PARIS • If Europe has a strategy to stop the spread of Covid-19, it's keeping it well hidden.

France's President Emmanuel Macron has vowed not to go back to the dark days of national lockdown, preferring instead to "live" with the coronavirus disease, but his government is struggling to halt a jump in cases.

France reported more than 10,000 new cases in 24 hours over the weekend, a grim postscript to its decision to cut the required quarantine for positive cases in half to seven days.

It is a similar story in Spain, the country with the most number of cases in Europe and the first to cross the barrier of more than half a million in total.

Prime Minister Pedro Sanchez has also ruled out a national lockdown, but messy public health disagreements between Madrid and regions such as Catalonia - and an initially lax approach to nightlife - have worsened a post-lockdown surge in cases.

Taking population into account, the seven-day average rate of new cases in France and Spain is above that in the United States.

British cases are not too far behind, hitting their highest level since May.

Austria is warning that this is the start of a "second wave".

We're not there yet in terms of deaths and hospital admissions, which remain well below the virus' April peak. For now, the bulk of new cases seem to be asymptomatic or mildly symptomatic young adults.

Still, young people do not live in a vacuum, and infections are spreading to those who are older and more vulnerable. The drive to get adults back into the office and kids back into classrooms, however laudable, is accelerating the virus' spread.

Estimates of the reproduction rate from Bank of America suggest it's above 1 in all big European countries bar Germany, meaning one infected person will, on average, spread it to more than one other person.

Doctors warn of a rough winter ahead without a vaccine.

That is why filling gaps in the testing, tracing and isolation of cases will be crucial in breaking chains of transmission over the next few months.

Europe is testing far more than at the start of the pandemic, with the share of tests coming back positive at 10 per cent or below, but the allocation of resources is still pretty woeful. The opening of the testing floodgates to almost any suspected case has overwhelmed laboratories.

Tales of waiting for as long as eight days for a result in France, or the reported backlog of almost 200,000 tests in the United Kingdom, are a farcical counterpoint to the countries' headline-grabbing political targets of one million or more tests per week. They're a drag on public confidence and on the economy, given the need to self-isolate while waiting for the results. No wonder people often ignore stay-at-home rules.

The tracing part of the equation has also flopped. Digital tracing apps designed to easily track potential transmissions from one positive case have failed to attract a critical mass of users in some countries.

The UK has yet to even launch its redesigned version. Human tracers are struggling with a decline in contacts identified per positive case - in France, it's currently around 2, while in Spain, the figure is about 3.

This is needle-in-a-haystack territory.

In France's northwest Mayenne region, where a flare-up of cases was successfully curbed last month, mass testing was rolled out alongside a target of delivering results within between 24 to 48 hours.

Why not simply aim for this turnaround time nationally? It might make those "no more lockdown" promises a little easier to keep.

BLOOMBERG