[PYTHON] Day 71 I tried to predict how long this self-restraint will continue with the SIR model
I calculated the SIR model.
How long will the new corona epidemic continue? Yesterday's NHK Special "New Coronavirus Border Offense and Defense-Report from the Frontline of Prevention of Infection Spread-" I calculated it with reference to.
What is SIR model?
An equation used to calculate epidemics-convergence of infectious diseases.
Implement the SIR model in Python
The code implemented in Python was on scipython.com, so I used it.
SIR.py
import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt
# Total population, N.
N = 1000
# Initial number of infected and recovered individuals, I0 and R0.
I0, R0 = 1, 0
# Everyone else, S0, is susceptible to infection initially.
S0 = N - I0 - R0
# Contact rate, beta, and mean recovery rate, gamma, (in 1/days).
beta, gamma = 0.2, 1./10
# A grid of time points (in days)
t = np.linspace(0, 160, 160)
# The SIR model differential equations.
def deriv(y, t, N, beta, gamma):
S, I, R = y
dSdt = -beta * S * I / N
dIdt = beta * S * I / N - gamma * I
dRdt = gamma * I
return dSdt, dIdt, dRdt
# Initial conditions vector
y0 = S0, I0, R0
# Integrate the SIR equations over the time grid, t.
ret = odeint(deriv, y0, t, args=(N, beta, gamma))
S, I, R = ret.T
# Plot the data on three separate curves for S(t), I(t) and R(t)
fig = plt.figure(facecolor='w')
ax = fig.add_subplot(111, axis_bgcolor='#dddddd', axisbelow=True)
ax.plot(t, S/1000, 'b', alpha=0.5, lw=2, label='Susceptible')
ax.plot(t, I/1000, 'r', alpha=0.5, lw=2, label='Infected')
ax.plot(t, R/1000, 'g', alpha=0.5, lw=2, label='Recovered with immunity')
ax.set_xlabel('Time /days')
ax.set_ylabel('Number (1000s)')
ax.set_ylim(0,1.2)
ax.yaxis.set_tick_params(length=0)
ax.xaxis.set_tick_params(length=0)
ax.grid(b=True, which='major', c='w', lw=2, ls='-')
legend = ax.legend()
legend.get_frame().set_alpha(0.5)
for spine in ('top', 'right', 'bottom', 'left'):
ax.spines[spine].set_visible(False)
plt.show()
In case of influenza
First, let's take a look at the influenza that was set as an example.
Influenza (no immunity)
N =1000 #The population of 1000 is per school, company, neighborhood association?
I0 =1 #Infected person. At first one person.
R0 =0 #A person who has recovered and acquired immunity. 0 people at first
S0 =N - I0 - R0 #People who are not immune and are susceptible to infection. First N-I0-R0 people
beta =0.2 #Number of people infected per day
gamma =1./10 #Recovery rate
t =160 #period(Days)
One infected person infects 0.2 people a day. The infection period is 10 days. Once you recover and gain immunity, you will not be infected after this contact. When the immunity is more than half, it will converge.
From one carrier to the peak, 67 days, 15.3%, 153 people were infected and converged. It's like this when the class is closed due to the flu.
Influenza (20% immunity)
Consider the case of getting immunized by vaccination before the flu season. The first is when an influenza epidemic occurs where 20% of people have acquired immunity.
# Initial number of infected and recovered individuals, I0 and R0.
#I0, R0 = 1, 0
I0, R0 = 1, (N*0.2)
Only 20% of people have immunity, and the epidemic has been suppressed considerably. The vaccine is amazing.
Influenza (50% immunity)
The Influenza vaccine regular vaccination rate in 2019 was 50%.
# Initial number of infected and recovered individuals, I0 and R0.
#I0, R0 = 1, 0
I0, R0 = 1, (N*0.5)
It is completely suppressed. It's safe if this happens.
For COVID-19
Consider the case of the new corona. Assuming a city of 10 million people such as Tokyo and Wuhan, the infection period was set to 3 weeks (21 days). Other properties are the same as influenza.
COVID-19 (no immunity)
N =10000000 #Population 10 million(Assuming Tokyo and Wuhan)|
I0 =1 #Infected person. At first one person.
R0 =0 #A person who has recovered and acquired immunity. 0 people at first
S0 =N - I0 - R0 #People who are not immune and are susceptible to infection. First N-I0-R0 people
beta =0.2 #Number of people infected per day
gamma =1./21 #Reciprocal of the number of days required for recovery
t =160 #period(Days)
With only 21 days of infection, the peak number of infected people was 42%, or 4.2 million, and the virus has evolved into a vicious virus. Of these, 20% develop and 1% die ... 840,000 people will be affected, 42,000 will die, and it will be resolved in 228 days.
It's hell.
After seeing this graph, it went down for a few days.
However, when I saw this tweet, I thought that there might be hope.
Impact survey results ... In Heinsberg County, where the first outbreak of the new corona occurred in Germany, an immunological survey was conducted on about 500 people, and it was said that about 15% of the people had been infected. The number of infected people per 100,000 population in Heinsberg's PCR test was 604.4, and the known sensitivity rate was only 0.6%. https://twitter.com/R3000C/status/1248594913589002240
COVID-19 (immunity 15%)
In Japan today, 15% of people are infected. 89 days until 15% of people become infected.
Lock down on the 89th day to stop the epidemic.
Suppose that after one month everyone recovers and 15% have immunity. Release the lockdown. The epidemic is rekindling, but ...
The curve of the second wave was loosened by 15% immunity.
Just before the peak again, we will lock down with an infection rate of 15%. This time it was the 119th day.
After a month, everyone recovers and gains immunity, with a total of 30% having immunity.
COVID-19 (30% immunity)
The third wave peaks in 178 days. The infection rate is up to 20%. It took 149 days to reach an infection rate of 15%.
COVID-19 (immunity 45%)
The fourth wave has a peak of 252 days and an infection rate of up to 11%.
If you come to this point, you will be able to overcome it with loose self-restraint.
How long will this self-restraint last?
15% infection → lockdown → recovery → release in 3 sets (89 days + 30 days) + (119 days + 30 days) + (149 days + 30 days) = 447 days
It will be necessary to devise a way to survive for 447 days, but the number of victims will be small.
If it is a strategy to infect the economy while turning the economy, 99% of the lives will not be different and it will take 228 days. Some people may not be able to withstand the temptation of the devil.
Wuhan City lifted the blockade on April 7. Even if the second wave comes, it should not be as large as this time. I am concerned about the immunity acquisition rate. Thorough management can help keep the epidemic down. In that case, Wuhan City will be the first city in the world to recover, and will SF be the future?
And the vaccine. With this, the situation will be overturned at once. Hand wash, gargle, social distance. The curve is suppressed sharply. Then inspection. If half of the population can get immunity, it can be completely suppressed.
It's going to be a long battle.
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