Simulation and comparison of several epidemic prevention models / Sheng Hong


1、 Simulation results
A. No Measures (or lying flat)

Note: the “+” sign in front of each measure represents that this measure is an additional measure based on the previous measures, and the results are cumulative. The same after.

Look at the leftmost column in the figure, “No Measures”. The infected index (the number of infected people on a day is equivalent to the percentage of the previous day) exceeds 100%, which is 215%. It is obviously an exponential expansion, and the virus infection does not converge. Compared with the increase of various epidemic prevention measures, such as reducing unnecessary contacts, non-face-to-face transactions, maintaining social distance, personal protection, etc., its the infected index is the highest, and the death caused by Covid-19 is also the highest (0.14).

B. Dynamic zero-COVID policy

“Dynamic Zero-COVID” reduced the death toll of Covid-19, but it was not significant, from 0.14 to 0.03. However, the additional deaths from other causes are as high as 5, which is obviously disproportionate. Meanwhile, the GDP index decreased from 100% to 5%. The economy was hit hard. This shows that the benefits of the epidemic prevention measures cannot cover its costs, including the cost of lives.

C. Non-mandatory Measures + the infected home isolation


 After taking six measures such as reducing unnecessary contacts, non-face-to-face transactions, maintaining social distance and personal protection, the infected people index fell below 100%, to 98%, indicating convergence. But it is still close to 100%, which should be said to be on the edge of convergence and expansion. At this time, the measures of the infected home isolation (assumed to be 7 days), reduce the basic reproduction by half. Because anyone who tests positive for nucleic acid at any time will be quarantined immediately. Due to the large number of people, on average, it will reduce the time of infecting others by half. At this time, the infected index further dropped to 71%. The death toll fell to 0.05. No additional deaths. GDP remained unchanged.

D. Simple comparison

I will put reducing unnecessary contacts, non-face-to-face transactions, non-contact transactions, maintaining social distance, personal protection, institutional protection and other measures together as “non mandatory measures”, and put them together with the infected home isolation as a model.
Closing the market, closing the community and difficult medical treatment are called “Compulsory Measures” as the “Ddynamic Zero Covid” mode.

Obviously, in the three models, in reducing the the infected index, “No Measures” is 219%, which has strong divergence, and the number of infected people will increase rapidly, which is obviously undesirable. The “Dynamic Zero-COVID” mode is the best, which is 47%. However, compared with “Non-mandatory + Home Isolation”, the benefit is limited. The latter index is also significantly lower than 100% , 75%, which is convergent. In nature, they are all inhibiting the spread of the virus, but the speed of “Non-compulsory + Home Isolation” is not so fast.

In terms of reducing the death of the Covid-19, “No Measures” did not reduce. Although the death of the Covid-19 on the first day was 0.14, but because the infected index was 219%, there would be many after many days, but the upper limit was limited by the total population. So it’s not advisable. The “Dynamic Zero-COVID” mode is the best, but it is limited. There are only 0.02 fewer people in a day than “non-mandatory + home isolation”. However, at the same time, the “Dynamic Zero-COVID” mode has the largest number of additional deaths from other diseases, up to 5 people per day. This will increase with the extension of the implementation days, and the additional death toll is equivalent to 5 people multiplied by the number of days. In the sense that life is equal, the “Dynamic Zero-COVID” mode directly leads to death, violates the basic moral principles of behavior, and brings more deaths, which is costly. The additional death toll of “No Measures” and “Non-compulsory + Home Isolation” is zero.

In terms of GDP index, both “No Measures” and “Non-compulsory + Home Isolation” remain 100%, that is, epidemic prevention will not affect the economy. The “Dynamic Zero-COVID” mode is 5%, indicating that the economy has been hit hard.

Comparatively speaking, “Non-compulsory + Home Isolation” is the best in various indicators and comprehensive effect. The infected index is 75%, which is obviously convergent; the additional death toll is zero; its GDP index is 100%, which does not affect the economy.

E. Some notes

The models here are pure and does not exist in reality. There is no complete model of No Measures, there are still some measures, such as banning large-scale gatherings, vaccination, self-isolation of the infected persons, etc.. There is no perfect Zero Covid-19 mode. It is assumed that the “Dynamic Zero-COVID” mode does not have the cross infection caused by crowded nucleic acid detection, rush to buy before the closure of the city and grab food in the shelter; there are no administrative departments that violate human rights and harm people’s livelihood, and so on. However, if the perfect “Dynamic Zero-COVID” mode is not desirable, those with these phenomena are even less desirable.

