Models of COVID-19: Part 2

DOI: https://doi.org/10.58248/RR23

• How did data from Wuhan inform UK models of COVID-19?
• How might different suppression and mitigation strategies affect coronavirus transmission?
• This breakdown of the Imperial College models is part of our rapid response content on COVID-19. You can view all our reporting on this topic under COVID-19. 
• This article will be updated as the research progresses. 

The following reports were all published online by the Imperial College London COVID-19 Response Team and included in the first release of information underpinning SAGE decision-making.

Epidemic size estimation in Wuhan City (17 Jan)

This initial estimate was published on 17 January and has not been peer-reviewed. By 16 January there had been 41 cases (and two deaths) in Wuhan City. There had been a further three cases in travellers – two in Thailand and one in Japan. Most of the people had links to the Wuhan seafood market. However, while the travellers had been to Wuhan, they had not visited the market.

The authors estimated that by 12 January there were an estimated 1723 cases of COVID-19 in Wuhan. This was based on a few assumptions:

1. Wuhan International Airport serves 19 million people.
2. The average delay between infection and diagnosis was estimated to be 10 days.
3. 3301 international passengers per day travel from Wuhan.

By modelling a range of values for these assumptions, the researchers estimated between 996 and 2155 cases of COVID-19 in Wuhan by 12 January.

Epidemic size estimation in Wuhan City (22 Jan)

An updated estimate was published on 22 January. By this time there had been 440 cases (including nine deaths) across 13 provinces of China. There had been seven international cases.

Based on these numbers, the authors re-ran their model and got an estimate of 4000 cases of COVID-19 in Wuhan City by 21 January. In addition to the three assumptions above, additional assumptions were:

1. Airport exit screening (from 15 January) had no impact on exported cases before 16 January.
2. All cases in travellers flying outside mainland China are being detected.

A range of plausible values in the assumptions led to an estimate of 2300 to 5000 cases by 21 January.

Transmissibility of COVID-19

In this non-peer-reviewed study the authors estimated how easily human-to-human transmission occurs. This built upon the estimate above of 4000 cases of COVID-19 in Wuhan by 18 January. Such a large number of cases could only be explained by sustained human-to-human transmission occurring. They produced simulations of how the outbreak may unfold in Wuhan. Initial assumptions were:

1. There is a lot of variability in the number of people infected by each infected person.
2. Generation time (average time between one person being infected and the next) is the same as in SARS (8.4 days).

They also produced estimates for a shorter generation time – if it causes more mild to moderate illness that is transmissible.

The authors found it was highly likely that virus transmissibility was high enough for sustained transmission (R0 over 1). The estimate of R0 depends on two numbers:

1. Total number of cases by 18 January.
2. Number of cases as a result of zoonotic exposure (animal to human).

The estimate most likely to be true was if there were 4000 cases and only 40 came directly from animals. This produces an R0 of 2.6. By varying the two numbers above, R0 ranges between 1.5 and 3.5. There was one scenario in which R0 was less than 1 (no sustained human-to-human transmission). However, this required a very low number of total cases (2000) and for 200 of these to be from animals. The virus genetics suggested this was unlikely – most of the viruses sequenced were very similar to each other.

The generation time (time between one person being infected and them infecting the next) had the following impact:

• Shorter generation time – R0 decreases to 2.1.
• Longer generation time – R0 increases to 3.1.

This study provided the initial best estimate of R0 of 2.6 that was then used in the further reports below. With this R0, control measures would need to block over 60% of transmissions to be effective.

Severity of COVID-19

This is a non-peer-reviewed study that provided early estimates of the case fatality ratio (CFR) of COVID-19. The authors note from the start that CFR is difficult to estimate during an epidemic. This is because:

1. Surveillance generally picks up severe cases, leading to a higher CFR. Once milder infections are recognised, the CFR is likely to decrease.
2. There is a delay of 2 to 3 weeks between a patient experiencing symptoms and their final outcome. Therefore you cannot simply divide the number of deaths by the number of reported cases. 

This report was published on 10 February. At that point, the majority of cases detected in mainland China had been on the severe end of the spectrum (pneumonias). Internationally, surveillance was focused on people with a fever and history of travel to China. So this is likely to have been picking up milder cases.

To calculate CFR, the authors looked at aggregate data in China. This means all the cases are considered together rather than individually. International cases were fewer in number and could be considered individually.

