C-19: Estimating epidemiological characteristics of the disease

Updated: May 11

The novel nature of the virus SARS-nCoV-2 and its associated disease, COVID-19, mean that the full epidemiological characteristics for the viral disease have not yet been definitively estimated. In this article we attempt to study and provide estimates for 5 specific characteristics by utilising the analysis we have conducted thus far. While we were able to provide conclusive estimates for three, the others however still require more research to determine valid estimates. We will however offer an in depth discussion on them and weigh up the challenges encountered in conducting our analysis.

The characteristics we will explore here are:

(A) Median time between infection and death

(B) Median time between infection and detection

(C) Case detection delay and test error by country

(D) Estimated true mortality rate from COVID-19

(E) Proportion of potential asymptomatic carriers in the population

(A) Median time between infection and death

Our estimates suggest this is firmly at 14 days. This derivation came from studying the onset of mobility decline due to lock-downs and matched that to transmission factor changes with a 14 day timelag - click here to read that article. A sample figure illustrating this follows below showing quite clearly how a 14 day delay introduced in the transmission factor coincides well with the change in mobility during the course of the locking-down period;

Figure: Spain mobility change during lockdown vs. transmission factor derived from death statistics

(B) Median time between infection and detection

(C) Case detection delay and test error by country

Clearly the median time between infection and case detection would differ from country to country, as each would have its own unique regime for test procedures and minimum requirements for test eligibility. By studying official statistics from a range of countries, we found this to be ranging between 0 and 22 days, with median = 9.5 days, mean = 9.3 days - see bar charts further below for tabulated data. This was determined by fitting a mathematical model around case detections and measuring the scale and time-shift required to fit the theoretical curve. We now include this in our daily projections reports, as illustrated in the example below for the Netherlands;

Figure: Netherlands actual vs modelled case detection, infection, and deaths. A scale factor of 9.3% was applied to the theoretical infection curve (derived @1.2% mortality), with a time shift of 9 days denoting the detection delay. Notice how the infection curve is the same as the death curve, just scaled and shifted - at least we can confirm that the mortality rate is constant through time!

Figure: Summarised testing errors and testing delay by country. Note South Korea, Singapore and Sweden omitted from median and mean computations of delay

(D) Estimated true mortality rate from COVID-19

(E) Proportion of potential asymptomatic carriers in the population

These two characteristics are particularly hard to independently estimate, as in practice they are both part of a circular argument concerning on the one hand, testing and infections, and the other, death and mortality. We have attempted to illustrate the inter-relationship between the two in the conceptual map below;

To explain the map: there are many factors that affect death statistics from which mortality is estimated; and on the other hand, infection statistics, which are formally determined via official records of confirmed case detections. At this point, there are also many sub-level factors that dictate how these two behave that have yet to be definitively mapped, understood and quantified; for example, it is still not known whether environmental factors play a role on symptom development and mortality from COVID-19. Or if test sufficiency and timeliness is a sizeable constraint on case detection, so much so that a large proportion of the infected population go undetected. This also makes comparison across countries often a difficult exercise, if not futile.

To illustrate one (of many) problem(s) arising from this: there is potentially a circular debate as to whether the true mortality rate of COVID-19 infection is in fact constant* and therefore the differences in case fatality measured from country to country indicates errors on the testing side; or that testing is adequate (albeit perhaps not perfect!), and therefore the mortality or death computation is in error. (*notwithstanding 'minor' differences due to age and prevalence of underlying medical conditions). So, in short one cannot determine one without first conclusively quantifying the other.

In case it is not clear to the reader: practically, no single factor on the map can be solved for definitively without solving for all the factors and unknowns at once.

We have compiled a list of online literature that discusses some of these factors in more detail for the reader;

  1. Excess deaths: https://www.ft.com/content/6bd88b7d-3386-4543-b2e9-0d5c6fac846c

  2. Mortality/case fatality rate differences: https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(20)30244-9/fulltext https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(20)30245-0/fulltext

  3. Asymptomatic transmission: https://jamanetwork.com/journals/jama/fullarticle/2765378 https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2020.25.10.2000180

  4. Test-kit shortages: https://www.nytimes.com/2020/04/06/health/coronavirus-testing-us.html

  5. Test-kit accuracy: https://www.aljazeera.com/news/2020/04/false-negatives-complicating-covid-19-testing-200411100741669.html https://www.bloomberg.com/news/articles/2020-04-11/false-negative-coronavirus-test-results-raise-doctors-doubts

But which of these factors can we potentially rule out or at least prioritise as significant or less significant factors? Unfortunately we do not have a definitive view and it will likely take the scientific community some time before they can agree on one too; however, the following are some notes gathered from gleaning available literature that could be helpful 'jog' the discussion;

