What the data say about Coro­na and what doesn’t
With the new coro­n­avirus, new num­bers hit us every day — more infect­ed peo­ple, new deaths, plus cal­cu­la­tions on dou­bling rates and death rates. We explain what that means, what is often done wrong and where sci­en­tists still argue.

What do we know about the spread of the virus?
The best strat­e­gy for a virus to sur­vive is to spread itself as quick­ly as pos­si­ble. It depends on the host cells to mul­ti­ply. Before the immune sys­tem can take up the fight and win it, the virus must have jumped over to the next per­son. How often this hap­pens is indi­cat­ed by the base repro­duc­tion num­ber (R0). A val­ue between 2 and 3, as is also assumed for SARS-CoV­‑2, means that one per­son infects at least two oth­ers, these peo­ple in turn at least two and so on.

The basic repro­duc­tion num­ber looks like it is set in stone. But it is not. Dif­fer­ent insti­tutes and author­i­ties name dif­fer­ent val­ues ​​or ranges. The base repro­duc­tion num­ber is a con­stant rate of repro­duc­tion. In the case of an ongo­ing epi­dem­ic or pan­dem­ic, there is no con­stant ris­ing line, but a curve. The num­ber of infect­ed peo­ple ini­tial­ly devel­ops rather slow­ly with a slight increase, at the end it lit­er­al­ly explodes. It is an expo­nen­tial growth.

The effec­tive num­ber of repro­duc­tions varies depend­ing on the mea­sures tak­en and how much con­tact there is between peo­ple. This ulti­mate­ly results in the exact course of the curve. In order to curb the spread of the coro­n­avirus, the num­ber of repro­duc­tions must be pushed below the val­ue of 1.

There is often a dis­pute about whether the R val­ue is 0.9 or 1.0. Rather, the fact is that there is a pos­si­ble area. This con­fi­dence inter­val indi­cates, for exam­ple, that the val­ue is with­in a range with a 95 per­cent cer­tain­ty. At the end of April this range was between 0.8 and 1.1. The R‑value is only a snap­shot depend­ing on the tests car­ried out: If the sum of the tests increas­es, the num­ber of cas­es very like­ly increas­es too. Espe­cial­ly at the begin­ning of the epi­dem­ic, the expan­sion of the tests could have a sig­nif­i­cant impact on the R‑value.

Fluc­tu­a­tions of 0.1 in the R val­ue are more like­ly to be sub­ject to esti­ma­tion errors than actu­al trends.

An R‑value below 1 is still only an aver­age val­ue. Even then, there can be local out­breaks in some places if no one is infect­ed any­where else at the same time. The report­ed cas­es are often shown as a dia­gram and show just such a curve. The report­ed cas­es are sim­ply added up — after a cer­tain time this becomes over­dra­ma­tized. Because if you only add up the report­ed cas­es, you are neglect­ing all healthy patients. As more peo­ple recov­er than are new­ly infect­ed, the total num­ber of active, known cas­es decreases.

Every­one can view the lat­est live sta­tis­tics and case num­bers on var­i­ous news sites. They pro­vide infor­ma­tion on mor­bid­i­ty, i.e. the fre­quen­cy of an ill­ness in the pop­u­la­tion. One actu­al­ly speaks of the preva­lence. This would say how many peo­ple in Ger­many are sick with Covid-19 at a cer­tain point in time.

Usu­al­ly, the report­ed cas­es are relat­ed to a defined pop­u­la­tion (amount of peo­ple), for exam­ple the entire pop­u­la­tion or per 100,000 inhab­i­tants. For this infor­ma­tion, how­ev­er, every infec­tion would have to be known — we will explain why this is not the case lat­er. What is meant are the report­ed, pos­i­tive lab­o­ra­to­ry results — not the actu­al case num­bers (this uncer­tain­ty per­sists). Numer­i­cal val­ues ​​for an entire coun­try are of lit­tle or no prac­ti­cal use. In Italy, half of the Covid-19 cas­es were con­cen­trat­ed in north­ern Italy. This infor­ma­tion is lost in coun­try num­bers. A bet­ter clas­si­fi­ca­tion is the fre­quen­cy of 100,000 peo­ple per fed­er­al state. The num­ber of cas­es per avail­able hos­pi­tal and inten­sive care beds could be more effec­tive for polit­i­cal decisions.

