The Proper Target for Fighting against the COVID-19 is to Reduce the Basic Reproduction Number to Below 1 / Sheng Hong

Note: Recently, the proportion of vaccinated population has reached the level of herd immunity in many countries, and a new wave of COVID-19’s massive spread has emerged. The reason is that the effectiveness of various vaccines is far lower than expected. China and other countries have found many cases of infection after vaccination, and the virus mutation is accelerated. Most of the mutant strains can avoid vaccine antibodies, have serious side effects, and are more infectious. A British study said, “COVID-19 variants that make all vaccines fail now are almost inevitable”. This situation disrupted the strategy of vaccination to form mass immunization. Some people have proposed to give up the confrontation with COVID-19, and some countries have returned to extreme state. For example, China has closed the infected societies and even the building gates in the new outbreak, and Britain has returned to complete “freedom”. In this dilemma, I found that the “The Proper Target for Fighting against the COVID-19 is to Reduce the Basic Reproduction Number to Below 1” proposed by me in April last year is still an appropriate goal that takes into account epidemic prevention and economy, health requirements, freedom and communicative nature. This does not depend on technical means, but only requires people to change their behavior habits slightly. Wearing masks, social distance and washing hands are easy. Because of the long-term coexistence with COVID-19, these habits will probably change forever. (August 3, 2021)

basic infected number3

At present, most countries in the world fight against the COVID-19 pneumonia. The goal is to reduce the number of additional infections to zero. However, this is neither realistic nor cheap. The “unrealistic” means that asymptomatic infected persons appear. If we want to find them all and isolate them in time, we need to conduct nationwide testing. Although some countries, such as the United States, have announced free nationwide testing.However, there is no way to solve the problem of interactions with foreigners. Let alone many countries, especially developing countries, can not do it. On the other hand, if we can not test the whole nation, but want to prevent the spread of the virus, we should regard all the people as suspects who are asymptomatic to carry the virus. The cost will be too high if we would like to fall the additional number of the infected people to zero. Assuming that only 1% of the asymptomatic infected people in the crowd, apart from testing we are unable to distinguish, 100% of people should take quarantine measures. Because modern economy is highly dependent on human interaction, this means stopping the operation of the economy and stopping the creation of income and wealth. According to the estimation of the SIEM model in my article, “We need Transaction while Epidemic Prevention”,because of the isolation of the city and the community, Wuhan’s GDP dropped 99.4%.

Then, whether it is too loose if only reducing the basic reproduction number (R0) to below 1. To say so because people do not know about the exponential nature of infectious diseases. The so-called “index type characteristics” refers to that the rate of transmission of infectious diseases is highly sensitive to the exponential, the exponential increases a little, the number of infected persons increases largely; the exponential decreases a little,the number of infected persons decreases largely. I take the basic reproduction number ,3.77, and the average interval of infection, 7.5 days, presented by the Zhong Nanshan team, as the basic parameter, by   3.77 power 7.5 , get 19% (expect experts correct) as increase rate of the average number of infected persons per day . From December 1, 2019 to January 23, 2020, the number of infected persons in theory was increased to about 78159. If the basic reproduction number is less than 1, for example, 0.94, the cumulative infection rate will increase by 0.96% on average.The number of additional infections is -1% daily. In the same 54 days, theoretically infected people accumulate only 148 people, can be easily handled by the Wuhan medical system, and it does not impede everyone else’s normal travel.

Fig. 1 Different results caused by different basic reproduction numbersbasic infected number1Note: this map takes December 1, 2019 as the starting point, and January 23, 2020 as the end point. It depicts the change track of the number of infected persons with basic reproduction numbers of 3.77 and 0.94 respectively. Because the difference between the two data is too large, the coordinates on the left and right sides should be used as the scale of the basic reproduction number 3.77 and 0.94, so that the latter can be revealed.

It is assumed that the number of infected persons increased by 15464 per day in Wuhan, but if the number of basic reproduction number dropped to 0.94, the number of additional infections would also decrease day by day (see chart below). This means that the infection of COVID-19 pneumonia is convergent. As long as the time is long enough, the number of additional infections will drop to zero.

