In this article, 2020 Year 3 Month twenty three Date data is used.
Data source: European Center for Disease Prevention and Control ( ECDC )
The momentum of the new coronavirus is raging more than expected, and it is reported that the number of infected people is increasing rapidly in the United States and Europe. In Japan, the number of infected people is increasing day by day, but I don't think there is much sense that it is increasing rapidly like the United States and Europe.
In this article, we will apply a model to the data on the number of infected people in each country and examine the degree of increase in the number of infected people. JMP Let's use the "reliability growth" platform of reliability? Doesn't it have much to do with infection data? You may think that, but I learned a lot when I used it.
What is the “reliability growth” platform?
JMP Then in the menu bar [ analysis ] > [ reliability / Survival analysis ] As you follow [ reliability growth ] menu can be found. probably JMP Even for core users of , this feature may be unfamiliar.
"Reliability Growth" is a platform that mainly analyzes failures of things and systems. Based on the Poisson process based on the data on how many failures (events) have occurred over time Crow-AMSAA fit the model. By fitting, it is possible to see whether the number of failures is increasing or decreasing, and it is possible to obtain the mean time to failure (average interval between failures), which is an indicator of system durability. .
Crow-AMSAA The model follows the exponentiation. Considering the example of the new coronavirus this time, the image is that the number of infected people increases with the power of time.
The actual model of infectious disease should be more complicated, and this platform is not intended to analyze the number of infected people this time, but we also consider exploratory analysis, Let's model the occurrence situation of the number of customers by this "reliability growth".
Visualization of the cumulative number of infected people
Except for China, where the number of infected people increased first, the countries with more cumulative infected people than Japan are twenty two country. including Japan twenty three Let's plot the daily cumulative number of infected people for each country in the graph builder.
The graph is divided by region, with the horizontal axis representing the date and the vertical axis representing the cumulative number of infected people on that date, but the vertical axis is on a logarithmic scale.
In light blue of Japan (upper left graph), 3 Month twenty three The cumulative number of infected people as of today is 1089 I'm a person. In Japan, infected people were found early, but compared to other countries, you can see that the number of infected people has not increased so much. The same Asian country, Iran (in pink), which first detected its first cases later than other Asian countries, now has the highest cumulative number of cases in the Asian region.
Europe (upper right graph) in many countries 3 The number of infected people has increased rapidly since the beginning of the month, and you can see that the number of infected people in the United States, Canada (lower left graph), and Brazil (lower right graph) is also increasing rapidly.
Fit the model with "reliability growth"
For the countries visualized above, using the “Reliability Growth” platform, Crow-AMSAA I try to fit the model. The data to be used depends on each country ( location ) in the day (date) infected people per (Confirmed) is entered, click the "Date Format" tab and specify the columns as follows.
Then click the red triangle button, [ Fitting the model ] > [Crow AMSAA] Choose.
The green curve is the fitted one. Visually confirming the goodness of the fit, some countries fit well, while others do not fit well. Here, including Japan Four Consider the fitting situation for one country.
* Please note that the vertical axis (cumulative number of infected people) in the graph below has a different range of values for each country.
usa
3 The number of infected people has increased sharply since January, but it can be said that the model captures this phenomenon well.
Japan
According to the data used this time, the first infected person was recorded in Japan 1 Month 15 It's day. For that reason, the number of infected people is suppressed compared to other countries. As a model, there are times when it does not fit well, but it can be considered that it is a model that generally captures the characteristics of the number of infected people.
Iran
The first recorded case of infection in Iran was 2 Month 20 It's day. from here 3 The number of infected people is increasing rapidly from month to month. 3 Month 7 Since the actual number of infected people is located above the fitted curve from the day, it shows the rapid increase in the number of infected people at that time.
Korea
You can see that this model cannot explain the infection situation in South Korea at all. 2 increased sharply from the second half of the month, 3 It does not explain the slowdown from the beginning of the month.
When the trend of infection frequency changes?
In the example above, Iran and South Korea did not fit well. One possible reason for this is that the trend in infection frequency has changed since a certain period of time.
In "reliability growth," [ Division Weibull-NHPP change point detection ] There is a fitting method that detects the point in time when the trend changes from the data (change point), and has separate shape parameters (β) before and after the change point Crow-AMSSA You can fit the model. For Iran and South Korea, where the model did not fit well this time, we will try to fit a model divided by this change point.
The blue curve is the Weibull-NHPP This will be the fitted line for change point detection. Also not shown here is a report of parameter estimates and change points.
Iran
the change point is 3 Month 8 It's day. for that reason 3 Month 8 A model with different shape parameters before and after the day is fitted. Visually, the fit of the model divided by this change point (blue curve) looks better. In the "model list" at the bottom of the report, there is an index showing the goodness of the fit AICc or BIC is displayed. Smaller values of these indices indicate a better fit, so even when judging by the indices, it can be seen that the models divided by change points fit better.
Korea
the change point is 3 Month 7 It's day. Even the model divided by this change point is by no means a good fit, but it is visually more visible than the first fitted model (green). AICc or BIC You can also see that the fit is better when you look at it with . The model (blue) divided by the change point is 3 Month 7 This explains to some extent the decrease in the frequency of infections since March 2019.
Consideration by intensity function
In Confidence Growth, there is an option to display a graph of the strength function for the fitted model.
“ Strength ” indicates the density of infection at that time, ” intensity function ” is a function of intensity over time. here Crow-AMSSA The time derivative of the model is the intensity function, which is the limit of the probability of infection in a very short time divided by the time interval. By looking at the graph of the intensity function, we can see whether the number of infected people has increased sharply or decreased.
Below is shown earlier Four Iran and South Korea are intensity functions for each change point fitted model.
*Please note that the range of values on the vertical axis is different in the following graphs as well.
usa
Japan
the United States 3 Month 15 It can be seen that the intensity function increases rapidly from around the day. The news also reported that the number of infected people increased sharply from around here. Japan is also on the rise, so I'm worried about the future, but the strength value itself ( Y axis values) are small compared to other countries.
Iran
Korea
Iran and South Korea change the color of the intensity function before and after the change point. Iran is 3 Month 1 The number of infected people increased sharply from day to day, which is a turning point. 3 Month 8 Although the increase has slowed down slightly since then, we can see that it is still increasing. In contrast, it can be said that the rapid increase in South Korea has been suppressed after the turning point. It is true that the number of infected people is still rising, but it is a good trend that may lead to convergence.
Trends in the number of infected people in the future
The "reliability growth" introduced this time is by no means a platform focused on future predictions. From the current data, we investigated the increasing trend of the number of infected people, the degree of increase, etc.
Currently, the number of infected people is increasing rapidly around the world, and it is pointed out that it may become a pandemic. The scale parameter β of the intensity function is 1 A smaller value indicates that the number of infected people decreases over time, so for any country, the value of β is 1 I just wish it was smaller. I will continue to collect and analyze data.
