This author believes that by using a simple, reductive approach to estimating community infection, it can be demonstrated that there are substantially more COVID-19 carriers in the community, than confirmed, active cases.
The key risk to highlight is that the public may misread the current situation by underestimating their exposure to the virus. The goal of sharing this piece of work is to shift the media dialogue towards a focus on community level infection and transmission. A better understanding of risk is important both now, and in the future.
While it relies on crude assumptions, the simple model[iii] output suggests at 9 April there may have been around 20,000 carriers of COVID-19 in Australia, rather than the 3,000 or so active confirmed cases as reported[iv].
This means the community rate of infection could be about 6-7x that the media is reporting. While, this is a simplistic exercise, the key point is that the reported data is an order of magnitude less than the actual data. With access to more granular data, particularly around the demographics of those tested and the dynamics of the viral transmission, these estimates could be improved.
The public is comfortable with political commentary around public opinion, using opinion polls which have a sample size of approximately 1,000 and which are designed to reflect the electorate.
For COVID-19 we have a sample of 330,000 people tested, which is over 1% of the population. It is reasonable for the public to expect to be provided with experts’ estimates of community infection rather than focussing purely on confirmed cases.
With appropriate data on the sample versus the population, and with more random sampling on the broader population, it would be possible to start to refine our understanding of, and hence, the public’s understanding of the community infection rate.
As restrictions are relaxed there will need to be an increase in testing and tracking in the community, preferably including random sampling. From the resulting data, it will enhance the management and control of the virus, and public awareness of true risk, if estimates of community level infection can be made, and reported in the media.
The model workings, and all the assumptions are contained below.
As at 3.00pm on 9 April 2020, the following data has been sourced from Australian Government Department of Health:
- Tests conducted 330,000
- Confirmed cases 6,103
- Deaths 51
- Recoveries 2,987
- 81 cases in ICU, 262 cases in hospital
- Median age of case = 47, median age of death = 79
- Majority of cases acquired overseas
- State breakdown of tests, cases and deaths
- Estimate of median incubation period of 5-6 days
- 80% of carriers display only mild symptoms
- Testing is encouraged, only for high risk groups (i.e. symptomatic, in contact with carriers, travellers)
Additionally, from the Report of the WHO-China Joint Mission on COVID-19 the following can be sourced
- Median period from onset to recovery: two weeks
- Median period from onset to recovery (severe/ critical): 3-6 weeks
- Time period from onset to severe : approx. one week
- Time from onset to death : 2-8 weeks.
This latter set, may not be directly applicable to the Australian situation, and hence could be improved to get a clearer picture than that which follows.
From the data-set I can note the following, Australia-wide:
- 1.3% of the population have been tested(using ABS data on population)
- 1.8% tests are positive
- 0.8% of those testing positive have died. Population wide, we have seen two deaths per one million people at this stage.
- Of those positive cases, 49% have recovered.
- The case fatality rate of 1.7% where there is an outcome (death or recovery).
- 11% of active cases are currently in hospital (one-quarter of whom are in ICU).
Taking the following three facts together, allows me to make an ‘educated guess’ at the carrier mortality rate:
- The case fatality rate is 1.7% where there is an outcome
- 80% display only mild symptoms
- Testing is targeted at this stage at those with high risk. Most people with mild symptoms are unlikely to be tested, at this time.
While a purer approach to modelling would generate a range for an estimate, crudely, based on the above three facts I assume a carrier mortality rate of 0.5% for the purposes of illustration.
The second crude assumption, based on the data from the WHO study in China, which Australian health officials may be able to enhance for the local experience, is that simplistically it takes three weeks from infection to death. As this model is for illustrative purposes, it allows it to remain simple and reductive.
If we have a constant carrier mortality rate and a constant time from infection to death, for the purposes of modelling, we can infer new carriers at a point in time, from deaths at a later point in time. This is the critical insight that the model exploits.