Figure 2  Assuming that the basic reproduction number in Wuhan is 0.94basic infected number2Note: ordinate indicate the number of infected persons. Abscissa indicates time, and time unit is day. There are 365 days in total.

The question is, how can we reduce the basic reproduction number to less than 1? In fact, determining the basic reproduction number, there are natural factors , such as the infectious characteristics of the virus itself, and also the social factors. Without careful consideration, the basic reproduction number seems to be dominated by natural factors. In fact, since it is an infectious disease, it must be related to the interaction characteristics between people.It is what it is only in the normal state of the existing social interaction. For example, every person has to work with other people, gather with friends and family, travel and so on every day. If in a farming society, the basic infection  number of the COVID-19 virus will be much lower than the present value. Even in the normal state of interaction in nineteenth Century, the basic reproduction number will be lower than today.Humans can also reduce basic reproduction number by changing social factors, that is, changing behaviors.

There are two important variables that affect the basic reproduction number. One is population density, the other is frequency of interaction. Static population density is relatively fixed, such as the distribution of people’s residence and work is relatively fixed, while the dynamic population density is not so fixed. Such as watching ball games, plays or movies, religious worship, irregular business or political gatherings, etc. This is also known as the “time density” of the population. The frequency of interaction, that is, the higher the frequency of interaction in unit time, the greater the probability of human to human transmission of virus.The population density and frequency of farming society or Nineteenth Century are lower than today.

It is assumed that the basic reproduction number is the product of natural factors and social factors, expressed as:

Basic reproduction number = Natural factor coefficient × Social factor coefficient

This means that the basic reproduction number will change proportionally with the change of the coefficient of social factors. If we calculate the average number of contacts per day as 100%, assuming that reducing the frequency of contacts will reduce the basic reproduction number in the same proportion, that is, if our average number of contacts is reduced by 10%, the basic reproduction number will also be reduced by 10%; if our average number of contacts is reduced by 50%, the basic reproduction number will also be reduced by 50%; then we can infer that if we reduce the frequency of contacts to a certain number, the basic reproduction number will drop to below 1. For example, when the basic reproduction number is 3.77, if we reduce the frequency of interaction to 25% of the normal level, the basic reproduction number will be reduced to 0.94. This means that as long as we reduce the frequency of interaction to 1 / 4 of our daily life, we can reduce the basic reproduction number to less than 1. That is to say that the target to prevent novel coronavirus pneumonia can be achieved without closing cities and staying homes.

First of all, we can make an analysis of our daily interaction. It can be divided into at least two parts. Part is “necessary interaction”, part is “unnecessary interaction”. The necessary interaction is mainly work interaction, because there is no economic income without work, so we can’t maintain our life. In addition, there are also non work interaction with high intensity, such as school, strongly emotion driven visit to relatives and friends, desire for tourism, on-site view of important ball games, etc. Unnecessary contacts are dispensable, such as shopping, chatting, watching movies to kill time, etc. First of all, people can reduce unnecessary contacts. The proportion of necessary interaction and unnecessary interaction can be obtained through sociological and behavioral surveys. Now it is assumed that the proportion of necessary interaction is 80% and that of unnecessary interaction is 20%. Then people can at least reduce the frequency of interaction by 20% without unnecessary interaction.

In the necessary interaction, people can also maintain economic transactions, without carrying out personal contact, leading to virus infection. In my article “We need transactions while epidemic prevention”, I put forward that “non face to face trade” can be carried out. In particular, producer services, such as finance, information technology, e-commerce, education, consulting and other industries, can basically use the Internet for transactions or exchanges and create value. In 2007, producer services in the United States reached 46.6% of GDP. In the first half of 2019, China’s service industry reached 54.5% of GDP. If we estimate that the proportion of producer services in service industry in Wuhan is 60%, the proportion of producer services in China is as high as 32.7%. Assuming that GDP, that is, all the added value provided by people’s work, corresponds to 70% of all people’s contacts, the corresponding contacts of producer services in China account for about 22.89% of all contacts. If this part of the work of producer services takes the form of non face-to-face, such as working at home, online meeting, distance education, video consultation, online negotiation, etc., in fact, it is equal to reducing the direct contact interactions and the possibility of infection without reducing the work interactions. Added with 20% unnecessary contacts mentioned above, there are 42.89% interactions in total not to reduce economic income without direct contacts.

