Preface

Recently, when remarkable progress has been made in the prevention and control of the COVID-19 epidemic in China, the epidemic situation in South Korea, Japan, Italy, Iran and other countries is becoming more and more serious. Experts at home and abroad have warned that novel coronavirus may become a risk of long-term coexistence of epidemics and human beings.

Released by the author on February 3"when will the inflection point of the epidemic occur-- the prediction of novel coronavirus's spread based on mathematical model"In the report, novel coronavirus's basic infection number R0 is calculated, the decline of infection coefficient after strict prevention and control measures is reasonably speculated, and the scale of epidemic transmission, changes and inflection points of new cases are predicted.

It has been nearly a month since the article was released a few days ago. by reviewing the prediction effect of the model, this paper analyzes the infection coefficient after strict control measures in China, and uses it as a yardstick to evaluate the difficulty and prospect of overseas epidemic prevention and control.

Main conclusion

1) the novel coronavirus transmission forecast based on the mathematical model released on February 3 is consistent with the actual situation of the domestic epidemic situation: the model predicts that the inflection point of new cases will occur on February 12 (under optimistic assumptions) or February 17 (under neutral assumptions). As of February 29, the cumulative number of confirmed cases (excluding Hong Kong, Macao and Taiwan) announced by the Health Commission was 79824, and the forecast value of the model was 78775, with a difference of only 1.3%. Promoting the resumption of work under the measures of zoning and grading of epidemic prevention and control will not bring obvious repetition of the epidemic.

2) through strict prevention and control measures, the infection coefficient has been reduced to about 0.5 (on average, each patient can only infect 0.5 people), and to achieve this effect, it may be necessary to reduce the frequency of contact between people by 80% than usual.

3) take the rigor and effect of domestic prevention and control measures as the yardstick to evaluate the difficulty of overseas epidemic prevention and control: the prospect is not optimistic, the probability of getting out of control is high, and speeding up the development of specific drugs and vaccines may be the top priority to deal with the global COVID-19 epidemic. From the perspective of the epidemic transmission model, the number of basic infections must be reduced to less than 1 in order to control the epidemic, and under the premise that other parameters are controlled at the same level as in China, the contact frequency of personnel is more than 66% lower than usual, which may pose great challenges to the organizational and mobilization capacity of many countries.

4) the spread of overseas epidemics may be difficult to control in the short term, and its harm may be significantly higher than that of other outbreaks in the past few decades, which will have a greater adverse impact on global personnel mobility and economic activities, and the downward pressure on the global economy will increase significantly. Be optimistic about the investment value of interest rate debt and gold.

Figure 1 Forecast effect of the model under neutral hypothesis (released on February 3) (as of February 28)

Risk Tips:1) the calculation results are sensitive to the parameters; 2) the implementation of the policy has a great impact on the epidemic situation.

一、Review of the effect of novel coronavirus Communication Prediction based on Mathematical Model

Estimation of the basic number of infections R0:In hindsight, it was not overestimated.

The basic number of infections R0 refers to the average number of individuals per patient can be infected without additional epidemic prevention measures. At that time, the R0 estimated by the model was 5.38, which was much higher than that of SARS and novel coronavirus R0 estimated by other literatures at that time. Judging from the speed of the subsequent development of the epidemic, the number of confirmed cases of novel coronavirus increased to more than 70, 000 in about two months, more than 10 times the total number of confirmed cases of Chinese mainland SARS in 2003. It can be seen that the transmission capacity of novel coronavirus without epidemic prevention measures is obviously greater than that of SARS, and our estimate is closer to the actual situation.

In the process of collecting literature and research, we found that it is difficult to determine the input parameters and the output results are very sensitive to the parameters in calculating the basic infection number R0 (also known as the basic reproduction number) based on the SEIR epidemic transmission model. The estimated results of the same epidemic (such as SARS) in different literatures at home and abroad may be very different. In fact, in the initial stage of epidemic transmission, there is a lack of necessary research and statistics, and the incubation period, infection period and case statistics of the virus are very inaccurate, but the value of R0 is very sensitive to these parameters.

