Wikipedia:Reference desk/Archives/Science/2020 December 8

= December 8 =

Covid vaccine
As I understand it, the basic reproduction rate (R0) of Sars-Cov-2 is around 5.0. Now there's a finding that the Astra-Zenica vaccine is about 70% effective. Does that mean if everyone is vaccinated, 70% of the transmission is eliminated, so R0 drops to 0.3*5.0 = 1.5? And is that not still a contagious virus, especially if everyone drops the minimal precautions that they're taking now? I feel like we need a stupidity vaccine to go along with the Covid vaccine. Thanks. 2602:24A:DE47:BB20:50DE:F402:42A6:A17D (talk) 21:49, 8 December 2020 (UTC)
 * We don't know how any of the vaccines affect transmission. All that has been measured is protection against symptomatic infection. Graham Beards (talk) 22:01, 8 December 2020 (UTC)
 * They don't test for presence of the virus, as opposed to looking for symptoms? Lots of people test positive who are asymptomatic.  They are still capable of transmission, from what I understand.  Then there will also be the issue of multiple strains of the virus etc.  Anyway, thanks. 2602:24A:DE47:BB20:50DE:F402:42A6:A17D (talk) 22:08, 8 December 2020 (UTC)
 * A problem with quoting specific values for the basic reproduction number (not "rate") is that it depends on the behaviour of individuals in the population; in a society where the typical indivual meets many others, shaking hands if not kissing, the number will be higher than in a less gregarious society whose cultural norms in greeting are more constrained. But in this context we should not look at the basic reproduction number, but at the effective reproduction number (before vaccination). Let's do some maths. I'll work with fractions instead of percentages. If the effectiveness of a vaccine is given as $e$, I take it to mean that, whereas a fraction $s$ in the control group developed symptoms during a given period, that fraction was reduced by a factor $1−e$ to $(1−e)s$ in the experimental group – those that were vaccinated. Among this group of asymptomatic vaccinees, some will nevertheless be infectious carriers. For simplicity I define "carrier" to mean "infectious carrier" – I think it will be rare for a carrier to be both symptomatic and not infectious, and we'll let asymptomatic non-infectious carriers fly under the radar. It is not unreasonable to assume that the ratio between symptomatic and asymptomatic carriers among vaccinees is similar to that in the general unvaccinated population. Denote the fraction of asymptomatic carriers among all carriers by $a$, so the number of asymptomatic carriers equals the number of symptomatic carriers time a factor  $a/(1−a)$. Among the experimental group, a fraction $(1−e)s$ became symptomatic, which would imply a fraction $(a/(1−a))×(1−e)s$ of infectious but asymptomatic vaccinees. To make any progress we need further assumptions: all individuals who develop symptoms self-quarantine, and the probability of a vaccinee becoming infectious and transmitting the disease before immunity would normally kick in is small enough to allow it to be neglected. In the same period, a fraction $(a/(1−a))×s$ of infectious but asymptomatic vaccinees from the unvaccinated population will walk around. If a fraction $v$ of the population is vaccinated, they will then contribute a fraction $v×(a/(1−a))×(1−e)s$ of infectious but asymptomatic to the total population, whereas the unvaccinated individuals contribute a fraction $(1−v)×(a/(1−a))×s$; together $v×(a/(1−a))×(1−e)s + (1−v)×(a/(1−a))×s =$ $(v(1−e)+(1−v))×(a/(1−a))×s$, compared to $(a/(1−a))×s$ without vaccination (equivalent to setting $v = 0$). The reduction in ambulant infectious individuals is then by a factor $v(1−e)+(1−v)$. As this simple calculation shows, to see the effect of a large-scale vaccination programme we do not need to know a numerical estimate for $a$ – which is estimated to be about 0.4. If $e = 0.7$ and $v = 0.75$, that comes out as $0.475$. The effective reproduction number can be expected to go down by the same factor, which may be enough to quell the epidemic.  --Lambiam 12:14, 9 December 2020 (UTC)