Over the past two weeks, a growing number of people have questioned the dramatic measures being taken to stop the spread of Covid-19. The chorus began with John Ioannidis of Stanford, who has argued that we have under-counted cases of Covid-19, leading to an overestimation of the death rate.
Since then, Covid-19 skepticism has found a home on the right. The Federalist, the Wall Street Journal and the American Thinker have all published similar arguments.
Superficially, these arguments make sense. Many celebrities and athletes have tested positive for Covid-19, despite experiencing only mild symptoms or being asymptomatic. Most people don’t go to the doctor because they have a sore throat and a fever, ergo a dramatic undercounting of cases seemed possible.
However, the number of undiagnosed cases is not quite as dark a dark number as Dr Ioannidis and the editors of the Federalist believe. In countries that successfully contained the spread of Covid-19, you can place a ceiling on the total number of undiagnosed cases. This allows you to account for undiagnosed cases when estimating case fatality rates.
In an infectious disease, the basic reproduction number (R0) represents the number of people to whom the average infected person transmits the disease. For example, if the R0 of a disease is 10, the average person who has the disease spreads it to 10 people.
To stop the spread of a disease, you need to push the R0 below 1. You can accomplish this by finding those with the disease and placing them under quarantine. Scientists estimate that Covid-19 has an R0 of around 3. To contain Covid-19 through quarantine, you would need to detect at least two thirds of all new cases and place them under quarantine.
We know of two places that have succeeded in containing Covid-19: South Korea after 11 March and Hong Kong before 13 March. During the periods in question, the number of new cases per day remained constant. From this, one can infer that the number of contagious people not under quarantine remained the same. To maintain this equilibrium, these localities must have detected at least two thirds of all cases.
As of today, 28 March 2020, South Korea has recorded 9,478 cases, 144 deaths and 4,811 recoveries. This works out to a 1.5% fatality rate, if you divide by total cases, and a 2.9% fatality rate, if you divide by closed cases. If we adjust these numbers to reflect a two thirds detection ratio, we are left with a 1–2.9% case fatality rate, depending on whether we divide by total cases or by closed cases.
On 13 March, the number of new Covid-19 cases in Hong Kong started rising. On 12 March, Hong Kong had 131 total cases and 3 deaths, which works out to a death rate of 2.3%. Performing the same adjustment gives a death rate of 1.5%, using total cases as our denominator.
Readers should keep in mind that my estimate of the number of undetected cases represents an upper bound. We know that Covid-19 patients spread the disease to doctors, nurses and non-Covid patients. If we accounted for new infections caused by known Covid cases, it would lower our estimate of undetected cases.
Dr Ioannidis would likely attribute the reduction in R0 to social distancing and the use of masks. This wouldn’t alter our estimates by much. If social distancing and masks reduce the R0 of Covid from 3 to 2, we would lower our estimate of the Hong Kong death rate from 1.5% to 1.2%. That would still be a death rate of above 1% for a novel disease to which we have no immunity.
In his article, Ioannidis estimates that the true case fatality rate for Covid-19 could be as low as 0.05%. For that to be true, 29/30 cases in South Korea would have to go undetected, and masks plus social distancing would have to completely explain their success. One would love to believe that, but it is mathematically untenable.
The dark truth is that South Korea and Hong Kong represent best case scenarios. Their populations are healthier than America’s, and their health care systems weren’t overrun with patients. If we look at Spain and Italy, we see what a worst case scenario looks like, with official death rates of above 8–10% and older patients left to die.
Hopefully, we can dispense with the pangloss and address the issue. If we don’t figure out a solution, we will face a catastrophe similar to the Spanish flu or possibly worse. We need to find a solution to this medical and economic problem, and we need to find it soon.