Our estimate of R0 can be closer to the actual situation, probably mainly because of the following improvements:

The main results are as follows: 1) the differential equations of SEIR are expressed in discrete form and transformed into iterative equations, so it is convenient to use the numerical simulation method. This not only simplifies the complex process of solving differential equations, but also makes it possible to calculate R0 without relying on data at a certain point in time (Y (t), the cumulative number of cases at a point in time (t time) needs to be determined when calculating R0 according to the SEIR model, which is likely to be seriously distorted at the beginning of the epidemic).

2) the scale of infection in Wuhan in the incubation period was inferred from the incidence of the population who moved to various provinces and cities from January 14 to 21 in the following week, which could be used to solve the model. In the early stage of the epidemic, there is a large omission in the statistics of confirmed cases, so it is not suitable to be directly used to solve the model. It is much more reliable to estimate the average size of infected people over a period of time by counting the incidence of a period of time than using the data at a certain point in time, because the data at a certain point in time may be disturbed by many factors, such as detection efficiency, statistical caliber, release delay and so on.

3) take the days of infection period as an undetermined parameter, estimated by the numerical model, rather than directly specify a certain value. In the literature at home and abroad, when using SEIR model to estimate R0, the length of infection period is basically set directly according to observation or experience. For example, the infection period of SARS is generally set to 3 to 4 days. Many articles estimated by novel coronavirus also draw lessons from this parameter of SARS directly.

However, the result estimated by our model is that the average infection period of novel coronavirus is 7 days (without taking epidemic prevention measures). This is because there are many mild patients in novel coronavirus, who may not seek medical treatment or home cultivation for a long time after the onset of the disease, but are in an active state of transmission. In fact, the longer infection period is the main reason why novel coronavirus R0 is significantly higher than SARS.

The parameter setting of the propagation model after taking preventive and control measures:The neutral hypothesis is very close to the actual situation.

After a more accurate estimation of R0, the prediction of the development of the epidemic mainly depends on whether the infection coefficient after taking preventive measures is reasonable. In the February 3 article, we made two assumptions: optimistic and neutral:

Neutral hypothesis:

1) suppose that since January 23, people travel and gather less, and the number of contacts per unit time decreases by 50%. Due to increased vigilance against the epidemic, patients with mild symptoms will seek medical treatment in time, reducing the duration of infection from 7 days to 4.5 days. Due to wearing masks, disinfection, etc., the probability of single contact infection has been reduced by 15%. The number of basic infections will be reduced from 5.38 to 1.47.

2) suppose that since February 15, due to the strict implementation of the isolation and observation system, most of the new cases are on the isolation observation list, and the possibility of re-transmission has been basically lost, and the basic number of infection has decreased to 0.5, which is slightly higher than that in the later stage of SARS (WHO study believes that R0 dropped to 0.4 after strict control measures were taken in the later stage of SARS).

Optimistic assumption:

1) assuming that the average number of contacts per unit time decreases by 55% since January 23, and the rest remains the same as the neutral hypothesis 1), the basic number of infections decreases from 5.38 to 1.32.

2) suppose that from February 10, the quarantine observation system began to take effect, and the basic number of infections decreased to 0.4.

Under these two assumptions, the development of the epidemic can be predicted as follows:

It is estimated that in the future, the total number of novel coronavirus patients will reach about 88500 (under the neutral hypothesis) or 58000 (under the optimistic hypothesis), and the number of newly diagnosed cases will reach an inflection point on February 17th (under the neutral hypothesis) or February 11th (under the optimistic hypothesis).

From the actual development of the subsequent epidemic situation, the neutral hypothesis is relatively reasonable and very close to the actual situation. But at that time, many people questioned that our assumptions and forecasts were too optimistic, because in just a decade or so, the number of confirmed cases soared from dozens to more than 20,000, and the daily increase was still on the rise.