This means that three ranges of CFR can be estimated. The most severe will be for the China epidemic at the time of publication. The second estimate will be for cases in travellers and the third, an estimate for all infections (including those undiagnosed in the community). The third one will be the least severe as it is likely there are many mild cases and therefore the patients dying will be a smaller proportion.

• CFR for China (severe illnesses and hospitalisations): 18%.
• CFR for travellers (obviously symptomatic): 1.2% to 5.6%.
• CFR for all infections: 0.8% to 0.9%.

Phylogenetic analysis of SARS-CoV-2

This non-peer-reviewed report introduces viral genetic information into the models already discussed. Phylogenetics is the study of the evolutionary history of one or more organisms. As viruses pass from animals to humans, and from human to human, they mutate. The rate of these mutations can be used to estimate transmission. This is called phylodynamics. The evolutionary history can also help estimate when the virus first passed from animals to humans. It can also be used to estimate the overall virus population size, and therefore how many people are infected.

The authors looked at the available genetic sequences of the virus from 53 people infected with SARS-CoV-2 up to 3 February. The common ancestor of these viruses would have existed sometime between 5 and 8 December 2019. The genetic models suggested exponential growth in virus numbers. The estimated doubling time of cases was every 6.6 to 7.1 days.

At this early point in the outbreak, an accurate estimate of the full extent of infection of the population was difficult. Viral genetics suggested between 26,000 and 38,000 infections on 3 February in China. This would give an R0 value of around 2.15.

Relative sensitivity of international surveillance

This non-peer-reviewed report was published on 21 February, by which time 29 countries had cases. The authors compared countries’ detected cases with their flight volumes  from Wuhan. This was to give an estimate of how sensitive each country’s surveillance system was. 

Singapore was found to have detected many more cases than would be expected from its monthly flight traffic from Wuhan. The authors then compared other countries to Singapore. They found that Finland, Nepal, Belgium, Sweden, India, Sri Lanka and Canada all detected more infected passengers per flight than Singapore. Further analyses of these countries suggest that 426 to 576 exported cases should have been detected outside of mainland China. In reality by this date only 156 cases had been detected. This suggests that between 63% and 73% of exported cases remain undetected. 

Infection prevalence estimated from repatriation flights

This was a later non-peer-reviewed report building upon the last one. Wuhan started its lock-down on 29 January. Other countries then carried out repatriation flights the last of which were completed on 27 February. These countries quarantined citizens on these flights, and many also carried out PCR screening tests. The authors therefore used these flights to provide snapshots of the situation in Wuhan.

During this time, 8597 people were repatriated on 56 flights from Wuhan and 3 flights from Beijing, travelling to 55 countries. Most countries then implemented a 14-day quarantine period. The authors identified 47 flights that carried out screening of their passengers. From these:

• 15 flights tested only passengers showing symptoms
• 32 flights tested all passengers.
• In total 5720 passengers were tested for SARS-CoV-2.
• 36 passengers tested positive
• This gives an overall infection prevalence (proportion of people infected) of 0.63%

Or looking at only the flights that tested all passengers, an infection prevalence of 0.60%. 20 flights undertook testing upon arrival, testing 2433 passengers. Only 13 of these passengers tested positive for the virus. This provides a low prevalence estimate of 0.53%. The highest prevalence was found for flights arriving 30 January to 1 February, close to the epidemic peak in Wuhan. At this point the highest prevalence reached was 0.87%.

Symptom progression of COVID-19

In this non-peer-reviewed report, the authors summarised the findings of 13 clinical studies from China. They also included case reports from Hong Kong, Japan, Singapore and South Korea. In China, the most frequently reported diagnosis upon seeing healthcare professionals was pneumonia. However, in other countries fever was recognised before pneumonia developed. Pneumonia was seen more commonly in patients aged over 60 years. This suggests that people may have sought healthcare at an earlier stage of disease outside of China. 

Fever was generally the first symptom, with the average time between having fever and seeking healthcare being 0.77 days. The average time between the first symptom and pneumonia was 5.88 days, usually when the patient was admitted to hospital. The average time from the first symptom to seeking healthcare was 2.1 days, and to hospitalisation was 5.76 days. The time between onset of illness and recovery or discharge was 20.51 days. 

In China, about 17% of reported cases were severe. Over 41% of cases were reported in patients aged over 60 years old. This dropped to 33% in international cases. This likely reflects the different stages of healthcare seeking behaviour. By the time COVID-19 had spread overseas, there was much greater awareness, with people seeking healthcare much earlier.

Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand

This non-peer-reviewed report was widely reported in the media. It examined non-pharmaceutical interventions (public health measures). The following is a summary of their modeled impacts on mortality and healthcare demand.

