Efficiency of genetic and serologic tests in reducing R0

Update: this is based on data available at the time of writing which is probably outdated now.

We have two testing methods — genetic and serologic. The genetic method detects the virus RNA, the serologic tests detect the antibodies that our body produces to fight the virus. Some countries (for example Poland) concentrate their testing strategy on genetic tests, mostly because serologic tests can detect infection about week later than genetic tests, but my crude calculations below show that for asymptomatic people serologic tests can be 6 times more cost effective for reducing R0 because genetic test are about 10 times more expensive and require more time and specialized labs. Additionally serologic tests detect immune people who could get ‘immunity passes’ after two weeks.

If symptomatic people self isolate anyway (because they don’t want to spread their disease even if it is not COVID-19), people who develop symptoms develop them before they can be serologically tested and we don’t test asymptomatic people because of lack of resources— then serologic tests don’t make much sense because they would not catch anyone spreading the disease. But if we have many carriers who never develop symptoms — then we need to start testing also asymptomatic people.

Let’s assume that:

• serologic tests can detect the virus response about a week after infection
• we can have 10 times more serologic tests than genetic tests
• infected person spreads disease for 3 days before developing symptoms or never
• symptomatic persons are isolated
• about 50% of infected persons never develop symptoms and infect for about 3 weeks

Then with serologic tests we don’t reduce infection spreading days for people who eventually develop symptoms — but for carriers who never develop symptoms they reduce the disease spreading days from 3 weeks to 1 week. Let’s call the “ratio of infected people in the sample” X. With one serologic test we reduce the infection spreading days by X * 50% * 2 weeks = X * 7 days. In comparison with a genetic test we reduce the infection spreading days by X * (50%*3 days + 50% * 3 weeks) = X* 12 days. But we can have 10 more serologic tests than genetic tests so with serologic test we can reduce the disease spreading days by X * 70 days — while with genetic tests we can reduce it only by X * 12 days that is nearly 6 times less.

Of course this is a very rough calculation and there are caveats:

• Testing is important for information and not only for limiting infection spreading days.
• We don’t know when exactly the antibodies can be detected. I assumed one week — but I have seen estimates ranging from a few days to 3 weeks and 3 weeks would make my calculations completely fail. But maybe it is a strong antibody response that makes someone asymptomatic carrier — then the antibodies should be detectable earlier.
• I don’t know how much competition there is between the tests — I guess at least there is some competition for money if not for other resources.
• There are degrees of isolation and people who have some symptoms but are not tested will never isolate so thoroughly as people who tested positively.
• This calculation is very sensitive on the ratio of completely asymptomatic carriers to those who eventually develop symptoms among the tested individuals. Initially it was assumed that there are no asymptomatic carriers — but the Icelandic data suggest a 50/50 ratio in the general population, the Diamond Princess had about 37% (410 out of 1106) and other sources suggest 20%-80% in the general population. It can be different in the tested sample.
• Asymptomatic people who test serologically positive can be carriers or they can already be cured and immune. Should we quarantine them all for two weeks? Should we test them all genetically? Or maybe some combination, depending on current statistics and their memory of COVID-19 like symptoms?

Updates:
One source suggests that completely asymptomatics are contagious only for 2 weeks — that would reduce the efficiency gain for serologic tests from 6 to 3: