Estimating Effective R0: COVID-19 Data Resources Should Report This For All Countries

James Lyons-Weiler, PhD – 3/18/2020

WE KNOW that at any given time during the growth phase of COVID-19 pandemic the number of cases reported represent perhaps only as many as 20% of cases present. We also know that the number of cases we see today are the product of exposure from infected individuals 4-5 days prior.

Therefore, if we use the ratio of the number of cases on a given day, Nx, to the number of cases five days prior (N_(x-5)), we can track the effects of interactions.

Notably, this rough estimator will only be relevant during the growth phase; during retraction, the Effective R0 will become <1 but that could be misleading as it would imply that infected people are preventing infection.

That neat trick is possible via plasma convalescent therapy, but that’s a different but equally important point.

For the outbreak in in the US, the increase since Day 1 looks like this

Now here is the rough Effective R0 estimator for the US over the same time period.

The very simple estimator of the Effective R0 shows that the rate of increase has fluctuated greatly. During times when no testing was being conducted, no new cases were being reported, and thus R0 might also be overestimated later on. Still, it seems useful as an approach to evaluate ongoing interventions such as social distancing and therapeutics.

How to Interpret Effective R0

Effective R0 can be used to get an idea – a very rough idea – on the dynamics of the rate of increase during the growth phase of an epidemic. The goal is to push Effective R0 below 1, and keep it there.

How NOT to Interpret Effective R0

Effective R0 is not R0. It is a product of the outcome of infection, testing, reporting and interventions and other factors.

Don’t Be Complacent. When the R0 start to decline, it is time to continue effective interventions and to add new ones that will push it down even further. Like pulling someone out of the water, you’re not in the clear until they are on dry land. Dry land is Effective R0 = 0/0 — no new cases for a sustained period of time.

Now, let’s push for therapeutics – plasma convalescent therapy and antivirals – because it does not appear that we will defeat SARS-CoV-2 worldwide by Social Distancing alone.


  1. Can you explain exactly what a Flu Shot does to the lungs? Japan has begun using a Flu Shot to treat coronavirus patients and there are doctors on the web recommending people get a Flu Shot so I’d like to know-what does it do in the body?

  2. now they are talking of a S and L version of the SARS-coV-2 that spread differently fast!? “With population genetic analyses of 103 genomes of SARS-CoV-2, we found that SARS-CoV-2 viruses evolved into two major types -L and S,” said the preliminary study published in the journal National Science Review.”

    What are these L and S types!? How do they matter and what do we need to understand from this development?

    Please explain in layman terms! πŸ˜‚πŸ‘πŸ» kind regards, from Sweden

  3. Where did you get that 20% number!. Most infectious diseases and adverse events are only reported 1-10% of the time , mainly for serious cases. That study came from Harvard. Even flu tests less than 10% of ESTIMATED cases each year, and half are negative so only 5% of estimated cases are confirmed and reported . Only 5% of the estimated hospitalizations from flu were laboratory confirmed as of Jan 25

    I think the 20% figure overstates the reality. A report out of John Hopkins estimated actual cases may be more than 10 times reported cases

  4. Dr Jack,
    On Tucker Carlson (3-18) they had someone citing a recent study by an eminent French virologist claiming that chloroquine was 100% effective on covid19 in his study with 40 patients . Have you seen this study and can you comment yet?
    Also, If many people have had this virus and recovered, as I suspect. How long can they donate blood to help the health care workers and other people on the front lines? Will there antibodies be effective for a long period? This is in regards to your blog post on convalescent plasma therapy and this was also discussed on tuckers show the previous night.
    Thanks for all you do.

  5. After reviewing the research, the main problem that needs to be understood with COVID-19 spread is shown by a new model from the peer-reviewed Journal Science which predicts that people who had not yet been tested/diagnosed with COVID-19, but exposed and are asymptomatic were the infection source of 79% of the reported cases in China. 86% of all infections are shown in the model to be in untested/undiagnosed carriers who are asymptomatic in the early stage. So these untested people who have been exposed go about their business since they do not have symptoms and spread it to others.

    It has further been shown that in areas with extensive testing of everyone to find these asymptomatic carriers and isolation of those diagnosed but asymptomatic, the levels of overall deaths of those that are more vulnerable could be reduced greatly and allow others to continue working etc at a reduced level. The researchers explained they had tested all inhabitants twice and that the study led to the discovery of the decisive role in the spread of the coronavirus epidemic of asymptomatic people. EXTENSIVE TESTING AND ISOLATION IS THE SOLUTION. Also look at South Korea which did far more extensive testing and isolation which has far less deaths.

    1. Isolation and therapeutics are key. Testing is not so important except
      for resource prioritization (triage) and pinpointing who should receive

      We should combine therapeutics ASAP w/social distancing to avoid the need for triage.
      Test inaccuracy of the testing has been dangerously misleading.

      Here I show that mathematically, testing is 100% irrelevant to making Eff R0 useful.

      If Nx is the number of cases on day X, and N(x-5) is the number of cases on day X-4, use T as the proportion of cases tested.

      Nx/(N(X-5) = T(Nx)/T(N(X-5)

      Here are some simulated data in case it helps.

      Day #Cases Day EffR0 EffR0 w/testing
      1 0 1
      2 1 2
      3 4 3
      4 8 4
      5 11 5
      6 18 6 18 18
      7 28 7 7 7
      8 48 8 6 6
      9 76 9 6.909 6.909
      10 125 10 6.944 6.944
      11 200 11 7.142 7.142
      12 322 12 6.708 6.708
      13 519 13 6.828 6.828947368
      14 833 14 6.664 6.664

  6. ‘Herd immunity’: Why Britain is actually letting the coronavirus spread

    London: In the weeks since coronavirus exploded around the globe it has become increasingly apparent that this freight train simply can’t be stopped.

    Lockdowns, school closures and flight bans will go some way to reducing pressure on hospitals but these measures will not halt widespread transmission. Health authorities warn hundreds of millions will probably get infected and the vast majority will survive. Some of society’s most vulnerable will still bear the brunt, however, and the death toll could be very high.

    On that basis, some difficult decisions must be made. Britain has made some tough calls already but their go-it-alone approach carries significant risk and is proving divisive.

    In crude terms, Boris Johnson’s government is mounting the argument that the outbreak is now so far gone that it is actually desirable for people to get infected. And a lot of people – potentially up to 70 per cent of the country’s population, or roughly 47 million.

    A risky strategy? Very. At complete odds with the rest of the globe and the World Health Organisation? Definitely. Politically unpopular? Absolutely. But sensible? Quite possibly.

    Britain’s approach has three core elements: enact social distancing measures much more slowly than other countries; shield at-risk groups like the elderly and sick from contact with the general population; and then let COVID-19 slowly sweep through everybody else.

    The latter approach is called “herd immunity” – a phrase likely to enter the lexicon shortly in the same way as “flatten the curve”. Herd immunity describes a scenario where so many people become resistant to a disease – either through vaccinations or exposure – that it becomes much harder for the virus to spread through the rest of the population. Mass immunity could effectively cause the virus to burn out over the course of one or two seasons, or buy time until a vaccine is developed and distributed.

    more a link.

  7. Since there is more than 1 corona virus, can the current corona virus test be detecting strains of the other corona viruses as well as COVID-19? Considering the MSM has said that the results of many have been confusing. Ex: the doctor in Washington State who tested negative. He than began showing symptoms and retested positive.
    Are Coronavirus Tests Accurate?

    Could some of the people who are positive or have very mild symptoms tested positive from one of the other strains of the virus that’s not so aggressive?

    Just a thought.

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