### Summary

**The analysis suggests that 1 in 13 people (7.7%) who test positive for COVID-19 are admitted to hospital approximately 7 days after testing positive.**

As of 7th March 2021 there were 4,226,676 cases recorded in the UK.

This analysis suggests that there were a possible additional 1,413,059 cases in the first wave that were not detected due to lack of testing capacity.

The analysis also suggests that the number asymptomatic cases until 7th March 2021 would have been 2,193,230

**The total number of cases of COVID-19 up until the 7th of March is estimated to be 7,832,965**

The number of deaths until 7th March 2021 was 124,906. **This gives an estimated case fatality rate for COVID-19 of 1.59%.**

The UK population is 66.89 million. **Therefore, without lockdowns and vaccines an estimated 1,065,205 would have died.**

### How many COVID-19 Cases have there been?

Unfortunately due to lack of test capacity at the start of the pandemic we do not actually know. The lack of testing is further compounded by asymptomatic cases and people with symptoms who do not present for testing.

However, it may be possible to make a good estimate.

To obtain an estimate the following assumptions have been used.

- UK Testing capacity was sufficient to test all symptomatic cases in the 2nd wave
- Hospital Data for Patient Admissions with COVID-19 is accurate in the 1st and 2nd wave
- The number of asymptomatic cases detected as part of mass testing in the 2nd wave is negligible

The number of truly asymptomatic cases has been estimated by New and Emerging Respiratory Virus Threats Advisory Group (NERVTAG) in the UK. NERVTAG Asymptomatic Report

The study estimates that the number of truly asymptomatic cases of COVID-19 (SARS-CoV-2) is 28%

### Methodology

To get an estimate of the number of COVID-19 cases in the UK the data from the 2nd wave of the pandemic is used to estimate what the first wave may have been like. The number of hospital admissions from the 2nd wave is compared to the number of cases in the 2nd wave and the correlation between the them determined. Then the possible number of cases of COVID-19 in the first wave of the pandemic is calculated from the first wave hospital admissions data.

### 2nd Wave Analysis

The 2nd wave data starting from the 1st of August 2020 until the point vaccination started in the UK has been analysed. Two sets of data were analysed.

1st August to 7th December. The first vaccine in the UK was on the 8th December

1st August to 29th December. The vaccines would not have been effective until 22days after their first use.

The ratio of cases to admissions, the offset days and the coefficient of determination *R ^{2}* for the two data sets are shown below.

Both sets of data have a best fit for hospital admissions occurring approximately 7 days after cases, with a ratio of 13 cases to each admission.

### 1st Wave Possible

The possible number of cases in the 1st wave of the pandemic is then estimated as Cases(Day) = Admissions(Day+7) x 13.2

The ratio 13.2 = (12.9 +13.5)/2 is the average of the ratio at 7 days.

Unfortunately hospital data for England and Wales is not available before 23rd March. Hospital data is available for Scotland and Northern Ireland.

### Total Likely Cases

To get an estimate for the total number of cases we need to allow for the likely 28% of truly asymptomatic cases. These people will only be detected as part of mass screening.

### Case Fatality Rate

The case fatality rate is the number deaths divided by the number of cases.

Calculating a realistic figure for this is difficult as medical science in relation to COVID-19 has advanced significantly since the start of the pandemic. The virus has also had several significant mutations which have affected how it spreads and possibly how many deaths it causes.

However, we can get a rough estimate by dividing the number of deaths within 28 days of a test by the number of estimated cases.

The number of deaths until 7th March 2021 was 124,906 and the estimated number of cases is 7,832,965.

This gives an estimated case fatality rate for COVID-19 of 1.59%.