The reproduction number R for COVID-19 in England: Why hasn’t “lockdown” been more effective?

Abstract

<jats:p>The reproduction number R, the average number of people that a single individual with a contagious disease infects, is central to understanding the dynamics of the COVID-19 epidemic. Values greater than one correspond to increasing rates of infection, and values less than one indicate that control measures are being effective. Here, we summarise how changes in the behaviour of individuals alter the value of R. We also use matrix models that correctly recreate distributions of times that individuals spend incubating the disease and being infective to demonstrate the accuracy of a simple approximation to estimate R directly from time series of case numbers, hospital admissions or deaths. The largest uncertainty is that the generation time of the infection is not precisely known, but this challenge also affects most of the more complex methods of calculating R. We use this approximation to examine changes in R in response to the introduction of lockdown restrictions in England. This suggests that there was a substantial reduction in R before large scale compulsory restrictions on economic and social activity were imposed on 23rd March 2020. From mid-April to mid-June decline of the epidemic at national and regional level has been relatively slow, despite these restrictions (R values clustered around 0.81). However, these estimates of R are consistent with the relatively high average numbers of close contacts reported by confirmed cases combined with directly measured attack rates via close interactions. This implies that a significant portion of transmission is occurring in workplaces; overcrowded housing or through close contacts that are not currently lawful, routes on which nationwide lockdown will have limited impact.</jats:p>

Temporary “Circuit Breaker” Lockdowns Could Effectively Delay a COVID-19 Second Wave Infection Peak to Early Spring

“…To curb an initial rapid increase in COVID-19 cases, the UK entered a nationwide “lockdown” on March 23rd 2020, where people were instructed to stay in their homes except for essential journeys. This generally proved successful, decreasing the R 0 value to approximately 0.81 ( 2 ) during this period. The UK has since begun to ease these lockdown measures, with businesses being allowed to operate and social gatherings permitted subject to certain limitations.…”

The effectiveness of the three-tier system of local restrictions for control of COVID-19

“…This was then compared with the sum of new cases over the previous seven-day period. R was estimated using the equation given by Grant (2020) as = Where Y1 and Y2 are the numbers of cases in two consecutive weeks, T is the generation time for the infection (here taken as 5 days) and j is the interval between the midpoints of the periods over which cases are counted (here 7 days). This estimator performs particularly well when R is close to 1 (Grant 2020).…”

Modeling latent infection transmissions through biosocial stochastic dynamics

“…4. Averaging over the infected agents in a given period, we can get a local measure of the infection spreading, a quantity similar to what is in the epidemiology literature known as "R-factor" 46,47 . Our network presentation of the process clearly shows that the R-factor is given by the relative ratio between two successive layers of the Hnods.…”

“…Our network presentation of the process clearly shows that the R-factor is given by the relative ratio between two successive layers of the Hnods. Recently, studies have shown that the reproduction rate is a local measure with a limited predictive value, see the discussion and the empirical data analysed in [46][47][48] .…”