We are not aiming to eradicate, only to not have too many catch it all at once. We are all getting it sooner or later, the government just want us to have it in controllable numbers. As soon as they relax the lockdown even slightly the numbers will climb again. There will probably be a few of theses waves. It's just about keeping them flat enough for the NHS to manage.
I've spent the last week working on recovery plans and forecasting the mid term performance for my company, and every table and chart I've seen has a big spike of cases in April followed by an equally big drop as social distancing pushes the infection rate down, then a wave with smaller spikes in August/September, November/December, February/March 21 and then finally in May/June 21 before a vaccine is finally available. I've come to the conclusion that despite Nick Hancock's protestations, the purpose of the social distancing isn't to save us from infection, but to water down the rate of the infections to a level which is manageable for the NHS.
So yes we're in it for the long term. The experts are suggesting an average of 14 to 16 months, with most/many of us having caught the virus and recovered a long before a pharmaceutical solution is available. The question is are you prepared to put your life on hold for 14 to 16 months, and more importantly with the lock down costing the country £2.0bn+ per day how long can the Government afford to flat line the economy before they're forced to ease the controls