A paper for SAGE released yesterday analyses hospital admissions post vaccination. Reinforcing the point that one dose does not give full protection, 400 people entered hospital and subsequently died who displayed symptoms after vaccination.
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The majority of these (72%) showed symptoms within 21 days of the jab, so probably were infected prior to the jab, or before immunity develops. However, 113 people only showed symptoms after 21 days or more (likely "vaccine failure").

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You can see also that the "over 21 day" cases weren't confined to the few days after, but are spread over a longer period. (Note these graphs relate to admissions, but the point is the same.)

The decline in the green zone will be at least partly due to declining prevalence.

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Note in the first two tables, those in vaccine tier 1 (CH residents) have typically been allocated to Tier 2, due to lack of information to categorise them separately.

The colouring in the previous graphs is explained here.

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The paper notes the large number admitted within 7 days of vaccination, and discusses the possible reasons for that here. These include the possibility that an asymptomatic case at vaccination had symptoms triggered by the vaccine.
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In total though the number admitted post vaccination are a very small percentage of the total admitted in the second wave, evidence that clearly disproves those who have suggested that the vaccination programme caused the dramatic increase we saw in December and January.
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