Can't speak directly as I'm not there, but I'd imagine a lot of people taking their own proactive measures to social distance and encouragement by local officials to do so, is what has kept the numbers down to some extent.
A view from the UK (from someone, who as a retired law enforcement employee, was engaged in emergency planning for the previous flu pandemic scares): The UK has a fully integrated local/regional and national response plan for civil emergencies that holds regular, and sometimes extensive table-top exercises and which is now being used for real.
Nationally, the Prime Minister Chairs COBRA (named after the Cabinet Office Briefing Room A where the meetings are held) and all Cabinet Secretaries attend as needed. Senior military, senior technical staff/scientists and even senior business representatives may attend. Daily, or even twice daily if needed, status reports and data is provided to COBRA from Regional Resilience Forums which are similarly staffed -- data provided is all to the same format.
Below that, Local Resilience Forums exist in each county, usually chaired by the Chief Constable and these report daily to the Regional body providing data and flagging any concerns with shortages of supply. hospital beds etc. The local and regional forums will have local government chief executives present, hospital chief executives, local military base commanders, all emergency services' chiefs, utility and transport company reps and possibly major local employers attending meetings. Information flows up-wards from the local to regional and then national, but scientific data flows back from national to regional and local as well as information about patterns elsewhere in the country. At local level, the local government authority in parallel with the broader Resilience Forum, chairs a recovery group which plans for the things needed to recover quickly from the emergency; the public health team chairs another group which looks at the medical issues, local epidemiology and the logistics for delivering the right medical interventions. Each of these groups can flag issues to COBRA via the local and regional resilience forums.
It's not perfect and shortages of equipment, or issues of hospitals unable to cope with surging numbers will happen regardless of how good the plan is, but it is all integrated, practiced, and involves all of the right people/positions. It does depend on the person at the top -- our Prime Minister -- making the right call at the right time.