To fight against the COVID-19 pneumonia, of course, we must make efforts in medical technology. However, the most important danger of this disease is its spread. We can adjust our behavior to the spread of the virus. When people have to go out for social contact, people can also avoid infection by establishing new rules of behavior. Now some people have exaggerated judgments about the COVID-19 epidemic.It is believed that this has changed the trajectory of the world. In fact, human history has experienced many infectious diseases, such as plague, malaria, and so on, human beings have avoided them by adjusting their behavior rules. For example, during the black death period in Europe, Jews had greatly reduced the rate of disease by traditional isolation rules.After the epidemic of infectious diseases, human beings also include the rules of behavior to avoid infection into the daily rules of behavior. For example, the behavior rules to avoid AIDS can prevent the outbreak of infectious diseases for a long time,and normal transactions will continue. Until now. The basic reproduction number can be reduced by changing the rules of behavior slightly.

For example, social distancing. This generally refers to a distance of two meters or more to keep real spatial distance with others. This includes on the road, in the office, in the workshop, in any public place. It is reported that Ford Motor Co has made employees wear social distance bracelets, and when two people are less than 6 feet away, they will vibrate and remind.We can imagine that maintaining social distance rules can not be foolproof. We assume that maintaining social distance reduces the infection probability by 90% than normal interaction. That is also a great thing. Most primary industries and second industries can produce in a way that keeps social distance.In agriculture and in highly automated workshops, the normal distance between people is more than two meters, so there is no problem. Even in labor-intensive workshops, shift production can reduce the population density, so that the distance between workers is greater than two meters. The working contacts in the primary industry and the second industry account for 32% in total GDP, assuming that there is a probability that 10% of the social distance rules will be contagious.On the whole, it only increased 3.2% of infectious contacts. From another perspective, it increased the number of transactional but non infectious contacts by about 28.8%. Up to now, it has totaled 71.7%.

Another way is to “do not touch transactions”, which I mentioned in “epidemic prevention and transaction”. In the necessary contacts, life service industry seems to be inevitably faced with face-to-face services. However, this can also be improved. Modern technology can make people do not directly contact when they are in service. Supermarkets and stores that we have thought of have self checkout, and customers in restaurants can also help themselves to order. and robots can send food to them, and the hotels can also self-help check in. Most of Airbnb customers are already used to book  their rooms on the Internet, and to open the electronic code lock at the residences they booked. People can also change their behavior rules to reduce the peak. Such as supermarkets can divide the hours into groups, the agencies can also avoid the peak to work, and they can avoid the peak bus. Even the school may get half of the students to school every week.The other half listen to the online lectures. The result is the creation of conditions for social distance. In.2018, the total value added of China’s wholesale and retail trade and catering industry accounted for 11.5% of GDP, and the number of contacts was about 8% of the total amount of contacts. If “no contact transactions” could reduce the infection probability of 90%, it would be equivalent to an increase of 7.2% of the transactions which are not contagious but  tradable. Up to now, it has accumulated 78.9%.This means that reducing the interactions possibly infected to less than 25% of normal level, that is, the minimum goal of reducing the basic reproduction number to less than 1, has now been achieved.

Fig. 3  Cumulative effects of various measures to reduce the basic reproduction number on the number of additional infections in the case of GDP unchangedbasic infected number3Note: this map is made by the simulation of spatial economics and institutional economics planning model (SIEM). The number of GDP and of infected people are index, so they can be compared. The time span is one month. The effect of different measures is cumulative. The reason why the last measure, “Social distancing” looks having a great influence, is once the basic reproduction number is less than 1, it will show obvious convergence immediately.It is not the influence of this factor.

