The value of R0 depends upon the virus itself – how infective it is – and social effects such as the way that an infected person might interact with others in the community. At this stage we cannot do much about the virus itself but we can change behaviour. Unfortunately for COVID-19 individuals may be infective well before symptoms are evident, so behaviour change cannot just be limited to known cases. Social distancing is one method of reducing R0, hopefully to less 1 so the epidemic will just die out. This should work over several generations of the virus, provided that no new cases are being imported. In the long run a vaccine will enable us to have the proportion susceptible to be less than a third (ideally much less) without relying upon the virus itself to achieve this. (There were reports that the UK government was planning to rely upon the virus to generate herd immunity. Fortunately, if that was ever their plan they changed very quickly.)
In the shorter term, if R is reduced but is still greater than one, the epidemic will be delayed, more spread over time and, most importantly, the peak in the number of people requiring treatment will be less, allowing the health systems to better manage them. This is “squashing the curve”. A very readable article is at https://plus.maths.org/content/how-best-deal-covid-19, while the modelling used to guide the UK response is here. An interesting video (not for the faint hearted) is here.
We see data daily, especially numbers of positively diagnosed cases and deaths, from all countries around the world. Websites such as https://www.worldometers.info/coronavirus/ and https://coronavirus.jhu.edu/map.html are updating the numbers around the world hour-by-hour. But what does this tell us? Unfortunately, the data is invariably incomplete, with key information often lacking. One of the main problems is that the level of testing varies between countries and has changed over time. Some countries seemed to have applied the old adage “if you don’t want to find something, don’t look”.
Many of these data issues are standard ones faced by statisticians:
- In almost all countries including Australia testing is focused on those who are more likely to have the virus. When there is a shortage of resources and the aim is to control the epidemic, this makes sense. However it is heavily biased “sampling”, and will badly overestimate the proportion of the population who are positive.
- Likewise only testing people who have critical symptoms may overestimate the fatality rate, as seemed to have occurred early in Italy.
- It follows from this that young children who tend to show minimal symptoms are rarely tested. Hence we know little about the prevalence amongst school age children. This, in addition to lack of knowledge on how infective a child can be, makes it difficult to set policies for opening or closing schools.
- Some degree of random sampling of the population is required to measure the actual prevalence. That is, a properly designed survey. Surveying a rapidly changing situation is not easy, and health authorities must also consider the effect of diverting testing resources away from those at greatest risk. However at some stage the need for real information will soon be paramount.
- Fatality rates are similarly affected by poor data. Many estimates of rates uses the numbers of reported cases rather than estimates of the number of actual cases. It seems likely that to varying degrees all countries have undercounted the actual number and hence fatality rates can appear quite high. For example, in Italy, the numbers of deaths is around 10% of the number of known cases.
At present, statisticians are trying to make do with the information they have. Key parameters needed for the models are the values of R0 for different social distancing regimes. At this stage, this often means making assumptions about the proportion of cases that remain undetected. (We are fortunate that Australia appears to have one of the higher rates of testing.)