It is highly implausible that lots of people (substatially more than half of those infected) have been asymptomatic cases, regardless of any modelling or guesswork. This is based on contact tracing experiences. Let S

_{x} represent symptomatic cases and A

_{x } asymptomatic cases and X->Y mean that X infects Y. If we have S

_{0}->S

_{1} then contact tracing easily explains how S

_{1} got infected. If we have S

_{0}->A

_{0}->S

_{1} or S

_{0}->A

_{0}->A

_{1}->S

_{1}, it's still easy - get plausible contacts for S

_{0} and S

_{1} and see the link that might have passed on the infection. Beyond that, things get difficult and it starts to look like S

_{1} got infected for no reason.

If there are equal numbers of S and A, then the probability of S->S is 0.5, S->A->S is 0.25, S->A->A->S is 0.125, which means all other possibilites are 0.125. As the proportion of A rises, this value also rises, so we can estimate the ratio of A to S by the proportion of symptomatic cases which seem to have no cause, and we can get a general feel for this by reading the news to see if in some parts of the world where contact tracing is done there are lots of unexplained cases or few. Lots of unexplained cases would be very alarming to anyone trying to do contact tracing, so would be very newsworthy. Since we read of contact tracing being very successful, we can conclude that there cannot be many A for each S. This means it's hardly worth bothering to read any paper which claims there is a huge number of asymptomatic cases.

Unless, there's a bad assumption, namely that S->A is just like A->S. If instead A->S is impossible, then we could have each S infect three more S and sixty A. That would mean we would never see unexplained infections, but there are twenty times as many asymptomatic cases as symptomatic cases. The problem with this hypothesis is that it should show up during contact tracing whereby when the contacts of an infected person are found and tested, in cases where there has been excessive delay in locating the individuals, we would see many people who test positive, are asymptomatic, and have not infected anyone else. That too would be quite remarkable, so I'd expect it would be newsworthy, so the lack of stories about it suggests it doesn't occur, undermining the plausibility of this mechanism.

Another odd case that would work is that S->A is rare, but A->A is common and A->S is impossible. That would make it hard to notice the S->A infections, while allowing the numbers of A to grow wildly. Of course this must mean that something very odd is happening in the S->A step - the disease is mutating into an asymptomatic variant. This seems extreely unlikely.

So overall, I consider the hypothesis that there are lots of asymptomatic cases to be sufficiently implausible that it requires very strong evidence to support it - that means actual testing and not just modelling.