The city closure policy of closing the market, restricting online shopping and closing the community will bring hunger panic and make people who are qualified to work at home panic all day. They spend most of their time on survival, such as grabbing vegetables and group buying. They are often harassed by the police and epidemic prevention personnel under the pretext of “epidemic prevention”, thus losing the conditions and time of work from home. Therefore, this model does not assume that people can work effectively from home during the closure of the city.

These models do not consider the role of vaccination. Because according to a large number of observations, the vaccine does not prevent infection, and if it has the effect of reducing severe illness or death, it has been included in the existing statistics.

2. Model introduction

The model used here is the “Ten Dimensional Spatial Economics and Institutional Economics Simulation Model” constructed by me, and its core concept is “agglomeration”. Market network externalities are generated by agglomeration, that is, the number of transactions between people will increase faster due to the increase of population density. The basic research unit is “transaction”. A transaction can bring transaction dividends and transaction costs. Spatial economics estimates the number of transactions according to the population density of different spatial locations, and then estimates the total income from the transaction dividend. Institutional economics also takes transaction as the basic unit of research, and transaction cost is the core concept. Therefore, spatial economics and institutional economics are connected here. This model can estimate the economic output according to the degree and scale of population agglomeration, and estimate the optimal industry in a specific location according to the population density. And we can also use the nature of institutional economics to test institutional change and policy. I explained the basic mechanism of this model in the article “Transaction and City”. We have used this model to compile three industrial plans for local governments, all of which are relatively successful.

Figure 5 Distribution of population density of a city

In order to simplify, this model assumes that epidemic prevention measures will be taken after the virus has been infected for 10 days and the number of infected people has reached 2549. Comparing the second day after taking epidemic prevention measures with the previous day, it is the concept of rate, that is, the change between two days, but it can also be seen that the general trend of epidemic prevention is expansion, invariance or convergence. The “death toll” in the model is also the absolute number of a day, which can be compared with the scale of the model itself (population, GDP, area).

After the outbreak of the COVID-19 in 2020, I found that the spread of the virus was similar to the transaction, which was realized through human contact. “Agglomeration” makes the virus easier to spread. Therefore, the original spatial economic model is extended to estimate the impact on economic output under the condition that epidemic prevention measures limit people’s contacts. I use the model to simulate the results of Wuhan City closure, which shows that under the limited effect of resisting the spread of the virus, the economic output is significantly reduced. I also tried to find a way to balance epidemic prevention and economy by reducing the contacts of virus transmission without hindering the transaction, so I wrote “We need both epidemic prevention and transaction”.

Later, I found that the Basic Reproduction Number (R0) of the virus has not only natural attributes, but also social attributes. It is related to the communication frequency and population density between people, which is related to social development and mode of production. When people reduce their contacts, the Basic Reproduction Number decreases. If we find a method that can reduce direct contacts without affecting the transactions, and do not pursue virus clearing, but just set the goal to reduce the Basic Reproduction Number to less than one, we can make the virus spread converge and eventually die out. I also extended the model with this consideration, simulated several measures to reduce contacts and maintain trading, and tested the results, so I wrote the article “The appropriate goal of fighting the Covid-19 is to reduce the Basic Reproduction Number to less than one”.


3、 Basic mechanism

First of all, we don’t have to pursue virus clearing, because it’s too expensive and difficult to achieve. As long as we reduce the Basic Reproduction Number to less than one, the spread of the virus will fade and eventually disappear. As shown below. This is the downward trend of the virus in 365 days. Although slow, if compared with the actual effect in the past two years, it doesn’t seem to be slow now.

Figure 6 schematic diagram of virus infection with Basic Reproduction Number less than 1


Assuming that the Basic Reproduction Number is the product of natural factors and social factors, it is expressed as:
Basic Reproduction Number = natural factor coefficient × Social factor coefficient
This means that the Basic Reproduction Number will change in the same proportion with the change of social factor coefficient. If we count 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 we reduce the average number of contacts by 10%, the Basic Reproduction Number will also be reduced by 10%; the average number of contacts decreased by 50%, and the Basic Reproduction Number also decreased by 50%; Then we can infer that if we reduce the interaction frequency to a certain number, the Basic Reproduction Number will fall below 1. For example, when the Basic Reproduction Number is 3.77, if we reduce the interaction frequency to 25% of the normal level, the Basic Reproduction Number will drop to 0.94. This means that as long as we reduce the interaction frequency to 1/4 of our daily life, we can reduce the Basic Reproduction Number to less than 1. In other words, we don’t have to close the city and roads, and we don’t have to stay at home to fight COVID-19 (Sheng Hong, 2020).

