Models of COVID-19: Part 1

• On 20th March, the Scientific Advisory Group for Emergencies (SAGE) released the evidence behind the government response to Coronavirus disease (COVID-19). This series of short articles summarises these 32 documents. You can view all our reporting on this topic under COVID-19. 
• This article goes over the research used to develop early COVID-19 models which in turn informed the thinking of SAGE.
• High profile models from Imperial College London will be detailed in Part 2.

A number of models have been developed to describe the potential spread of COVID-19 in the UK. Some of these models have informed the thinking of SAGE. These models are described below. Some models were produced at Imperial College London and are detailed in a separate post.

Early dynamics of transmission and control of COVID-19: a mathematical modelling study

In this study, the authors attempted to understand how COVID-19 spread in Wuhan initially. They focused on how transmission in Wuhan varied between December 2019 and February 2020. They developed a mathematical model and then fitted it to four data-sets. These were:

1. Number of new internationally exported cases (as of 26 January).
2. Daily number of new cases in Wuhan with no exposure to the wet market where COVID-19 was first found (1 December to 1 January).
3. Daily number of new cases in China (29 December to 23 January).
4. Proportion of infected passengers on evacuation flights (29 January to 4 February).

The authors used two additional datasets that they compared with the outputs of the model:

1. Daily number of new exported cases from Wuhan in countries with high connectivity to Wuhan (as of 10 February).
2. New confirmed cases reported in Wuhan (16 Jan to 11 February).

In January 2020, the R0 (average number of people infected by each case) was between 1.6 and 2.6. Travel restrictions in Wuhan were introduced on 23 January and after this R0 decreased. On 23 January it was 2.35 and on 30 January it was 1.05. Based on this figure, the authors also estimated the chance that the infection could take hold in other locations. They found that, where there were four independently introduced cases, there was a 50% chance that infection will take root.

Therefore, travel control measures likely did reduce COVID-19 transmission. However, before these measures were put in place, many chains of transmission may have already been established.

Inferring the number of COVID-19 cases from recently reported deaths

At the time of writing, this article has not undergone peer-review. The authors developed a method to estimate the number of COVID-19 cases in a population based on the number of reported deaths. As COVID-19 has non-specific symptoms and many cases are relatively mild, the disease can spread unnoticed. Severe cases and deaths are more likely to be detected.

Their approach involved two steps. First, they estimated the historic cases by assuming that non-fatal cases are undetected. Then they used those cases to project forwards. One important piece of information is the case fatality rate (CFR). This gives the expected number of deaths per case. So if the CFR is 1% then, out of every 100 people with the infection, one will die.

Using this model they estimated the likely epidemic sizes when a single death is reported. This was done for different R0 values (average people infected by each case) and CFRs. One model would therefore be:

• R0 = 2 (2 people infected by each case).
• CFR = 2% (2 people out of every 100 die from the infection).

Giving 276 population cases for every death detected. While there is a lot of uncertainty with this figure, the figures for Italy, Spain and France were all relatively close to it. At the time of the first death, Spain reported 202 cases, France 177 cases and Italy 2037 cases.

This model suggests that by the time the first death occurs, there may be around 200 cases in the population. However, this figure could be in the thousands.

Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts

This peer-reviewed study used a mathematical model to see if isolation and contact tracing can control imported cases of COVID-19. Outbreaks were classed as controlled if transmission lasted less than 12 weeks or led to fewer than 5000 total cases. They tested the model with the following conditions:

• Number of initial imported cases.
• Reproduction number (R0).
• Length of delay between symptoms onset and patient isolation.
• Probability of tracing all contacts.
• Proportion of transmission that occurs before symptoms.
• Proportion of infections with minimal symptoms.

They first tested it with only five initial cases and R0 of 1.5 with no transmission before symptoms. The outbreak can be controlled even when there is a low probability of identifying all contacts. However, with an R0 of 2.5, more than 70% of contacts need to be traced. And if the R0 is 3.5 then 90% need to be found.

If R0 is between 2.5 and 3.5 and 40 cases are imported, contact tracing and isolation is only possible if less than 1% of transmission occurs before symptoms. This means that highly effective contact tracing and case isolation could control an outbreak. However, if there are a large number of initial cases or transmission occurs before symptoms, then its effectiveness reduces.

Estimates of the severity of coronavirus disease 2019: a model-based analysis

This peer-reviewed study provides one of the most recent estimates on case fatality ratios (CFR). The CFR is the proportion of people with COVID-19 symptoms that die.