The authors considered two strategies:

1. Suppression. R0 is the number of people infected by each case. If R0 is reduced to less than 1 then this would stop human-to-human transmission. For suppression to work, this needs to be maintained until the virus stops circulating or a vaccine is available. 
2. Mitigation. Here NPIs are used to reduce the health impact of the epidemic. This strategy has been previously used for pandemic influenza. Population immunity would build up during the epidemic, leading to a decline in new infections. In this strategy, R0 would be reduced sufficiently to slow the spread.

The authors modified a previous influenza transmission model. They used information from the census, school and workplace populations. They also assumed that transmission between school children would be double that in adults. Based on this they estimated that:

• A third of transmission will occur within the household.
• A third of transmission will occur in schools and workplaces.
• A third of transmission will occur in the community.

Other virus assumptions included:

• Incubation period (time between infection to symptoms) is 5.1 days.
• Patients are infectious 12 hours before symptoms come on.
• Patients continue to be infectious until 4.6 days after infection.
• R0 (number of people infected by each case) is 2.4.
• Infected people with symptoms are 50% more infectious than those without.
• Upon recovery, individuals have short term immunity.

Further disease assumptions were made based on experiences at that time with the virus in other countries:

• Two thirds of cases are sufficiently symptomatic to recognise the need to self-isolate with 1 day of symptoms.
• Time between onset of symptoms and hospitalisation is 5 days.
• An overall infection fatality ratio (proportion infected that die) of 0.9% but varying by age:
  • 0.002% for under 9-years-olds.
  • 0.6% for 50–59 year olds.
  • 5.1% for 70–79 year olds.
  • 9.3% for over 80-year olds.
• Hospitalisation rate of 4.4%, varying for age:
  • 0.1% for under 9-year-olds.
  • 10.2% for 50–59 year olds.
  • 27.3% for over 80-year-olds.
• Proportion of hospitalised cases requiring critical care of 30%:
  • 5.0% for under 40-year-olds.
  • 70.9% for over 80-year-olds.

The following non-pharmaceutical interventions were considered:

• Case isolation. Those with symptoms stay at home for 7 days.
• Voluntary home quarantine. Family members of those with symptoms stay at home for 14 days.
• Social distancing for anyone over 70 years of age. Anyone over 70 stays at home.
• Social distancing for everyone. Majority of people stay at home.
• Education closures. Schools and universities close.

Effects of interventions for a mitigation strategy

Without any response, the authors predicted a peak in deaths occurring towards the end of May, at more than 20 deaths per 10,000 population. This would give total mortality figures of 510,000 and 80% of the population being infected.

Critical care bed capacity would be overwhelmed by the second week of April. During the peak, the need for critical care beds would be 30 times the NHS maximum capacity. Figure 2 from the report explores how different mitigation scenarios will impact the pandemic. It shows that mitigation alone cannot stop the NHS from being overwhelmed.

• Case isolation only.
• Case isolation and home quarantine.
• Closing schools and universities only.
• Case isolation, home quarantine and social distancing of anyone over 70 years of age.

In a mitigation-only scenario, the best combination of measures is case isolation, home quarantine and social distancing of older people. These measures would reduce peak critical care bed capacity by Two thirds. They would also halve the number of deaths. However, the peak would still be 8-fold larger than NHS critical care bed capacity.

Effects of interventions for a suppression strategy

In order to reduce the R0 value below 1, two combinations of measures were explored:

• Case isolation, home quarantine and social distancing for everyone.
• Case isolation, education closures and social distancing for everyone,

Measures were modelled to be in place for 5 months. Education closures appeared to be more effective than home quarantine (Figure 3 from the report). Figure 3B is a close-up from Figure 3A. This shows that the second combination (green line) will ensure the first wave remains below critical care bed capacity. 

The model included measures being relaxed from September. However, particularly with the second combination (green line), this will result in a second wave. This is how the epidemic will behave in the absence of vaccination. It is because suppression will lead to fewer people being exposed, and therefore less herd immunity.

One possible situation modelled was adaptive triggering of the strategy. In Figure 4, the authors modelled if suppression is triggered by 100 ICU cases per week, and switched off when there were under 50 cases per week. This would lead to the four suppressive measures being in place for two thirds of 2020 and 2021. These dates were based on a prediction of a vaccine only being available 18 months after onset.

One thing to note is that once case numbers have fallen, other strategies can also be included. These include intensive testing and contact tracing, plus some form of technological tracking.

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