Chart 2 the number of confirmed cases in early February increased exponentially

In the atmosphere of the fastest development of the epidemic and the spread of pessimism in early February, how can our parameter setting be more objective and reasonable?

Believe in logical reasoning and refer to the later prevention and control effect of SARS.

Logically, according to the transmission dynamics model: R0 = kbD, where k is the average daily contact times of a contagious patient with susceptible population, b is the probability of successful infection per contact, and D is the average number of days that each patient can be in the state of transmission. Under the neutral assumption, the final number of infections drops to 0.5. What needs to be done is:

1) by reducing people's travel and adopting the isolation and observation system for people who are likely to be infected, the number of contacts per unit time between patients and susceptible people is reduced by 80%.

2) raise the public's vigilance to the epidemic, and patients with mild symptoms should seek medical treatment in time, so that the duration of infection can be reduced from 7 days to 4.5 days.

3) advocate wearing masks, disinfection, etc., so as to reduce the probability of single contact infection by 25%. If we can achieve these three, the number of infections can be reduced from 5.38 to about 0.5. Judging from the strict prevention and control and isolation measures taken at that time, we think it can be achieved.

In addition, with reference to the effect of the later stage of prevention and control of SARS, according to the relevant research released by WHO, R0 decreased to 0.4 after taking strict control measures in the later stage of SARS. Considering that novel coronavirus is more contagious, but this time the prevention and control measures are obviously more stringent, so it is a more objective and neutral assumption that R0 decreases to 0.5 after taking prevention and control measures.

The views put forward at that time:The sharp rise in the number of new confirmed cases is due to the improvement in the efficiency of testing and the early backlog of a large number of patients to be tested, which is expected to decline soon.The confirmed data and media reports confirmed our judgment at that time, that is, due to the lack of diagnostic ability, there was a large backlog of patients to be tested in the early stage.

As shown in figure 3, the daily number of new confirmed cases announced by the Health Commission before January 26 is significantly lower than the model forecast, while after January 31, the published value is much higher than the model forecast.

Figure 3 comparison of the actual number of newly published diagnoses with the predicted value of the model

Prediction of the scale and inflection point of the epidemic:It was basically confirmed afterwards.

As the measurement of the model parameters is more accurate, the evaluation of the effect of epidemic prevention and control measures is more objective and neutral, and the prediction of the epidemic development of the model is basically confirmed afterwards.

On the scale of the epidemic: under the neutral assumption of the model, the total number of cases predicted by the model will reach 88500, while the forecast value of the model on February 29th is 78775, while the cumulative number of confirmed cases announced by the Health Commission is 79824 (excluding Hong Kong, Macao and Taiwan). Due to changes in diagnostic capacity and diagnostic criteria, the two trends deviated.

On the inflection point of new cases: the view of the model to judge the new cases is February 11 (optimistic hypothesis) or February 17 (neutral hypothesis). Due to the lack of early diagnosis and detection capacity, resulting in a backlog of cases, and the revision of the diagnostic criteria in Hubei Province on February 12th resulted in 14000 new cases on the same day, and then the daily number of new cases dropped significantly. It is difficult to accurately determine the inflection point of real new cases, but it is a high probability between February 11 and 17, so it can be seen that the model is also more accurate in predicting the inflection point of new cases.

Fig. 4 the prediction of the epidemic situation by the model under the neutral hypothesis is compared with the actual data published by the Health Commission.

The wave of resumption of work will not bring the second peak of the epidemic.

After the release of the forecast results of the model, many readers asked whether the return to work tide would cause the epidemic to ferment again, bringing a second peak, but we don't think so. Under the measures of regional classification of epidemic prevention and control, the areas with mild epidemic situation are the first to relax the restrictions on the movement of people, even if the infection coefficient increases in the short term due to the mobility of reworkers, but because the number of people in the state of infection is very small, the impact on the overall situation of the epidemic is very limited.