The authors collected data on patients that died in Hubei, China up to 8 February. They coupled this with data on cases for 37 other countries until 25 February. This allowed an estimate of the time between symptoms coming on and the patient’s outcome (either death or hospital discharge). The authors used the data of 24 people that died in China and 165 people who recovered outside China. They estimated that the average time period between symptoms and death was 18 days. Patients that survived were typically discharged from hospital 25 days after symptoms began.

Based on 70,000 cases in China, they estimated a crude CFR of 3.7%. If the authors controlled for undiagnosed cases, then this reduced to 1.4%. However, this was very age-dependent. For people under 60 years old, the CFR was 0.3%. For people aged 60 and over it was 6.4%. For 80 years and above it climbed to 13.4%. CFRs for countries outside China was 1.4% for under 60 years and 4.5% for 60 years and over.

Finally, the authors estimated the infection fatality ratio (proportion of infected people that die). This came out at 0.66%. The IFR is lower than the CFR because many infected people will have minimal symptoms and therefore will not be diagnosed as cases.

These updated estimates of the infection and case fatality ratios can be used for further modelling studies. They again confirm the significantly increased risk of death as people get older.

Novel coronavirus 2019-nCoV: early estimation of epidemiological parameters and epidemic predictions

This was an early study that has not been peer-reviewed. It provided an early estimate of R0 (average number of people infected by each case). Their model focused on the only data available, which at that time came from Wuhan only.

The authors’ model of transmission suggested that R0 was 3.11 in Wuhan, so just over three people are infected by each infected individual. With an R0 this high, case identification and contact tracing would have to stop 58–76% of transmissions. They also estimated that only 5% of cases were being identified in Wuhan, suggesting a total of 21,000 cases for the first 3 weeks of January. By that stage only 700 cases had been confirmed.

By the end of the month they projected 105,000 cases in Wuhan. Similarly, by modelling the main cities that Wuhan residents travel to, the authors estimated the next locations to be hit. By the end of January they expected 237 cases to be exported to other parts of China.

Estimation of country-level basic reproductive ratios for novel Coronavirus (COVID-19) using synthetic contact matrices

This non-peer-reviewed study looked at expected differences in R0 by country (average number of people infected by each case). The authors note that R0 is determined by the age structure of a population as well as the makeup of households. For this model they focused on the age structures and degree of social mixing between age groups. The ratio of children to older adults can be used to predict R0. This allowed them to predict that R0 would be highest in Eastern Europe and Japan. R0 would be lowest in Africa, Central America and SouthWestern Asia.

A spatial model of COVID-19 transmission in England and Wales: early spread and peak timing

This study has not yet been peer-reviewed. It was an early modelling study that sought to estimate the spread of COVID-19 in England and Wales. They based this on 2011 census data and the latest virus estimates from China. The authors predicted that an England and Wales outbreak would peak 126–147 days after the start of sustained transmission.

Therefore if person-to-person transmission were to start in February, it would peak in June.

Interestingly, while they predicted urban areas would be harder hit than rural, they didn’t predict that London would be the worse hit. Their Figure 3 (below) predicted higher peaks in the North East and North West of England.

They also predicted that seasonal changes in transmission rate would substantially affect the peak. Their Figure 5 (below) predicts changes in the shape of the epidemic based on changes to transmission. So a 50% reduction in transmission would lead to a small summer peak and a larger winter one. A reduction of 75% would lead to the outbreak being moved to the winter.

It’s unclear how seasonal changes will affect the transmission of COVID-19. This model considers a wide range of possibilities from no effect on transmission, to a 100% reduction of transmission due to seasonal effects.

All of the predictions in this early model were based on infections alone. They did not model interventions. The authors also did not model mortality and the treatment of cases.

The efficacy of contact tracing for the containment of the 2019 novel coronavirus (COVID-19)

In this non-peer-reviewed study the authors were interested in how contact tracing can reduce the size of the outbreak. They used surveys asking about social encounters. This could then be used to estimate how well the Government contact definition would work for tracing. Close contact was and still is defined as being within 2 metres for 15 minutes or more.

They estimated that less than 20% of cases will result in infected contacts that are untraced. However, to achieve this the public health authorities will need to identify an average of 36 contacts per case. This was based on the fact that:

• the average person has 90 contacts in a 2- week period.
• 59 of these contacts will be encounters of 15 minutes or more, at a close proximity (within 2 metres).
• 36 of these contacts will be known to the case and therefore traceable.

This shows there are lots of brief contacts, but only a small proportion need to be traced.

Therefore, while rapid and effective contact tracing can be very effective, it will be labour-intensive. Increasing the time at close contact to 1 hour would have little impact on the number of untraced contacts. However, greater than 4 hours would lead to the risk that cases will be missed.

You can find more content from POST on COVID-19 here.

You can find more content on COVID-19 from the Commons Library here.