In this article, I put forward measures such as “reducing unnecessary communication”, “non-face-to-face transaction”, “non-contact transaction”, “maintaining social distance”, “tested in advance of going to the gathering place”, “halving the carrying capacity of public transport”, “personal protection” and “institutional protection”, which can reduce infection and do not hinder transactions. The simulation is done with the model, and the results are feasible.

Fig. 7 Schematic diagram of cumulative effect of four epidemic prevention measures


Source: Sheng Hong, 2020b.

The above measures can be summarized into one category, that is, they are non-mandatory measures. Mandatory measures, such as “closing the market”, “closing the community” and “difficult to see a doctor”, are very different. First, while reducing virus infection, we will reduce transactions by a larger margin, so as to reduce economic output; second, compulsion is bound to go against the will of citizens. Because everyone is the best judge of himself, compulsion brings violations of civil rights and damage to interests, health, freedom and dignity. So mandatory measures are costly.

4、 Basic description of this model

This is to borrow a model of spatial economics. Its basic scale is 100 square kilometers, with a population of about 430000 and a GDP of 13.5 billion. The space consists of 100 * 100 grids, each of which is 1 hectare, i.e. 100 meters * 100 meters.

Because the transmission of the virus is uncertain, the infected people are randomly distributed, which varies with time and density.

Fig. 8 Random distribution of infected persons

For simplicity, I only consider the infection rate in one day. If it is greater than 100%, it is divergent, indicating that epidemic prevention is unsuccessful; if it is less than 100%, it is convergent, indicating that epidemic prevention is effective.

I estimated the infection rate based on the Basic Reproduction Number and the intergenerational interval of virus infection. Although the intergenerational interval is actually normally distributed, considering the staggered and successive time of many infected people, we regard the intergenerational interval as the average. The Basic Reproduction Number is calculated by the intergenerational interval (days), and the daily infection rate is obtained. Please experts correct this point.

Used to estimate the effect and cost. By multiplying the number of infections by the case fatality rate, we can see that the number of Covid-19 deaths reduced by infection’s reducing. At the same time, use the model to estimate the GDP under specific measures and obtain its economic cost. Additional deaths from other diseases caused by specific measures should also be estimated as the life cost of specific epidemic prevention measures. In this model, because the number is small, I use the absolute number instead of the ratio. However, it can be compared with the population size of this model.

In this model, the non-mandatory measures I adopt are to eliminate unnecessary contacts, non-face-to-face transaction, non-contact transaction, maintaining social distance, personal protection and institutional protection. Mandatory measures are to close the market, close the community and make it difficult to see a doctor. Closing the market includes closing physical stores and banning online shopping. Closing the community means that residents cannot go out of the community to work, study, purchase and entertainment. What is difficult to see a doctor is that epidemic prevention measures hinder and delay medical treatment.

All Non-mandatory Measures have the effect of reducing contact infection without reducing transactions; Mandatory Measures reduce contact infection and trade at same time. Reducing contacts reduces the Basic Reproduction Number; if the transaction frequency is reduced, the output brought by the transactions is reduced. In the specific calculations, the parameters affecting infection and transaction are different, so the results of infection or transaction of Mandatory Measures and Non-mandatory Measures are different.

5、 Data selection

The first is the Basic Reproduction Number and the Average Intergenerational Interval between infections. This is one of the main differences between Covid-19 original strain and Omicron. The original data I used was proposed by Zhong Nanshan’s team. The Basic Reproduction Number of the original Covid-19 strain is 3.77 and the intergenerational interval of infection is 7.5 days. At present, the Basic Reproduction Number of Omicron is 10 (epidemic investigation to the end, 2022), and the time interval is 3 days (China Network Live Broadcast, 2022).

Another important parameter is mortality. I noticed that there are two kinds of data in the official data of mainland China, one is “confirmed cases” and the other is “asymptomatic infected persons”. The current controversy over mortality may arise from this. Some people use confirmed cases as the base to estimate the case fatality rate, while Zhang Wenhong’s case fatality rate is based on all infected persons, that is, the number of confirmed cases and asymptomatic infected persons is added. Since the authorities regard all nucleic acid positive people as patients, they are forced to be isolated; therefore, we should base on all infected persons (nucleic-acid positive persons).

If we are stricter, we can use the case fatality rate and the infected death rate. Infection does not mean illness. Of course, here, this is equivalent to Zhang Wenhong’s “case fatality rate”. We are following the difination of Zhang Wenhong, but we can’t use the data of Shanghai. Because there are political factors behind this. In order to provide a legal basis for “Dynamic Zero-COVID”, officials have recently stuffed many non Covid-19 deaths into the Covid-19 death data (Liu Zhongliang, 2022). So we should avoid the data of Shanghai. Choose another large-scale but not politicized data.This is the data of Jilin Province.

