Using statistics and mathematical modelling to understand infectious disease outbreaks: COVID-19 as an example (preprint)

During an infectious disease outbreak, biases in the data and complexities of the underlying dynamics pose significant challenges in mathematically modelling the outbreak and designing policy. Motivated by the ongoing response to COVID-19, we provide a toolkit of statistical and mathematical models beyond the simple SIR-type differential equation models for analysing the early stages of an outbreak and assessing interventions. In particular, we focus on parameter estimation in the presence of known biases in the data, and the effect of non-pharmaceutical interventions in enclosed subpopulations, such as households and care homes. We illustrate these methods by applying them to the COVID-19 pandemic.

Challenges in control of Covid-19: short doubling time and long delay to effect of interventions (preprint)

The unconstrained growth rate of COVID-19 is crucial for measuring the impact of interventions, assessing worst-case scenarios, and calibrating mathematical models for policy planning. However, robust estimates are limited, with scientific focus on the time-insensitive basic reproduction number R0. Using multiple countries, data streams and methods, we consistently estimate that European COVID-19 cases doubled every three days when unconstrained, with the impact of physical distancing interventions typically seen about nine days after implementation, during which time cases grew eight-fold. The combination of fast growth and long detection delays explains the struggle in countries' response better than large values of R0 alone, and warns against relaxing physical distancing measures too quickly. Testing and tracing are fundamental in shortening such delays, thus preventing cases from escalating unnoticed.

Challenges in control of Covid-19: short doubling time and long delay to effect of interventions (preprint)

Early assessments of the spreading rate of COVID-19 were subject to significant uncertainty, as expected with limited data and difficulties in case ascertainment, but more reliable inferences can now be made. Here, we estimate from European data that COVID-19 cases are expected to double initially every three days, until social distancing interventions slow this growth, and that the impact of such measures is typically only seen nine days - i.e. three doubling times - after their implementation. We argue that such temporal patterns are more critical than precise estimates of the basic reproduction number for initiating interventions. This observation has particular implications for the low- and middle-income countries currently in the early stages of their local epidemics.