However, there is still some potential. In all kinds of services, tourism may be the industry that needs people to contact with each    other to provide services.It includes both public transport, such as aircraft, trains, long-distance buses, and tour guide services. First, people will take more and more short trips in the form of self driving, which will partly replace public transport such as planes and trains. Second, in form, free travel or self driving travel will greatly increase and replace tourist groups.Social distance control can also be adopted, such as airplanes or trains can only take up half of the passengers to set aside social distance. On the other hand, airlines or railway companies are allowed to adjust their prices upward. Travel agencies also need to change their form of service from large group to small group, or more services for family free travel and self driving.

Finally, the necessary non work contacts. For example, watching ball games, drama, movies or family gatherings. If you really want to go, you can also go. In addition to controlling the number of people, such as selling only half seat tickets, keeping social distance, you can also increase the requirements. For example, testing before going to the activities, the information should be recorded in public health institutions,and so on. On the one hand, it can restrict people to participate in highly gathered activities. On the one hand, it can also identify and grasp the information of infected persons beforehand and afterwards, and isolate and treat them in time.

On the basis of the above change of behavior rules, personal protection and institutional protection can reduce the infection rate. Personal protection is to wear masks and wash hands. This is a low cost measure and is easy to carry out. This means not only the low price of masks, but also the easy to wear and no need to always wear.It can be worn in places with low population density, that is, when the distance to others is greater than the social distance, it is not worn. The effect of wearing a mask seems to have no mature empirical parameters.The most conservative estimate is that wearing masks can at least reduce the risk of infection by 50%. While institutional protection includes testing body temperature, office disinfection and so on, the cost of addition is not very high. It also significantly lowers the infection  rate. If personal protection and institutional protection can reduce the infection rate by 70%,The above 21.1% necessary interaction can reduce the infection probability by 14.77 percentage points, with only 6.33 percentage points remained. It is much lower than the 25 percentage points required to reach the basic reproduction number 0.94, so that the basic reproduction number can be reduced to 0.2.

If a country implements the above measures and reduces the basic reproduction number to below 1, it will be able to accept the citizens of other countries that implement similar measures and actually reduce the number of basic reproduction number to less than 1. The measures will not be special.For example, the planes or trains may be required to take only half of the full passengers; or for passengers taking international flights or trains, they can be required for pre-detection and afterwards to save tourist information in the public health agency of the country. Entering a country, people should follow the rules of the country’s epidemic period. So that international contacts will basically resume.

So far, I have not discussed the medical or hospital factors. That is to say, no treatment is considered, nor the isolation of patients with symptoms is considered. We have not considered effective treatment after diagnosis, nor have we considered innate immunity, cured immunization, vaccine immunization and so on, we only conduct changes in the rules of behavior, reducing the basic reproduction number to less than 1.If the medicine or medical treatment is taken into account, the effect will only be better. Moreover, because this change of behavior rules will not bring the impact of the rapid increase in the number of patients to the normal medical capacity, it will make the medical strength and medical material resources play a better role.

If we think that such measures are proper and appropriate, we can look back and see that some of the measures currently adopted by the states may be useless or counterproductive. For example, when I put forward the idea of “We need transactions while epidemic prevention”, the prohibition of private cars in Wuhan may be a counter productive measure, which deprives the family of the dynamic isolation facilities.Forced to take a taxi or a 120 ambulance, it increases the probability of infection. For example, Wuhan prohibits individuals from buying vegetables in supermarkets, replacing them with grass-roots government organizations, and increasing the probability of infection. In addition, Wuhan closed residential communities, most cities in mainland China test residents’ body temperature and check them in and out of communities. Many cities in the world require residents to stay at home.It may at least be a “superfluous measure” that does not work. Compared with maintaining social distance, staying at home does not reduce the infection probability. There is even another possibility to increase the probability of infection. Because the experience of diamond princess has proved that perhaps this kind of concentration of people in a narrow building will increase the infection.It may also be squeezed into smaller spaces through neighbors. Besides, staying at home is not allowed to go out, and it will also cause damage to people’s health. In fact, if people go for a walk or exercise in the open area of the countryside, because of low population density, fresh air and plenty of sunshine, it will raise people’s health level and be good for resisting virus.

