Effective population size in simple infectious disease models.

Almost all models used in analysis of infectious disease outbreaks contain some notion of population size, usually taken as the census population size of the community in question. In many settings, however, the census population is not equivalent to the population likely to be exposed, for example if there are population structures, outbreak controls or other heterogeneities. Although these factors may be taken into account in the model: adding compartments to a compartmental model, variable mixing rates and so on, this makes fitting more challenging, especially if the population complexities are not fully known. In this work we consider the concept of effective population size in outbreak modelling, which we define as the size of the population involved in an outbreak, as an alternative to use of more complex models. Effective population size is an important quantity in genetics for estimation of genetic diversity loss in populations, but it has not been widely applied in epidemiology. Through simulation studies and application to data from outbreaks of COVID-19 in China, we find that simple SIR models with effective population size can provide a good fit to data which are not themselves simple or SIR.

Event-specific interventions to minimize COVID-19 transmission.

COVID-19 is a global pandemic with over 25 million cases worldwide. Currently, treatments are limited, and there is no approved vaccine. Interventions such as handwashing, masks, social distancing, and "social bubbles" are used to limit community transmission, but it is challenging to choose the best interventions for a given activity. Here, we provide a quantitative framework to determine which interventions are likely to have the most impact in which settings. We introduce the concept of "event R," the expected number of new infections due to the presence of a single infectious individual at an event. We obtain a fundamental relationship between event R and four parameters: transmission intensity, duration of exposure, the proximity of individuals, and the degree of mixing. We use reports of small outbreaks to establish event R and transmission intensity in a range of settings. We identify principles that guide whether physical distancing, masks and other barriers to transmission, or social bubbles will be most effective. We outline how this information can be obtained and used to reopen economies with principled measures to reduce COVID-19 transmission.

Quantifying the impact of COVID-19 control measures using a Bayesian model of physical distancing.

Extensive non-pharmaceutical and physical distancing measures are currently the primary interventions against coronavirus disease 2019 (COVID-19) worldwide. It is therefore urgent to estimate the impact such measures are having. We introduce a Bayesian epidemiological model in which a proportion of individuals are willing and able to participate in distancing, with the timing of distancing measures informed by survey data on attitudes to distancing and COVID-19. We fit our model to reported COVID-19 cases in British Columbia (BC), Canada, and five other jurisdictions, using an observation model that accounts for both underestimation and the delay between symptom onset and reporting. We estimated the impact that physical distancing (social distancing) has had on the contact rate and examined the projected impact of relaxing distancing measures. We found that, as of April 11 2020, distancing had a strong impact in BC, consistent with declines in reported cases and in hospitalization and intensive care unit numbers; individuals practising physical distancing experienced approximately 0.22 (0.11-0.34 90% CI [credible interval]) of their normal contact rate. The threshold above which prevalence was expected to grow was 0.55. We define the "contact ratio" to be the ratio of the estimated contact rate to the threshold rate at which cases are expected to grow; we estimated this contact ratio to be 0.40 (0.19-0.60) in BC. We developed an R package 'covidseir' to make our model available, and used it to quantify the impact of distancing in five additional jurisdictions. As of May 7, 2020, we estimated that New Zealand was well below its threshold value (contact ratio of 0.22 [0.11-0.34]), New York (0.60 [0.43-0.74]), Washington (0.84 [0.79-0.90]) and Florida (0.86 [0.76-0.96]) were progressively closer to theirs yet still below, but California (1.15 [1.07-1.23]) was above its threshold overall, with cases still rising. Accordingly, we found that BC, New Zealand, and New York may have had more room to relax distancing measures than the other jurisdictions, though this would need to be done cautiously and with total case volumes in mind. Our projections indicate that intermittent distancing measures-if sufficiently strong and robustly followed-could control COVID-19 transmission. This approach provides a useful tool for jurisdictions to monitor and assess current levels of distancing relative to their threshold, which will continue to be essential through subsequent waves of this pandemic.