Analysis of the high risk of Beijing during the SARS
During the SARS period, there is no complete pass so far, but it has been exposed to the end of the end, and the number of people daily infected is also greatly reduced. Recalling that the number of people in more than 100 patients has spread in the crowd, and people are in the vicinity, as if SARS is in the vicinity, it will be infected.
Now the climax has passed, I tried to use the knowledge you have learned, calculate how much in Beijing, may be infected, this number is that after the government has adopted a series of measures, it is still possible to infect SARS. Due to human intervention, this number is no longer the sum of Beijing population (2000 census, Beijing 11.075 million, in 2003, it is estimated to be 12 million here), but should be small than the total.
Model hypothesis
If you do health, the proportion of patients in the total population is S (t), i (t), then s (t) i (t) = 1 (1)
The patient's day contact rate is
After healthy people have been exposed to the patient; the cure rate is that the average number of contact people in each patient is = /. The total number of Beijing is n = 12000000.
It is the high risk of high-risk, which means that Beijing is still infecting SARS after adopting isolation measures.
Model composition
The model assumption, you can have a daily increase rate formula:
(2)
Rethink (1):
(3)
Solution:
Number of health:
(4)
Dip from 3, 4, DT:
(5)
Solution: (6)
Let S = S-> Endless, and since the initial value I0 is generally small, it can be omitted, so it is obtained:
(7)
This time, I0 and IW are 877 / g and 2600 / g (estimated), respectively, and S = 1-i can derive the value of S0 and SW, which can be obtained.
According to the public information of the Ministry of Health, the cure rate of SARS is 75%, ie = 0.75, depending on = /.
Then you can solve (3).
According to the data from Beijing 4.23 --- 6.6, you can draw a total map of Beijing patients, compared to i (t), can generally estimate G
Model solve
Beijing 4.23-6.6 patient accumulated picture: (Excel made)
From the starting point (4.23) to the slow (5.13) of 20 days
Solve with Mathematica:
When G is 7000:
You can get an I-T profile:
This diagram describes the curve from T = 25 to 45, and from the actual curve from 4.23 to 5.13.
Therefore, the number of high-risk people in Beijing is 7,000.
Model analysis
It can be seen that although people think that SARS is very easy to infect, after a series of measures of the Beijing Municipal Government, the number of infections may be greatly reduced, only less than 10,000 people, this is more than 12 million people in Beijing, which can be said to be Compare less. Therefore, after this natural disaster coming, there is no need to do unnecessary panic, as long as the measures are proper, the hazard can be reduced to the lowest level. In addition, it can be speculated that the date of Beijing SARS is 25 days before April 23, that is, in early Acember, if it attaches great importance to SARS, it can quickly curb the momentum of the trend.
Reference:
1. Daily epidemic released by the Ministry of Health;
2. Jiang Qiyuan "Mathematical Model"
