Most European Union member states will have sufficient Covid vaccine supplies to immunize the majority of people by the end of June, much earlier than the bloc’s official target, according to an internal memo seen by Bloomberg.

Germany, France, Italy, Spain and the Netherlands will be in a position to fully inoculate more than 55% of their total populations, projections in the document show. The EU wants to immunize 70% of adults by the end of the summer, which -- depending on the demographics of each member state -- corresponds to around 55-60% of total population.

The projections by the European Commission provide some hope that the EU’s vaccination campaign will improve after a disastrous start dominated by delays, mixed messages and political fighting. The commission expects deliveries of vaccines to increase to about 360 million doses this quarter from just over 100 million in the first three months of the year.

The document, dated April 1, details the exact number doses that will be available to each government by the end of June. While the overall picture is positive, some member states, including Croatia, Bulgaria, Slovakia, the Czech Republic and Austria are projected to lag behind. Others, such as Denmark and Malta, will reach the immunity threshold much earlier.

The estimates seen by Bloomberg factor in an agreement last week to redistribute part of an accelerated batch of deliveries to countries where supplies are scarce.

The laggards did not draw the full allocation of the coronavirus vaccines they were entitled to under the EU’s purchase agreements with BioNTech SE and Pfizer Inc., as well as Moderna Inc., opting instead to focus on AstraZeneca Plc’s cheaper shot. With Astra deliveries behind schedule, these member states may face delays in the reopening of their economies, even after taking into account the mechanism agreed to help them catch up.

EU Commissioner Thierry Breton, who’s leading efforts to ramp up production, has said the bloc will have the capacity to deliver enough doses to reach collective immunity by July 14, provided the doses are injected. The date is symbolic, to coincide with Bastille Day in France.