At present, the number of daily new cases outside Hubei has dropped to single digits, indicating that the epidemic control in many places has achieved good results. It is very reasonable and necessary to relax the restrictions on personnel mobility and promote return to work.

Figure 5 the daily number of new cases outside Hubei has dropped to single digits

二、Take the domestic prevention and control effect as the yardstick to evaluate the prospect of overseas epidemic prevention and control.

At present, the number of confirmed cases of novel coronavirus has reached more than 50 countries, and the number of confirmed cases has exceeded 50 in 9 countries. the epidemic situation overseas is developing rapidly, and the cumulative number of confirmed cases is increasing exponentially. A number of experts have warned that novel coronavirus may lose control and become an epidemic that coexists with mankind for a long time.

Figure 6 the global epidemic is developing rapidly

So, how difficult is it to prevent and control overseas epidemics, and what is the probability of getting out of control? This paper analyzes the three factors of transmission dynamics respectively, and takes the strength and effect of domestic prevention and control measures as the yardstick to evaluate the probability of overseas epidemic out of control.

According to the transmission dynamics model: R0 = kbD, where k is the average daily contact times of a contagious patient with susceptible population, b is the probability of successful infection per contact, and D is the average number of days that each patient can be in the state of transmission.

First of all, the average number of days per patient in the state of transmission (D), by improving the vigilance of the public, those with relevant symptoms to seek medical treatment in time, shorten the number of days of patients in the susceptible population, can effectively reduce the infection coefficient. If it is consistent with the effect of domestic prevention and control, overseas countries can also reduce the average infection period from 7 days to 4.5 days, that is, a decrease of 35.7%. As novel coronavirus has a large number of mild patients and even cases with contagious ability without obvious symptoms, it may be difficult to further shorten the average infection period. )

Second, by wearing a mask, reduce the average probability of successful infection per contact (b). Due to the serious shortage of masks (China accounts for 50% of the global production of masks, which is now in short supply), and people in some countries may reject the habit of wearing masks, and some occasions are not suitable for wearing masks (such as dinners, parties, etc.), so the effect of measures such as wearing masks to reduce the success rate of infection is likely to be lower than the domestic effect.

It is assumed that it can reduce the average probability of successful single contact infection by 15% (the assumption in the domestic model is 25%, because masks are mandatory in many parts of the country, and masks are purchased from all over the world, and various enterprises temporarily change production lines to produce masks, etc., most of these measures are difficult to achieve abroad).

Finally, controlling the number of contacts (k) is perhaps the most critical. When the scale of the epidemic is very small, the k value can be controlled to a very small level by strictly screening patients' contacts and taking strict isolation measures. Once the outbreak has spread, it is difficult to track the contacts of each patient, and strict measures to comprehensively control the movement of people are needed to reduce the number of contacts.

In the domestic prediction model, it is assumed that measures such as strict restrictions on the movement of people, tracking and isolation of patients and contacts reduce the number of contacts by 80%, thus reducing the infection coefficient from 5.38 to 0.5. Taking into account the differences in the social system of overseas countries, there is a large gap between their governments' organizational capacity, mobilization capacity, speed of action, and the cooperation and patience of the people, and in controlling personnel movement and contact, the effect is expected to be significantly lower than that of China.

What is the probability of overseas outbreaks getting out of control?

For the epidemic to be brought under control, the coefficient of transmission must be reduced to less than 1. Under the previous analysis and assumptions, the average number of days per patient in the state of transmission (D) can be reduced by 35.7%, and the average probability of successful infection per contact (b) can be reduced by 15%. If the infection coefficient is reduced from 5.38 to less than 1, the average number of contacts will be reduced by more than 66%. (5.38 × (1-35.7%) × (1-15%) × (1-66%) = 1)

From a domestic point of view, when strict epidemic prevention measures are taken, the number of potential infections in Wuhan is already relatively large, and it has moved to all parts of the country during the Spring Festival transportation a year ago. The Chinese government and people have taken unprecedented stringent measures to reduce the flow of people and contacts by 80% in a short period of time and control the infection coefficient to 0.5, reducing the scale of the epidemic.