From March 1 to May 4, 2022, there were 36818 asymptomatic infections, 39640 confirmed cases, together is 76458 infections and 2 deaths in Jilin (Baidu, 2022). The case fatality rate was about0.000026.

According to China Health Statistical Yearbook 2020, the number of outpatient and emergency patients is 65643 80000 person times (National Health Commission, 2020, P. 181), about 0.469 of the total population. Admissions per 100 emergency patients are 4.41(National Health Commission, 2020, P. 130). The emergency admission rate of residents was 0.02. 0.000056 per day. This parameter represents the rate of serious illness in the emergency department. If it is delayed, patients may die. It is assumed that it is difficult to see a doctor due to “epidemic prevention”, resulting in the delay of treatment of about 50% of patients, of which the probability of death is 20%. The death rate of residents with delayed emergency was 0.0000056.

6、 A few more words

(1) If the unit cost remains unchanged, when the basic parameters of virus transmission, the Basic Reproduction Number and the average inter-generational interval of infection change to the extent that Omicron is compared with the original Covid-19 strain, the cost of epidemic prevention is completely unbearable. The change of this parameter has a great impact. If the two novel coronavirus types start to infect at the same time, the number of people infected by Omicron on the 20th day is 134821 times that of the original strain. As shown below. Even if the epidemic prevention cost of Omicron is 1 / 10 of that of the original strain due to economies of scale, the cost is still unbearable. This is an important factor that needs to change the epidemic prevention mode.

Figure 5 multiple of the number of people infected with Omicron relative to the number of people infected with the original coronavirus


(2) At this time, it is a requirement to distort the allocation of medical resources to emphasize that “all must be inspected if should”, “all must be quarantined if should”, “all must be collected if should”, “all must be treated if should”. The so-called “all must be inspected if should”, which means that all medical resources are used for nucleic acid testing, which is a simple work, crowding out professionals for the treatment of various diseases; The so-called “all must be quarantined if should”, “all must be collected if should”, “all must be treated if should”, the boundary is the most mild patients – asymptomatic infected people, which makes the scarce medical resources occupied by lighter patients, and excludes the severe patients with other diseases, and even the really severe Covid-19 patients.

(3) In the “Dynamic Zero-COVID” mode, from the idea of “early detection, early report, early isolation and early treatment” to “early closure of the city”, it is believed that the virus can be suppressed and the city be unsealed as soon as possible, but it is not. Since the emergence of the virus is random, people do not know when the virus will appear. No matter how fast the city is closed or unsealed, it will interrupt the transaction and production. The modern division of labor system requires that cooperation is stable and predictable. The loss of city closure is not measured by the length of time, but the uncertainty brought by “Dynamic Zero-COVID” will lead to the instability of economic division of labor and the loss of contract, even losing markets forever.

(4) The comprehensive closure of the city and the forced isolation of others beyond patients and close contacts obviously also bring the price of unwarranted restriction of human freedom. This cost can be compared and weighed against the lives saved. Therefore, the upper limit of quarantine is that the social cost should not be higher than the social benefit. See the following formula.

Social cost: number of people isolated × Days ≤
Social benefits: the reduced number of infections due to quarantine × Mortality × (reduced life expectancy of Covid-19 death) × 365 days (Sheng Hong, 2021)

At present, the practice of closing cities with few cases is a great waste of social resources and human life.

(5) Forced nucleic-acid positive but asymptomatic infected persons leave home for shelter isolation, which is even worse than home isolation in terms of reducing infection and treating diseases. The actual data show that asymptomatic people turn negative in about seven days without special treatment (Lei Ceyuan, 2022), so they can achieve this goal at home; shelter isolation increases the risk of cross infection, while home isolation does not. Moreover, shelter isolation has also increased the investment of a large number of public resources. Home isolation only uses residents’ ready-made houses.

(6) Originally, the problem that the power of the party and government system in mainland China is not constrained has not been solved. Excessive epidemic prevention provides them with the opportunity to abuse public power for personal gain and violate human rights. They took advantage of the opportunity of epidemic prevention to restrict market supply, suppress competitors, and even take support materials from other provinces and sell them to residents at high prices. Without any legal basis or following any legal procedures, police or epidemic prevention personnel have repeatedly broken into civilian houses and kidnapped residents.