It would also be help­ful to state the num­ber of tests car­ried out and to cre­ate a ref­er­ence val­ue. In Ger­many, only around six to nine per­cent of sus­pect­ed SARS-CoV­‑2 cas­es are pos­i­tive. The dou­bling rate depends large­ly on how many tests the lab­o­ra­to­ries car­ry out. If there are few­er tests than infec­tions, the dou­bling rate can nev­er tell you how the dis­ease will spread. If the test capac­i­ties are then dou­bled and, accord­ing­ly, more cas­es are diag­nosed, this has noth­ing to do with the speed of propagation.

The delay in report­ing also influ­ences the dou­bling rates. If lit­tle is report­ed on the week­end, the curve is flat­ter on Mon­day. Again, the cause is not the spread. In the news there is also the dai­ly reports about the deceased, the mor­tal­i­ty or death rate or mor­tal­i­ty. With Covid-19 one means a case- or dis­ease-spe­cif­ic mor­tal­i­ty. The term mor­tal­i­ty rep­re­sents the deaths in rela­tion to the entire pop­u­la­tion (or a defined sub-group there­of, e.g. all res­i­dents of North Rhine-West­phalia, or more sen­si­bly: per 1000 inhabitants).

A dis­tinc­tion must be made between this and lethal­i­ty. This term rep­re­sents the deaths in rela­tion to the num­ber of all sick peo­ple. The mor­tal­i­ty rate is often giv­en across all age groups. This is use­ful for com­par­i­son with oth­er dis­eases and infec­tions, but over­dra­ma­tizes the risk for young peo­ple with Covid-19 and under­es­ti­mates it for old­er peo­ple. With more pre­cise patient data, you can also cal­cu­late indi­vid­ual age-spe­cif­ic death rates, which show, for exam­ple, that old­er patients in par­tic­u­lar die with Covid-19. This makes sense because the like­li­hood of dying from Covid-19 is more than 70 times high­er for peo­ple over 80 than for 20 to 30 year olds, accord­ing to Chi­nese data. Usu­al­ly the death rate is giv­en for a peri­od of one year. Dur­ing an ongo­ing epi­dem­ic or pan­dem­ic, they are snap­shots — which are con­stant­ly chang­ing. More on that later.

And deaths are often cal­cu­lat­ed on the same day. The RKI reports 91,714 lab­o­ra­to­ry-con­firmed cas­es and 1,342 deaths on April 5. This would result in a same-day mor­tal­i­ty rate of 1342 / 91.714 = 1.5 percent.

Item Sec­tion:
Accord­ing to pre­vi­ous data, patients with severe cours­es spend an aver­age of ten days in hos­pi­tal before they die. This peri­od lies between the death and its offi­cial report. For a com­par­i­son with April 5th, the num­ber of cas­es from March 26th must be used. There are 36,508 lab­o­ra­to­ry-con­firmed cas­es. That would be quite a high val­ue for lethal­i­ty. It is well above that of the sea­son­al flu (2017/2018: 0.4 per­cent) and the esti­mates that experts gave at the begin­ning of the pan­dem­ic. These were between 0.3 and 0.7 per­cent. It is actu­al­ly not a ques­tion of lethal­i­ty, at best a pre­lim­i­nary cal­cu­la­tion. One speaks of the case fatal­i­ty rate (CFR), because the denom­i­na­tor does not con­tain the actu­al num­ber of infect­ed peo­ple, but the num­ber of report­ed cas­es. The num­ber of peo­ple actu­al­ly infect­ed is high­er. This means that the death rate will also be low­er than the pro­por­tion of peo­ple who died in a case.

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