Tag Archives: R0

Developing News on the Wuhan Corona Virus, nCoV2019

This post links to some important new findings about the corona virus, nCoV2019, from Wuhan, China.  I’m neither an epidemiologist nor a public-health expert, but I study microbial population dynamics and evolution from a basic-science perspective. So I have a pretty good sense of what the experts are saying, what is reliable within the stated limits of uncertainty and assumptions, and so on. However, keep in mind that this is a very rapidly developing situation, so the “facts” (data and interpretations) may change quickly.

Genomic analysis points to a single recent origin of this outbreak [from Trevor Bedford (@trvrb) and @nextstrain]

Excellent multi-slide presentation of important inferences based on the first 27 sequenced genomes of the virus. These data clearly point to a single recent origin of the outbreak, with rapid expansion from there.

Genomic analysis also points to bats as likely source of infection [also from Trevor Bedford (@trvrb) and @nextstrain]  

Phylogenetic analysis of genomes of the Wuhan outbreak virus and other corona viruses indicates close relationship with isolates from bats.

The closest bat isolate and the current outbreak strain probably diverged several decades ago, given genomic differences and rates of sequence evolution in related viruses. That might seem a long time ago for such a recent outbreak, but it’s not as though this individual bat gave rise to the infection that started the outbreak. (That individual bat has probably been dead for some time.) It’s cousin, so to say, or maybe even a different species of bat, was probably the source.

In any case, the very few genetic differences among the human isolates imply a single, recent origin of the current outbreak. Various estimates point to the initial infection in Wuhan having likely occurred sometime in November or thereabout.

Detailed report estimating epidemiological parameters [from Jonathan Read (@JonRead15) and colleagues]

A detailed report of epidemiological parameter estimates taking into account many factors.

Just how many people are infected in Wuhan?

Nobody knows for sure, but it’s certainly well above the number of confirmed cases.  Several estimates from different groups suggest tens of thousands, and perhaps even hundreds of thousands.

Article quoting Neil Ferguson, an expert at Imperial College: “My best guess now is perhaps 100,000 cases right now” [as of Sunday, Jan 26]. “Almost certainly many tens of thousands of people are infected.”

Above referenced report from Read and colleagues, page 4: “We estimate that on 22 January, in Wuhan there were currently 14,464 infected individuals (prediction interval 6,510-25,095), and a total 21,022 infections (prediction interval 11,090-33,490) since the start of the year.” [The difference in these estimates would reflect individuals who recovered or died.]

My own quick-and-dirty estimate of ~100,000, which shows one very rough way of making an approximation quickly and easily from public data. I emphasize that the other groups are doing far more thorough, competent, and expert analyses than my own. My approach is meant to illustrate one way of making a complicated problem more tractable.

How fast is the virus now spreading outside China? 

Again from Trevor Bedford: The number of international travel cases is still increasing exponentially. (Note the logarithmic scale on the y-axis, such that a straight line indicates exponential growth. The image below is from Bedford’s linked tweet.)

Corona virus international cases from Trevor Bedford

That’s unfortunate, but not too surprising at this stage, because there’s a delay between becoming infected, traveling, and entering another country.  The extent and seriousness of the situation has only been recognized in the last couple of weeks.  With the quarantine and isolation procedures in Wuhan and elsewhere, and with new travel restrictions and monitoring, we can expect this rate of increase to decline and, hopefully, reverse. However, when and by how much things improve will depend on unknowns including whether any additional hotspots take hold, whether some people can transmit the virus while they are asymptomatic (see below), etc.

R0 and what it means

R0 is an important quantity when trying to control an infectious disease.  In words, it refers to the average number of secondary infections that result from each new infection.  So if R0 for some disease is 2, it means that each infected person infects 2 other people before the first one is no longer infectious (say, because they’ve recovered). Any number greater than 1 implies a sort of chain reaction, unless control measures are taken.  (If the number is less than 1, then a disease will likely die out on its own—this can happen, for example, if the disease comes from another species but is rarely transmissible between humans.) The goal of public-health strategies—including vaccination (when available) and isolation/quarantine procedures—is to reduce the likelihood of secondary infections. So if R0 = 2 without public-health measures, the spread of the disease through a population can be halted by preventing ~50% of the transmissions that would otherwise occur without that measure.  If R0 = 4, then stopping the disease’s spread would require blocking 75% of the potential transmissions.  For the new corona virus, the latest estimates suggest a value of R0 of ~2.5 (with a plausible range from 2.0 to 3.1 in one recent estimation based on data through Jan-26).

Science writer Ed Yong has a very nice article about R0 and what it means and doesn’t mean.