(7) Although the strong infectivity of Omicron will be greatly alleviated by the low case fatality rate, it seems right to say that “the absolute number of deaths due to China’s huge population base is also large”. However, the conclusion that “Dynamic Zero-COVID” must be implemented is specious. First, even a huge population base has an upper limit. According to the current population of mainland China, even if all are infected, according to the case fatality rate we get from Jilin Province, the death toll will not exceed 37000. Second, the population base is huge, and the implementation of “Dynamic Zero-COVID” will lead to more additional deaths; Third, to say not to “Dynamically Zero-COVID” is not to go to the other extreme – “lying flat”, but to adjust to “non-compulsory measures + nucleic-acid positive home isolation”, which will inhibit the spread of the virus, reduce the Basic Reproduction Number to less than one, and will not lead to a great increase in the death of Covid-19.

(8) Due to the requirement of “Dynamically Zero-COVID” and the lack of probability concept, it will lead to the high-frequency testing of nucleic acid to “all”, which will not only waste resources, but also bring the result of gathering people for cross infection. If the goal is to “reduce the Basic Reproduction Number to less than one”, the method of random sampling can be adopted. For example, if a sample accounting for one thousandth of the total population is taken each time, it can judge whether the Basic Reproduction Number is less than one by observing whether the number (proportion) of positive samples in the two-time samples increases or decreases. This will bring great savings and
security.

(9) Because the current “Dynamic Zero-COVID” mode is strongly tied with all people nucleic acid, forced asymptomatic infected people to isolate out of home, closed communities, closed markets, obstacles to emergency treatment, etc., it is heavily dependent on the unrestricted administrative system, which is characterized by repeated aggregation and forced contact, resulting in it becoming a virus infection system, resulting in the long-term non remission of virus infection, And it will inevitably spread to other areas, so it itself is a huge obstacle to epidemic prevention, and the goal of “Dynamically Zero-COVID” can not be achieved.

(10) Now it seems that the current epidemic prevention policy lacks the data and research basis of human behavior. If spend 1 / 100 of the current cost of epidemic prevention, hire anthropologists and sociologists to observe and study the epidemic anthropology, and find out the epidemic prevention effect of people’s behavior, for example, which can easier lead to the spread of the virus, to buy from the market or to organize group purchase by the neighborhood committee? Which is more conducive to epidemic prevention and treatment, to isolate at home or in the shelter? And which can reduce virus infection more effectively, to set up checkpoints everywhere to check the health code or Nucleic acid proof or remove these checkpoints? And so on, on the basis of these observations and studies, the formulation of relevant epidemic prevention policies will be closer to the actual situation and achieve better results.

Finally, it should be emphasized that this model is a very simple model, and the simulated results only have schematic reference value. In particular, I am a layman in epidemic prevention, and there will be many unprofessional mistakes and even hard errors. I hope professionals can point them out. At the same time, I also believe that my different knowledge structure and perspective will enlighten and supplement them and help them improve their research and scheme suggestions. My simulation and comparison is also provided to policy makers as a reference if they see it and are willing to see it.

Reference

Baidu, “Real time big data report of epidemic situation \ Jilin Province”, Baidu, May 5, 2022.

National Health Commission, China Health Statistical Yearbook 2020, China Union Medical University Press, 2020.

Lei Ceyuan, “President of Shanghai fangcang hospital: many patients didn’t know how to get infected, but they turn negative in an average of 7 days”, Shangguan News, April 22, 2022.

Liu Zhongliang, “People’s daily interviewed Zhang Wenhong and Chen Erzhen. Does Shanghai and Hong Kong data tell you that you should fear the Omicron”, Headline Article, April 28, 2022.

Sheng Hong, “We need both epidemic prevention and trade”, FT Chinese, February 12, 2020.

Sheng Hong, “Transaction and city”, Research on Institutional Economics, No. 3, 2013.

Sheng Hong, “The appropriate goal of fighting the Covid-19 is to reduce the basic reproduction number to less than 1”, Professor Sheng Hong, April 23, 2020.

Sheng Hong, “Scientific epidemic prevention under the constitutional framework”, Forget talk Hill Study, November 27, 2021.

After the Epidemic Investigation, “Hard core evidence-based R0 = 9.5 = 1 transmission 10? What can’t R0 tell us?” Surging, April 26, 2022.

Live Broadcast on China.com, “The average generation spacing between Omicron infection cases is 3 days, and the transmission capacity is twice that of delta mutant”, Live Broadcast on China.com, April 27, 2022.

On May 5, 2022, in Fivewoods Study

Author: flourishflood

Economist, Confucianist

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