The goal of the social distancing, and in more extreme cases, "lockdowns," is not not necessarily to eliminate the virus altogether in the near term. Sure, that would be nice. But without installing incredibly draconian measures, it's probably not going to happen in this case before a vaccine is produced, which is over a year away. (probably closer to a year and a half)
No, instead the idea of the social distancing and lockdowns is reduce the spread of the virus so that it doesn't overwhelm our healthcare systems. Hundreds of thousands, if not millions of lives can be saved so long as everybody doesn't contract the virus at once.
When the healthcare systems are overwhelmed, doctors will have to decide who lives and who dies, simply because there's not enough ventilators and/or other equipment to go around for everybody at once.
That's the main goal -- to spread it out a little over time so our healthcare system is not overwhelmed at any given time. A secondary benefit of spreading it out over time, is that as time goes on, more and more enter the population who have
recovered from the infection. People who have fully recovered have become immune (once you've recovered from a particular strain of virus, it's very unlikely that you would be infected for a second time, at least not for several years). This increases the "herd immunity" for the rest of the population who haven't been infected yet (more on that later). Because of this secondary result, there will be fewer people infected overall. And for both reasons there will be far fewer deaths.
For further research, google "flattening the curve."
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You may be asking, "Well, why isn't the flu like that?" Strains of the flu that are in circulation today have been in circulation for a long time. For any given strain of the flu, it is likely that several people in your circle of friends and family have been infected with that particular strain of flu before; be it last year or maybe 5 or 10 years ago, or that they have been vaccinated. That means that you won't catch that particular strain of the flu from those particular people because those people still have some immunity to that particular strain. And since those are the people you interact with it means that it is less likely that
you will catch that particular strain of the flu (i.e., less people that you could catch it from). That's what's called "herd immunity." (I should also mention that if you've been vaccinated with a flu shot for a particular strain of flu, then that's another way you can become immune without being infected yourself).
And that's one of the things that makes this Coronavirus different. While there are other coronaviruses in circulation, they are not like this strain. This strain is new, or "novel." Almost nobody is immune to it yet. Pretty much
anybody can catch it from (or spread it to)
anybody else. There's almost no immune people blocking the transmissions. At least not yet. We need more people in the population who have recovered from COVID-19 before that has an effect. (And eventually, of course, we'll have a vaccine within a year - year and a half from now.)
The other things that makes novel Coronavirus different is it is more deadly than the flu. Conservative estimates put it at about 10 times more deadly for those that contract it, compared to the flu.