Only when the number of people in the infectious state is very small can the ordinary movement of people be restored, and the infection coefficient can be controlled through comprehensive screening, tracking and strict isolation of scattered new patients and their contacts. At present, many places outside Hubei Province meet the conditions for resuming the movement of ordinary people.

Taking the strength and effect of prevention and control in China as the yardstick, we can analyze the difficulty of epidemic control and the probability of getting out of control in overseas countries. For some countries where the scale of the epidemic is still very small, if measures such as strict screening, follow-up, and isolation of patients and their contacts and potentially risky personnel are taken as soon as possible, the number of contacts between patients and susceptible people may be more than 66% lower than usual, thus ensuring that the epidemic will not get out of control.

For countries where the epidemic has become divergent, it is difficult to fully track patients and their contacts and take isolation measures, and the epidemic prevention effect can only be achieved by comprehensively reducing the mobility of people. With reference to the strength of China's measures, it is relatively difficult for overseas countries to reduce the flow of people by 66% than usual. Moreover, a 66% reduction can only reduce the infection coefficient to just 1, which means that the scale of the epidemic will not expand, but it will not shrink, and this comprehensive restriction on the movement of people is clearly unlikely to last for a long time, and once relaxed, the epidemic will continue to worsen.

Judging from the degree of attention and the speed of action in the initial stage of the epidemic in overseas countries, the possibility of overseas epidemic spread is high, while in countries where the epidemic has reached a state of divergence, it is very difficult to prevent and control, and the probability of getting out of control is very high. It can be seen that the prospect of the overseas epidemic is not optimistic, and the probability of getting out of control is high, and speeding up the development of specific drugs and vaccines may be the top priority for the global response to novel coronavirus.

三、The impact of novel coronavirus's loss of control will be significantly greater than that of H1N1 and ordinary flu.

If novel coronavirus develops into an epidemic that coexists with mankind for a long time, how harmful will it be? Through the comparative analysis of several major outbreaks in the world in the past 20 years, we can have a more intuitive concept.

First of all, it is worth explaining that the time and region of each epidemic are different, the medical technology and epidemic prevention capacity are different at that time, and the quality of data statistics is also different, so we can only get a general conclusion through comparison.

From the mortality rate reflected by several epidemic data, novel coronavirus is significantly lower than SARS, MERS and H7N9 avian influenza, but novel coronavirus's mortality rate is significantly higher than that of H1N1 and ordinary influenza, which has become a seasonal epidemic.

Figure 7 several major global outbreaks in the past 20 years

Description: * the data of H1N1 in the United States in 2009 were modeled and estimated by CDC afterwards. At that time, there was no statistics and confirmation of the number of cases because the epidemic was out of control. According to the ex post WHO study, the mortality rate of H1N1 in Mexico was 2%, and that in other regions was about 0.1%.

* * some studies have suggested that the influenza data collected by the Chinese Centers for Disease Control and Prevention may be underestimated because laboratory tests are mainly used to diagnose influenza, but not all patients with symptoms of upper respiratory tract infection have been tested.

* * the US CDC released its weekly influenza surveillance report on February 21, estimating that there have been at least 29 million influenza cases in the United States during the 2019-2020 flu season, of which 16000 people have died of influenza-related diseases.

In the early days of novel coronavirus's epidemic, some people thought that novel coronavirus's mortality rate (outside Hubei Province) was significantly lower than that of H1N1 or even ordinary influenza, and that it was not worth paying such a high price for prevention and control. But with the development of the epidemic and the updating of data, this view is no longer tenable.

Even based on the confirmed cases outside Hubei Province, novel coronavirus's mortality rate has reached 0.84%. Considering that the existing critical cases have dropped to a relatively low level, there is little room for further increase in the mortality rate. Even considering that there are some errors in the statistics of each epidemic, the mortality rate of 0.84% is enough to show that the risk of novel coronavirus is significantly higher than that of ordinary influenza and H1N1.

