My background is public health and did my share of biology during my studies towards my PhD. My take for 2021 is on the optimistic side, especially the second half and think I have some good reasons to be like this.
The biggest reason of course is the roll out of vaccines. Based on known data, they are pretty effective. And in theory, with an average transmission rate of about 3-4 new infections from 1 infected, you need 66%-75% of the population to be immune to completely stop the transmission. But there is a big assumption here: the whole population of healthy, infected, recovered, etc. is homogenously distributed. In reality, people are in close contact with a very limited number of people, especially during the pandemic. If these "pockets" of people are well aware of the precautions and closely following them they can be fairly well protected even without a vaccine. On the other hand, there are also groups of people come in close contact with many people outside their circle. Healthcare workers, cashiers, salon workers, waiters, etc. If we can get these people vaccinated, that can go a long way of cutting off potential infections with them at the center. These people are usually more concerned about their risk of infection due to the nature of their work so even if the general population's acceptance towards getting vaccinated may be only 60% or 70%, these people may have a much higher acceptance rate of getting vaccinated and would take off a big chunk of potential transmission. With the heterogenous distribution of population and low/high risk of transmission and their respective behavior, I don't think we need 75% of the population to be vaccinated to effectively eliminate transmission.
Besides of vaccine there's also natural immunity after being infected. Granted, there is a lot of evidence suggesting natural immunity is not that effective and long-lasting, but it is still something. And regarding this, the US has done a "great job" of having probably the highest % of population being infected. This can serve as a base and along with vaccination rate, work towards a threshold we need to stop meaningful transmission.
As for the variants, generally speaking, pathogens would actually evolve towards higher transmission rate rather becoming more lethal. The purpose of the virus is not to kill humans but to replicate itself as much as possible. Killing or making people sick is something they don't "want", because that is bad for their survival and propagation and the variants that do this will eventually be outcompeted by those that chose the other path. Think SARS almost 20 years ago. That one had something like >10% fatality rate. People were really scared and nobody can treat it like a hoax. So people who got it either died and stopped the transmission or are very carefully quarantined, which also stopped the transmission. The impact of SARS as a result was fairly limited.
As of now there's no evidence those variants are more deadly and I won't be surprised they will turn out to be less deadly than the one going around for a year. That is not to say we should ignore them since if they are 25% less likely to kill and 75% more likely to spread, that will still cause roughly 30% more deaths in the same period of time. But my guess is that COVID-19 will eventually be just another type of flu, as some coronavirus are already. This is a common hypothesis shared by many people I know who work in related fields since last spring. How long will it become like that? Nobody knows. But if the Spanish Flu a century ago is of guidance, even with technology and healthcare system back then it took three years for that virus to run its course to become insignificant. I think it would take less time for COVID-19 given all the tools we have now. The process of getting there is ugly, but we'll get there.
How effective the mRNA vaccine will be for these variants? This is not within my expertise so I'm just making my best guess here. I think it will still be pretty effective. In the first few months someone from WHO gave a very good analogy when asked about mutations discovered back then. It was something like two cars of the same make and model, just with two different plates. Of course the variants we discovered recently is more substantial than that. But they are still cars. The vaccines are teaching our bodies to shoot the tires of the cars in this analogy. So I think they will still work pretty well against these variants.
So given the developments in vaccine, the evolution of the virus itself, and considering the pandemic has already been going on for a year, I do think we can put this to bed sometime in the second half of 2021. Masks and washing hands and social distancing will likely still be in place until 2022 but I think the more hardcore restrictions will be lifted as the risks from the virus gets smaller and smaller.