One obvious feature of reducing the basic reproduction number to below 1 is that the government’s coercive measures are greatly reduced. This means that a large number of choices can be made to citizens. In fact, there are great differences among individuals in the probability of being infected. Young people are less susceptible to infection than the elderly.They can take a more daring choice when they go out. People who depend on the income flow from market to  tend to work interactions more than those who earn fixed income. Those who prefer risk may assess the probability or cost of infection lower than those who hate it. More importantly,The consequences of personal decisions should be borne by the individual himself and his relatives and friends. Therefore, it will also be a family choice. A person will not choose too risky behavior because of family constraints. This does not require mandatory government measures.

So how do we know that the basic reproduction number has dropped to below 1? It is very simple that the newly confirmed cases published by various countries are a concise indicator. Most countries now have passed the peak in this index. Some countries, such as Italy and the United States, have been hovering at a high level after that, which is known as “plateau area”. This shows that the basic reproduction number is below 1.But it is still around 0.9x. If there is doubt about the data released by the government, it can also be entrusted to a non-governmental professional body by a public health institution. Once every few days, such as five days, a random sampling test will be conducted. According to the size of the area, the number of samples will be determined. For example, 10 thousand people are sampled every time. As long as in several times (such as five times) of the sampled tests, the number of additional COVID-19 infections have been decreasing, the basic reproduction number would be proved to drop to below 1. Of course, it is necessary to ensure that the sampling is absolutely random. This requires that the administrative organs should not be allowed to do such thing. Especially in mainland China, administrative agencies can not be allowed to control the data of COVID-19  through their organizations.

Figure 4 Additional diagnosed cases in Italy dailybasic infected number4Source: Worldometer,

Figure 5 number of additional confirmed cases in the United States dailybasic infected number5Source: Worldometer,

More generally, the strategy to reduce the basic reproduction number to less than 1 requires absolute authenticity of data. Otherwise, policymakers will have nothing to depend on. In mainland China, we need to change the way to collect COVID-19 information. Because we know that the number of infected persons and the number of confirmed cases is linked to “achievements” in the administrative system, linked to official positions or promotions.The data will never be accurate. Zeng Guang, who hosted the infectious disease report for 17 years, said: “during the past 17 years, the most serious problem is that after the outbreak of the local epidemic, the local health administrative departments do not allow the medical institutions to report, or even let the local disease control system report.It is also not ruled out that under some circumstances, the administrative department will report the opinions to the local government. The mayor or higher leader of the local government will not allow to report. “And the local officials who hide the report often get no punishment (Song Pan, March 29, 2020). Not only that, in order to conceal, the local government also controls through the network to suppress the disease information that appears among the people,as Wuhan has done for AI Fen and Li Wenliang et al. Therefore, as long as the infectious disease reporting system is controlled by the administrative system, the number is not credible. Therefore, in China, the most important thing is to implement the thirty-fifth constitution and abolish the system of controlling the epidemic information by the administrative departments at all levels.

Although no country has put forward the goal of reducing the basic reproduction number to below 1, many countries have taken similar measures. For example, Sweden, this country has its own way. As always, there are no closure of cities, no closure of roads, no downtime, no shutdown of shops, no restrictions on international flights.There is no call for people to stay at home. People work and live as usual. Judging from the trend of additional diagnosed numbers, Sweden has already reached its peak, with a peak of 812 additional diagnosed cases per day and 57 days apart from the first case. In general, the number of new confirmed cases is decreasing. This means that the basic reproduction number has dropped to below 1.The proportion of the confirmed population in Sweden is slightly higher than that in Norway 1.2/10000, Denmark 2/10000, Finland 6.1/10000 (calculated on the basis of Worldometer online data). Meanwhile, Sweden’s personal consumption is not much reduced, compared with Denmark’s and Finland’s 66% and 70% respectively, Sweden has decreased by 30%; Sweden’s relief applications are only Norway’s 1/4 (Fredrik Erixon, 21 April 2020).