Some Important Unknowns

There remain some extremely important unknowns.  One unknown concerns the distribution of the severity for those infected.  The reported numbers are extremely scary, with the number of reported deaths in Wuhan exceeding the number of recovered from this infection. (See 5:00 pm Jan 29 update below. Though still scary, the recoveries now exceed deaths, as was expected as more data came in.) However, those statistics deal with cases that are diagnosed in hospital settings, and so they are heavily biased toward the most severe cases. It also appears that individuals with other health issues are more susceptible, or at least are more prone to severe infections. But much remains unknown about the overall distribution of severity of infections at this stage, and how it depends on age and other factors.

A second important unknown concerns the timing of transmission. There are some reports that some individuals might be infectious before they show symptoms such as fever and the like.  If this proves to be true, and especially if it proves to be fairly common, then it makes it more difficult to control the spread of a disease because an infected person may have infected other individuals before being isolated and carefully monitored. Some experts are skeptical about these reports of contagiousness before symptoms appear—let’s hope they’re right, as that would help with timely interventions to break transmission chains.

I welcome any comments, corrections, additions from reliable sources, and updates.

NEW INFO 11:00 am (Jan 29):  A bit of good news from CDC. Now 5/73 = 6.8% tests of potential nCoV2019 cases in US have been positive to date. It had been 5/37 = 13.5% at last update. That means no new confirmed positive cases in US. As expected given the spreading infection and expanding concern, the number of pending (unresolved) cases has increased.

NEW INFO 12:15 pm (Jan 29):  I had read some discussions on the web that the nCoV2019 outbreak might be caused by a “recombinant” virus. This, in turn, led to some conspiracy-type speculation about a virus that escaped from a lab. Recombinants can occur naturally, as well as be made in the lab. So I wondered whether there was good evidence for recombination in these viruses and, if so, whether the recombination pre-dated or post-dated the split between the most closely related bat strain and the Wuhan strain nCoV2019. I turned, once again, to expert Trevor Bedford (@trvrb), since this is a phylogenetically based question (see first two entries in this post). He pointed me to in-depth analyses and discussion of these issues by experts.  First, some genetic recombination has occasionally occurred in these viruses in nature. Second, he sees no evidence of “recombination in the ~50 years since the ancestor of nCoV outbreak viruses split from RaTG13” (i.e., the most closely related corona virus in the data base, which derives from a bat in the year 2013).

NEW INFO 12:45 pm (Jan 29): Physicist Dirk Brockmann presents an analysis that uses actual worldwide travel data to estimate the relative probabilities (“import risks”) that travelers from Wuhan enter other countries via specific airports. The results align quite well with where new international cases have been turning up.  [h/t to Richard Neher @richardneher via twitter]

NEW INFO 5:00 pm (Jan 29): I’ve mentioned that we know little about distribution of outcomes with respect to disease severity and outcomes. The Lancet (a leading medical journal) has just published a paper analyzing 99 of the early cases in Wuhan, China, that were confiirmed as involving the new nCoV2019 corona virus. These cases involved hospitalization, during a period of considerable stress on the health-care system.  Half of these cases involved patients with other underlying chronic diseases. Nonetheless, about 75% of the patients now have a good prognosis, and about a third have been discharged from the hospital. However, many of the others developed “acute respitory distress syndrome” and 11 of the 99 died. Again, these are atypically severe cases. It’s also very interesting that almost half of all the cases involved individuals who worked at the Wuhan seafood market.  However, the earliest cases appear to not involve that market, which makes this association rather curious.  Also, we still don’t know much about the infections that are less severe for individuals, but which are nonetheless very important for understanding the viral transmission dynamics.

NEW INFO 5:20 pm (Jan 29): More nCoV2019 viral genomes have been sequenced from around the world and placed in their phylogenetic context by the @nextstrain team.  I’ve copied a screenshot below that shows the latest version, plotted in terms of mutational distance from the earliest Wuhan samples. It’s very interesting that there are clusters of some of the international-travel cases including (about 2/3 of the way down) the French (2 identical isolates), one from the USA, and a Taiwan case. They all share one mutation that none of the other isolates have. That might not seem like much, but with so few mutations in total (over the whole tree), it strongly suggests that these cases all have some secondary (or later) source in common along the viral transmission chain.  And just above that cluster is another cluster of isolates that all share 2 mutations with an interesting mix of international and non-Wuhan Chinese samples. So there might be some useful epidemiological clues in there, if this information can be coupled with careful studies of patient travel and contacts.

nCoV2019 nextrstrain phylogram

NEW INFO 6:10 pm (Jan 29): From Richard Neher via twitter, a report that 4 Germans who tested postitive after contact with a work-place visitor from Wuhan are apparently asymptomatic. It’s unclear from the short tweet whether the Germans never exhbited any symptoms at all, or only very mild ones, but they are now recovered. This finding supports the conclusion that there are many mild infections (good news), but it also implies that the number of infected people–some of whom might transmit the virus–is quite large (bad news), in line with some of the calculations of the number infected.



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