Sub-spreading events limit the reliable elimination of heterogeneous epidemics.

Kris V Parag

doi:10.1098/rsif.2021.0444

Abstract

We show that sub-spreading events, i.e. transmission events in which an infection propagates to few or no individuals, can be surprisingly important for defining the lifetime of an infectious disease epidemic and hence its waiting time to elimination or fade-out, measured from the time-point of its last observed case. While limiting super-spreading promotes more effective control when cases are growing, we find that when incidence is waning, curbing sub-spreading is more important for achieving reliable elimination of the epidemic. Controlling super-spreading in this low-transmissibility phase offers diminishing returns over non-selective, population-wide measures. By restricting sub-spreading, we efficiently dampen remaining variations among the reproduction numbers of infectious events, which minimizes the risk of premature and late end-of-epidemic declarations. Because case-ascertainment or reporting rates can be modelled in exactly the same way as control policies, we concurrently show that the under-reporting of sub-spreading events during waning phases will engender overconfident assessments of epidemic elimination. While controlling sub-spreading may not be easily realized, the likely neglecting of these events by surveillance systems could result in unexpectedly risky end-of-epidemic declarations. Super-spreading controls the size of the epidemic peak but sub-spreading mediates the variability of its tail.

Highlights

Emerging infectious diseases are a major and recurring threat to both global health and economies
In equation (2.4), we showed how variance-to-mean ratio (VM) ratios of the event reproduction numbers, Rs, directly control those of the incidence values, Is
The sub-spreading control scheme considerably shrinks the variation among zs curves. This proceeds from the results of the previous section, where we found that, at small mean reproduction numbers, limiting sub-spreading significantly reduces VM[Rs] and VM[Is] (see equation (2.4))

Summary

Introduction

Emerging infectious diseases are a major and recurring threat to both global health and economies. Key parameters which characterize the impact of interventions on the transmission dynamics of an infectious disease are the time-varying event reproduction number, denoted Rs at time s, with mean μs [1] and the dispersion level, k, of the offspring distribution of the epidemic [2]. The second defines transmission heterogeneity, i.e. it captures the variation of possible Rs about mean μs. The values of these parameters often inform intervention policy and much debate remains on their implications for both epidemic control and elimination [3,4,5]

Methods

Results

Conclusion