Figure 8 Mortality rate of novel coronavirus confirmed cases outside Hubei

It is worth pointing out,Some previous media reports and online articles may have misquoted the mortality data of H1N1 and common influenza.For example, in 2009, the mortality rate of influenza A H1N1 was as high as 17.4%, and the death rate of influenza pneumonia was 9%, so it is considered that novel coronavirus's harm is far less than both. This is obviously misquoted or misunderstood, and it is common sense that a virus with such a high mortality rate has a pandemic every year.

In fact, when the H1N1 epidemic in the United States became uncontrollable in 2009, the CDC stopped counting and updating the number of confirmed cases, and some people may have calculated a high mortality rate using subsequent deaths and the number of confirmed cases that stopped updating. The mortality rate of influenza pneumonia is 9%. Most of it quotes Professor Zhang Wenhong, director of the infection department of Huashan Hospital, as saying, but this means that the mortality rate in cases of influenza causing pneumonia is 9%, not that of influenza. From our common sense experience, most people who get the flu will not cause pneumonia.

A subsequent study by the US Centers for Disease Control and Prevention on the H1N1 epidemic in 2009 estimated that the mortality rate of H1N1 was about 0.02%. According to WHO's research, the mortality rate of H1N1 in Mexico in 2009 was about 2%, and that in other regions was about 0.1%. According to the national report on notifiable infectious diseases released by the Chinese Centers for Disease Control and Prevention, the mortality rate of influenza in 2018 is about 0.02%.

It can be seen that if novel coronavirus becomes an epidemic out of control, its harm will be significantly greater than that of H1N1 and ordinary influenza. Of course, if scientists can develop a specific drug or treatment technology to make great progress, novel coronavirus's harm can be greatly reduced. In addition, from the point of view of biological evolution, the toxicity of the virus tends to decrease after it has spread for a long time, because it mutates in the process of virus transmission, and if the virus becomes more virulent, it will cause the host to develop faster and have more severe symptoms. as a result, early hospitalization or even death is not conducive to the continued spread of the virus, while the weakened mutation is easier to spread.

四Be optimistic about the investment opportunities of interest rate debt and gold under the influence of the epidemic

The situation of the overseas epidemic is not optimistic, and the probability of getting out of control is relatively high, which has cast a deep shadow on the already weak global economy. Georgiyeva, managing director of the International Monetary Fund (IMF), mentioned during the G20 finance ministers' meeting that under the baseline scenario of the IMF forecast, China's economic growth is expected to be 5.6% in 2020, 0.4 percentage points lower than the updated World Economic Outlook forecast in January, and the global economic growth forecast for 2020 will be 0.1 percentage point lower than at that time to 3.2%.

According to Georgiyeva, the baseline scenario assumes that "based on the implementation of the announced policy measures, China's economy can return to normal in the second quarter." As a result, the impact of the epidemic on the global economy is still relatively small and short-lived. "

It can be seen that under the assumption that China's economy can return to normal in the second quarter, the global economic growth rate will be reduced by 0.1 percentage point, which only takes into account the impact of the epidemic in China in the first quarter and does not take into account overseas epidemics. If the overseas epidemic gets out of control and spreads on a large scale, considering the high rate of severe illness and mortality of novel coronavirus, it will put tremendous pressure on the global health care system, and the risk of infection and medical costs will reduce personnel mobility and consumption propensity, increase logistics costs and international trade costs, and have many adverse effects on the global economy.

Figure 9 weak growth in the world's major economies

Considering that the overseas epidemic situation is likely to worsen, which will have many adverse effects on the global economy, governments may adopt looser monetary policy in response, interest rates are expected to fall further, and are bullish on interest rate debt and gold.

Chart 10 downward interest rates are good for gold prices

Risk Tips:The epidemic spread and the economy was in the doldrums.