  • Mortality rate differences [low-very low] - unlikely to make a material difference beyond demographic factors and prevalence of underlying conditions, as the virus mutation is deemed as slow and it is not thought to significantly affect people differently from one person in one country, to the next in another

  • Excess death figures [high] - potentially a strong candidate for a high priority factor, given in Italy excess deaths (deaths detected as in excess when comparing month on month and year on year historic trends) were recorded at 3x official COVID-19 deaths; for Indonesia's capital Jakarta it was 15x; and for a particular province in Ecuador it was 40x (see the FT link above)

  • Testing sufficiency [med] - while this has been a widely cited issue the world over, and testing delays are clearly evident from the data gathered; the ease at which we were able to fit the infection curves with modelled regressions suggests either systematic errors (such as test SOP differences, or discrepancies in test-kit accuracy), or it is non-existent, i.e. testing resources is relatively uniform in its ability from country to country to test all patients showing symptoms or relevant illnesses

  • Test regimes and procedures [high] - some countries are cited to test infected persons 3 times during the course of the illness, that is, once to detect, and twice more before giving the all clear to be discharged; while some others, just one test for the entire duration. Different norms across countries, for example frequency of GP visitation and health coverage schemes may encourage or discourage the sick to seek out assistance for what they may deem as a common ailment. We are also aware of the interdependency of this factor with test-kit resources

  • Differences in test-kit accuracy [med] - in our opinion this has not been as widely and objectively discussed as much as it probably should be. The scramble to get tests rolled out has left a jumbled mix of different types of tests and test regimes administered in different countries, for example the number of total tests administered to infected persons. Given the frequency of false negatives and positives (reportedly as high as 30%), one can guess how a test regime taking multiple test passes would alter the fatality rate computation rather dramatically. While we have some reason to believe this may be a contributing factor, we defer to experts to provide a more definitive view in due time

What interests us most is to estimate the proportion of asymptomatic carriers of the virus within the population. In our view, this is crucial to determine even if at a low confidence level if a country is to gain some semblance of normal life with COVID-19; as otherwise it would be extremely difficult to isolate infected persons from the rest of the population.

A recently paper published in the Journal of the American Medical Association (linked above under asymptomatic transmission) highlighted a piece of research conducted in the United States over the month of March 2020, where COVID-19 tests were carried out on 408 participants in a homeless shelter in Boston. They found 36% of those tested were confirmed positive with COVID-19, and while only 7.5% had coughs, 1.4% shortness of breath, 0.7% fevers, an astonishing 87.8% were asymptomatic i.e. showing no symptoms whatsoever however were infectious to other people. This is an astonishing statistic. Meanwhile the research paper from eurosurveillance studied those aboard the Diamond Princess cruise ship in Japan, and found just over 50% of the 634 passengers who tested positive were asymptomatic.

Further study: prevalence of asymptomatic cases

If we were to hypothetically assume that all else could be held equal, that is the majority of factors on the earlier illustration map are unchanging from country to country, except for one factor: the prevalence of asymptomatic carriers; then the recorded testing errors are in other words a reflection of the proportion of asymptomatic infected persons with COVID-19. This hypothetical scenario is illustrated in the following table (for which the true mortality rate was assumed to be 1% and consistent testing thresholds exists across countries);

Table: highlighted statistics across countries - hypothetical asymptomatic carrier prevalence (as % of total infected persons). Other salient statistics have been included for reference

Note the very large differences in case mortality rates across different countries.

It is surprising how closely the computation for the US comes to what was found in the earlier study cited, that is, 82% vs the earlier 87.8%.

The results in this table would suggest that certain countries are at a clear advantage moving into the next phase post current lock-downs, as the prevalence of asymptomatic carriers of the virus could be up to 3 times less that compared to countries on the other extreme. Nonetheless, even at the lowest level, 1 in 3 people would still be able to unknowingly roam free - which is still a scary prospect given the speed of infection.

We duly hope that the scientific community is able to provide a clearer thought leadership on this, as it is crucially needed before countries reopen their streets and economies over the coming months.

Further study: test-kit accuracy and differences in testing regimes & procedures

Refer back to the last table again. And observe the third column representing asymptomatic prevalence in percentages.

It is rather curious there seems to be mildly distinct groupings within the data. The first group at approximately 25-35%, a second 60-75%, a third 80-90%, and lastly 90-95%. We are not entirely certain what may be dictating these distinctions, it could range from differences in test kits utilised, or perhaps the test regimes and procedures deployed in each country. It is unlikely however, given also the clear gradation levels, that biological, genetic or weather factors are at play as there is no major geographic distinction across the groups. Neither could it constraints in test resource availability, as the positive test rates (tests administered and verifying an infected person) do not generally tally. Hopefully the scientists will determine this in time, too.


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