Death data for the last three weeks in Australia shows :
- One death per day in week to 26 March.
- Two deaths per day in week to 2 April.
- Four deaths per day in week to 9 April.
Given the small numbers of deaths in Australia, this data is best smoothed. In some nations there are hundreds or more deaths per day which is a more robust dataset.
Applying the carrier mortality rate estimate of 0.5% to the death data suggests:
- There may have been approx. 200 new carriers per day three weeks prior to the week to 26 March (i.e. week to 5 March). Most of these seem to have acquired the virus overseas.
- There may have been approx. 400 new carriers per day in the week to 12 March.
- There may have been approx. 800 per day in the week to 19 March.
Summing these up, suggests that there were of the order of 10,000 carriers in the country on 19 March. This is vastly in excess of the 700 or so reported active cases at that time. This the key message to take from this illustration.
From 19 March to 9 April, assumptions must be made about carrier transmissions. The daily deaths data (smoothed) illustrates what this was historically. Smoothing this suggests around 15% daily transmission in the three weeks to 19 March. Note that increasingly, the public was becoming aware of COVID-19, and restrictions were being introduced predominantly for travellers, and gatherings.
This means over the period, each carrier has been infecting 0.15 new people. If a carrier was infectious for three weeks (crudely, for simple illustration, 20 days), a carrier would pass the virus to three people over that time. This is not inconsistent with various studies on R0 (‘Basic Reproduction Number’). To slow the spread of the disease this number needs to be as low as one. This is where social distancing remains key on an ongoing basis.
To estimate transmissions since March 19 there are two possible inputs:
- Australian case data shows new cases (as tested) went higher from 19 March, but peaked across a plateau from 23 March to 2 April, before falling away. Australia’s lockdown was effective from 23 March. Note it is likely that new cases are confirmed perhaps 5 days or more from infection. This plateau in confirmed cases likely equates to a peak in dailynew carriers between around 18- 28 March.
- The path of the carrier transmission derived from deaths data, in a similar fashion, in countries that were earlier to experience COVID and lockdowns (e.g. China, S. Korea, Italy, Iran)
The following assumptions are then made for illustrative purposes. Again, a model would look to derive ranges for the variables – the Australian case data can be smoothed, and it seems reasonable versus the overseas experiences. Worldometers.info stores the historic data, and hence for efficiency, it was sourced from there. It would be improved with better, or more granular data on who was being tested.
Assume therefore that:
- Community transmission has slowed to 12% for four more days from 19 March to 23 March.
- Community transmission dropped to 8% (1/3 fall) for five days as people adapted to lockdown, and there was in-home transmission.
- Community transmission dropped to 3% (further 60% fall) for the remainder of lockdown.
In order to allow from the lag from infection to testing, the case data used is lagged five days. For example, to understand transmission on 20 March, we look at New Cases v Active Cases on 25 March.
|Date||Active Cases (5 days later)||New Cases
(5 days later)
Applying the assumptions on community transmission to the population estimate of 10,000 carriers on 19 March, and with the reductive assumption that all carriers are contagious for three weeks from infection to either death or recovery then the path of the carriers may have been as follows.
[i] Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV2) – R. Li et al., Science 10.1126/science.abb3221 (2020)
[ii] Correcting under-reported COVID-19 case numbers: estimating the true scale of the pandemic. View ORCID Profile Alexander Lachmann, Kathleen M Jagodnik, Federico Manuel Giorgi, Forest Ray https://doi.org/10.1101/2020.03.14.20036178
[iii] Contemporary models would consider multiple scenarios, and put ranges around particular variables. This example is simplified and is for illustrative purposes only. It uses a mathematical, rather than medical perspective and hence there are limitations in its use. Where possible, publically available data applicable to the Australian situation is used, unlike the more theoretical models released by government last week.
[iv] Note that population of 20,000 carriers on the assumptions made, could be expected to have 100 deaths in the following 3 weeks. This is an average of around 5 per day.
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