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There is quite a bit of confusion in the media about some basic concepts from epidemiology. Even experts in the field are sometimes handled loosely. However, an understanding of these concepts is crucial in controlling the epidemic.

R 0 , in English the basic reproduction ratio , indicates how many people will be infected on average by each sick person when no one is immune yet. So, if someone with COVID-19 infects an average of 3 other people when no one is immune yet, R is 0 = 3 for COVID-19. So if R 0 > 1, then an infection will cause a waterfall effect, and the epidemic will grow exponentially - at least as long as the number of people who are immune is negligible.

However, as more people become immune, the average number of infections per patient will decrease. More precisely: if the fraction of people who are not yet immune is equal to f, the average number of infections per patient will only be f × R 0 ; amounts. This is the so-called effective reproductive ratio , often represented by the symbols R or R e .

In the control of the epidemic, R is most relevant: if R is less than 1, the epidemic decreases in strength (faster as R is closer to 0), R is greater than 1, then it increases in strength. Since R is the product of R 0 and f, it is favorable if R 0 or f drop. How can this be accomplished?

R 0 depends not only on the intrinsic infectivity of the virus, but also on the circumstances, such as the number of social interactions. By taking measures, R 0 can thus be reduced. Locking down, frequent hand washing, wearing face masks, and social distancing are examples of such measures.

The fraction f of people who are still susceptible, on the other hand, naturally decreases as the number of people with acquired immunity increases (note that it is still uncertain after how much time acquired immunity extinguishes again).

There is a lot to do around the threshold for group immunity: the percentage of people who need to be immune before R becomes less than 1. A frequently quoted number for this is 60-70%. Where does that come from?

Under normal circumstances (i.e. without lock down and similar measures), R 0 for COVID-19 is estimated at (slightly less than) 3 in most studies. This means that R becomes less than 1 once f is less than 1/3. A maximum of 33% of the population may therefore still be susceptible, or in other words at least 67% of the population must be immune.

However, this reasoning does not take into account a number of effects that can lower the threshold. Without going into detail, I mention one: differences between individuals in terms of the number of social contacts. (2) People with a lot of social contacts will (1) become infected faster and (2) infect more people than average (so more than R). In other words, the ‘most dangerous’ people become immune first, the least ‘dangerous’ last. As a result, R will drop faster than the simple analysis above predicts. The threshold could thus be substantially less than 60-70%, and more and more epidemiologists believe this.

However, this effect only plays in the same circumstances in which immunity is built up. Immunity built up in unnatural circumstances (such as when we give children their fundamental rights to play and education, under normal circumstances (when their fundamental rights are no longer violated, I hope the time will come) will offer less protection. It is then no longer the case that those who will normally infect people the most will also be infected first, because those first infections occurred under unnatural circumstances. Suppose that the epidemic is not permanently controlled, and a vaccine and adequate treatment are not forthcoming, then an unnatural lock down will in other words lead to more patients being needed before the threshold is reached in normal circumstances, and thus for the disruptive measures can be lifted. (3)

Does a lock down not have any positive effects? Surely, possibly.

Certain measures do not decrease R 0 more or less as there are more or fewer patients. The aforementioned measures are examples of this. Indeed: frequent hand washing will affect R 0 in the same way, whether there are 100 or 10,000 patients. The reason is that these kinds of measures are taken by every individual, including every sick person. Thus, its effect on the total number of infections increases proportionally with the number of patients, resulting in a constant effect on R 0 .

Other measures, however, do not increase proportionately to the number of patients. An example is contact tracing . Army tracers are limited in size, so the number of infestations they can prevent is limited. So it does not scale with the number of patients. The effect on R 0 of the available capacity for contact tracing is therefore greater the fewer the sick.

This is an argument for pro lock down and similar measures: it gives the government an extra tool, namely contact tracing , to keep R 0 low. Moreover, this is an instrument that is at least disruptive to society, unlike the other measures.

A major misunderstanding is that R would decrease the fewer the sick. Even leading biostatisticians claim that R would drop to 0 if the number of sick becomes 0. That is by no means the case: R does not depend on the number of patients.

This is important. Suppose we manage to get Belgium completely free of COVID-19, then R is still just equal to f × R 0 . Therefore, if R 0 can not be kept lower than 1 / f by contact tracing , a reintroduction from abroad will multiply inexorably unless disruptive measures are taken again. For example, suppose f equals 0.9 (a realistic estimate at this time), and R 0 equals 3. Then R = 2.7. This means that for every 27 new infections, the contact tracers must identify and isolate 17 before they have the chance to infect someone themselves. Is this feasible?

The key question is therefore how big the effect of contact tracing on R 0 in Belgium can be realistically, even in the most optimistic case that there are (almost) no more sick people. If that effect is limited, then with the current strategy we are doomed to quickly reintroduce the intrusive measures after each reintroduction, until there is an adequate treatment or vaccine. And I have the feeling that few virologists want to bet on money that that is for soon.

Herman Goossens’ plea for a large capacity in this area is therefore crucial to give the current strategy a chance to succeed: without a large and capable army of contact tracers , and the unconditional cooperation of the population with those people, the resulting strategy possibly a street without end.

(1) Sometimes R 0 is defined as the reproduction ratio when no one is immune and in normal circumstances , in other words without lock down or other measures. Wikipedia explains this in more detail.

(2) See: Britton, Ball & Trapmann, “The disease-induced herd immunity level for Covid-19 is substantially lower than the classical herd immunity level” .

(3) A lock down that takes into account the possibility that no vaccine or treatment will arrive would therefore be the best proportion of the number of social contactsto influence, rather than limit the same for everyone: ‘more social’ people should still be able to be ‘more social’, at least insofar as these are not the weakest (for example, children and young people have more social contacts, and are also hardly at risk; people in large residential care centers, on the other hand, also have a lot of indirect social contacts via the staff, but are weaker and therefore need to be protected more than proportionally). In that sense, requiring frequent hand washing and using face masks in public places is safer than limiting the number of social contacts. After all, washing hands and using a mouth mask reduces the risk proportionally (as long as people who go to the sea, take public transport, go to parties, etc., can still do this, provided frequent hand washing and use of a mask). A fixed limit on the number of social contacts, on the other hand, ensures that the healthy people who would quickly contribute to group immunity no longer do so.