201cImpact of Non-pharmaceutical Interventions (NPIs) to Reduce COVID-19 Mortality and Healthcare Demand\u201d

S Eubank,M Marathe,I Eckstrand,C L Barrett,B Lewis,S Venkatramanan

doi:10.1007/s11538-020-00726-x

Abstract

A recent manuscript (Ferguson et al. in Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand, Imperial College COVID-19 Response Team, London, 2020. https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-NPI-modelling-16-03-2020.pdf) from Imperial College modelers examining ways to mitigate and control the spread of COVID-19 has attracted much attention. In this paper, we will discuss a coarse taxonomy of models and explore the context and significance of the Imperial College and other models in contributing to the analysis of COVID-19.

Highlights

Infectious disease epidemiologists’ workhorse mathematical model throughout the twentieth century was the compartmental model, which partitions a population into a small set of possible disease states, e.g., susceptible (S), infectious (I), and removed (R), and specifies transition rates among the states
The overall growth in infections is proportional to the ratio of these transition rates
Compartmental models reproduce observed features of outbreaks, such as a selflimiting period of nearly exponential growth to a single peak followed by gradual decrease as the pool of susceptibles (S) in the population is depleted

Summary

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The overall growth in infections is proportional to the ratio of these transition rates. The rate at which new infections occur is determined by a dimensionless combination of model parameters known as the reproductive number, R. Social distancing aims to reduce β by limiting the number of contacts between infectious and susceptible people in which transmission can occur. Compartmental models can be elaborated (Hethcote 1994) by expanding the number of disease states (e.g., by adding compartments for exposed (E) or vaccinated (V )) or by partitioning the population by demographics such as age or location. Such models are well suited for representing demographically related heterogeneity in the course of illness or contact rates.

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