Figure 6 number of additional diagnosed cases in Swedenbasic infected number6Source: Worldometer,

There are other countries or regions, such as South Korea, Taiwan of China and so on, there is no closure of cities, nor too much restriction on the freedom of the people. The time from the first case to the peak is 14 days and 34 days respectively. The measures are similar to the “basic reproduction number below 1”. Compared with Wuhan’s measures, there are many redundant elements and under this system.The local officials will not really think about finding better measures, and just do it for the leaders to see, and it appears  “strongly”. So in fact, Wuhan has started to peak from first case of COVID-19, which is about 75 days. The effect gap is obvious.

Figure 7 Additional diagnosed cases in Koreabasic infected number7Source: Worldometer,

Figure 8 Daily number of additional cases in Taiwan, Chinabasic infected number8Source: Worldometer,

Calling “reducing the basic reproduction number to below 1” is a “suitable target”, I don’t mean that there is a better goal. In fact, the so-called “high goal” is actually the high goal of a single target. The goal of human society is comprehensive, not only to prevent COVID-19 pneumonia, but also to guard against other diseases; not only to prevent diseases, but also to maintain normal economic movement.People are able to earn normal income to maintain their living. Therefore, the proper goal is to take into account the best goal of the comprehensive goal. Therefore, this measure is also the best way to achieve the best goal. Using the “Spatial economics and institutional economics programming model” (SIEM) to expand the analysis of infectious diseases and economic operation at the same time,we can give the data of infection and economic results corresponding to the measures to achieve the goal.. We can see that, with the “elimination of unnecessary contacts”, “non face-to-face transactions”, “no contact transactions”, “social distancing”, “test in advance of the gathering area”, “public transport limiting half number of passengers”, “personal protection” and “institutional protection”.A society can basically keep working interactions and necessary non working interactions, and reduce the basic reproduction number to below 1, which ensures both normal economic income and effective control of the COVID-19 epidemic situation.

Fig. 9  Simulating the GDP index and infection index of Wuhan, if the basic reproduction number is 0.77 since January 22, 2020.basic infected number9

Note: It is assumed that the behavior rules of “reducing unnecessary interaction”, “non-face-to face transaction”, “non-contact transaction” and “social distancing” are adopted, and the basic reproduction number is reduced to 0.77, the GDP index and infected people index from January 23 to March 23, 2020.

Of course, the analysis of this paper is based on rough estimates of the effects of various rules of conduct. A better analysis should be based on, on one hand, tracing and studying the effects of different measures in different countries; on the other hand, experts conduct microscopic experiments on rules of conduct to get close and accurate empirical parameters.To form better rules of conduct. At present, the different epidemic prevention measures adopted by various countries are actually a competition between rules of conduct. Ultimately, the best rule of conduct will win. That is, the rule of behavior that will reduce basic reproduction number to less than 1 and ensure the normal operation of the economy will prevailed. This victory will bring real benefits to the winners.It is not the advantage of text wrapping. Because the virus is still present when the virus is deleted, and if there is a violation of the appropriate epidemic prevention rules, even if there is more power, it can not stop the spread of the virus or support the normal operation of the economy. This compels the countries of the world to move towards the appropriate rules of conduct. Of course, they are fast or slow.Which countries can discover and form these rules of conduct will reconstruct the world pattern after the epidemic.


Fredrik Erixon,“The Swedish experiment looks like it’s paying off”, The Spectator, 21 April 2020

Song Pan, “Zeng Guang: If there is no lesson in blood, the problem of concealing the epidemic can not be solved!” WeChat public No. “County Health Media”, March 29, 2020.

April 23, 2020 in the Forget-Word Hill House

Author: flourishflood

Economist, Confucianist

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