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“Boris Johnson has warned that many more British families ‘are going to lose loved ones before their time’ as he addressed the global coronavirus pandemic. Johnson said the UK has now officially moved from the ‘containment’ phase of dealing with the pandemic, to the ‘delay’ phase, which aims to hold-up the spread of the virus and ‘thereby minimise the suffering’. “[1]

British Prime Minister Boris Johnson said in a speech on March 12 that the UK will adopt a strategy of herd immunity and more British families “will lose themselves before losing their loved ones.”

Report of British newspaper on Boris’ speech (source: The Times)

What is herd immunity?

Herd Immunity is a form of indirect protection against infectious diseases. This form of combating infectious diseases can only occur after most people are immune to infection, thereby protecting against lack of corresponding immunity.People [2]. Dr. Zhang Wenhong also mentioned in a recent interview that when a certain percentage of the population is vaccinated, herd immunity can be formed to protect those who have not been vaccinated [3].

Simply speaking, if everyone except you is vaccinated against an infectious disease, no one else will be infected. Although you are not immune to the disease, you are relatively safe.

Calculation of herd immunity ratio

Many people have seen this picture recently:

Blue represents non-immune healthy population, red represents non-immune diseased population, yellow represents vaccine-free and healthy population

The first case indicates that there is no immune resistance and a large area of ​​the population is infected;

The second type is that a small number of people have immunity and still have large areas of infection;

The third is that most people have immunity, which can only cause a small number of infections.

Looking at the picture, we can roughly understand that when the vast majority of people have been immunized, then the susceptible population is also safe, but how to calculate the majority proportion

The first concept is introduced here, which is also familiar to us, R0 (we mentioned it before when we talked about the epidemic prediction model). Basic reproduction number (R0) In epidemiology, it refers to a patient infected with a certain infectious disease without external intervention and no one has immunity. The average number of individuals who will spread the disease.

In short, it is how many people a person can infect, but it is worth noting that R0 here is a statistical average, and a single case is not representative.

Second conceptIt is the Critical vaccination level, or Vc for short, which simply means that what proportion of the population is immunized before the spread of infectious diseases stops.

In fact, based on these two indicators, we can calculate the value of the infection rate of about 60%, said the chief scientific adviser of the British government, Sir Patrick Vallance.

The derivation process below is simple.

Let’s look at a simpler model first: when R0 = 4, that is to say, one communicator can pass to four susceptible persons, and then the four infected persons can pass to 16 susceptible persons. Or, as shown below:

At this time, if exactly 75% of the population has acquired perfect immunity, an interesting phenomenon appears (note the change of the arrow):

It can be found that infectious diseases can only be transmitted from person to person.

It is conceivable that when the proportion of immunized people in the population is greater than 75%, the ability to spread infectious diseases will become weaker and weaker [4].

Therefore, when R0 = 4, Vc = 75%, and when the product of the basic transmission coefficient and the proportion of non-immune population is 1, it is just the critical vaccination level, that is, the spread of the virus is stopped. We can get the formula:

R0 * (1-Vc) = 1

It can be understood that when R0 * (1-Vc)> 1, the infectious disease will continue to spread, and when R0 * (1-Vc) <1, the infectious disease will gradually disappear over time.

For new coronary pneumonia, researchers from the World Health Organization and the University of Hong Kong have summed up confirmed case data in the two months since the end of the epidemic matured in 2019, raising the R0 coefficient to 2.68 and narrowing the 95% confidence interval 2.47-2.86 [5].

Substituting R0 = 2.68 into the critical state formula, Vc = (R0-1) / R0 = (2.68-1) /2.68 = 0.63, which is about 60%.

That’s why 60% of people need to be infected to gain immunity.

Based on R0 and Vc, we can get a rough prediction curve of herd immunity to evaluate how many people need to be immune to resist infectious diseases.

However, the premise of the above prediction is that the infected survivors have perfect immunity, which is often unsatisfactory.

So we also add a parameter E (Vaccine effectiveness against transmission) to express the effect of immunity during the infection process. Therefore, the final complete formula is:

R0 * (1-Vc * E) = 1; Vc = (1-1 / R0) / E

It can be found that when E <1, that is, when the immune effect after infection is not perfect, a larger Vc, that is, a larger proportion of immunized people, is required to prevent the spread of the disease.

What happens in the UK?

The development of the epidemic has changed over time. The United Kingdom hopes that through the control, the development of the epidemic will be prolonged, the number of patients accumulated per unit time will be reduced, and the impact on medical resources will be reduced in a short time.

So how exactly will the epidemic develop? Assume that 60% of the British population is about 40,000,000. Based on the simulation of the SIR model, we consider 2 extreme cases:

1. The British government strictly controls and keeps R0 to a small value (slightly greater than 1) for a long time. It takes about 13 months to “realize” 60% of the population, with the highest peak being 600,000 infections per day. People (shown in the blue line above);

2. The British government’s control has been very weak. The case growth rate is fast and then slow. In about 5 months, the UK will “achieve” the goal of infecting 60% of the population, with the highest peak being 6.1 million people in a single day. (Shown in the red line above).

Reconsidering medical resources and lethality, the current situation of herd immunity through virus infection is very terrible without vaccines in a short period of time.

You may ask, why can’t the number of infected people grow linearly? Even through the control of the gods, the cases increase linearly. If the number of people increases by 10,000 per day, it will take 4,000 days or 11 years to infect 60% of the population and form herd immunity.

Presumably this may not be acceptable to Britain.

worst case scenario

The above predictions are based on the fact that the virus’s infectivity will not increase, and antibodies will always be present and effective.

Actually, as the disease spreads, viruses with stronger virulence and weaker transmission capacity will naturally decrease, and what remains may be transmission energy.The strong but weak virulence strain also changes with the valuation of R0.

At the same time, the E value representing the immune effect may not necessarily be 1. As the virus mutates and human antibodies decrease, the virus may cause secondary infections. When (1-1 / R0)> E, herd immunity will never be achieved.

What can we do?

The situation facing the group is critical. As individuals, there are still many things that can be done to ensure their safety:

• Wearing a mask, the mask can effectively reduce the respiratory transmission probability of the virus;

• If you do n’t participate in the rally, go to a place with few people. For yourself, you will reduce the value of R0;

• Ensuring a nutritious diet and adequate sleep, and improving autoimmunity are the fundamental ways to defeat the virus.
  

  Reference:

  [1] https://metro.co.uk/2020/03/12/many-families-will-lose-loved-ones-time-coronavirus-says- pm-12390071 /

  [2] Fine, P .; Eames, K .; Heymann, DL (1 April 2011). “‘Herd immunity’: A rough guide”. Clinical Infectious Diseases. 52 (7): 911–16.

  [3] https://www.bilibili.com/video/av87896793

  [4] Fine, P., Eames, K., & & Heymann, D. L. (2011). “Herd immunity”: A rough guide. Clinical Infectious Diseases, 52 (7), 911–916.

  [5] Wu, Joseph T .; Leung, Kathy; Leung, Gabriel M. Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study. The Lancet. 2020-01-31