Population density = 10% case (big city)

This is a case where there are 10 people in 100 cells. As you can see from the figure, it is an image of a big city. After a year, the group was in a bright red pandemic. Due to the logic of natural healing, the infection rate does not reach 100% and is saturated at about 90%, but this is not expected to converge.

Case of population density = 4% (60% reduction in contact)

Don't you think you're refraining from doing so? **No way! ** ** This kind of thing isn't enough. The infection rate has dropped to nearly 50% after one year, but it is still far from converging. In this world, the Olympics cannot be held even if it is postponed by one year.

Case of population density = 3% (70% reduction in contact)

Is it necessary to have 70% instead of 80%? ** Yes, 70% is not good. ** ** Sure, the infection rate is fairly low, but it has been increasing, albeit slowly, for nearly a year (slightly peaking out towards the end). Although the speed of infection has been suppressed, it seems that one year is not enough to reach natural convergence.

Case of population density = 2% (80% reduction in contact)

** The number of new infections and the number of healers are almost balanced. ** ** Although the new infection rate and the cure rate were decided appropriately, the result was quite beautiful. I'm a complete amateur, but is the number of 80% reduction in contact a kind of rule of thumb in infectious diseases?

Case of population density = 1% (90% reduction in contact)

** The number of infected people became 0 in just over 200 days. ** ** I hope the real world will be like this soon ~

python code

This is a specification that draws an animation that changes in real time. When the cell value is 0, there is nobody, -1 indicates a healthy person, and +1 indicates an infected person.

import numpy as np
from numpy import random
import seaborn as sns
import matplotlib.pyplot as plt
sns.set()

# parameter
density = 0.03
prob_infect = 0.20
prob_heal = 0.02
infected_initial = 0.05

# initialize earth
earth = np.where((random.random(10000) > (1 - density)), -1, 0).reshape(100, 100)
for i in range(int(10000 * density * infected_initial)):
    earth[random.randint(0, 100), random.randint(0, 100)] = 1

time = 0
infection_ratio = np.zeros(10 ** 6) * np.nan
infection_ratio[time] = 0
plt.close()
fig, ax = plt.subplots(figsize=(12, 6), nrows=1, ncols=2)

no_end = True
while no_end:
    for (x, y) in [(x, y) for x in range(100) for y in range(100)]:
        if earth[x, y] != 0:
            # infection
            (x_min, x_max) = (max(x - 1, 0), min(x + 1, 98) + 1)
            (y_min, y_max) = (max(y - 1, 0), min(y + 1, 98) + 1)
            if np.any(earth[x_min: x_max, y_min: y_max] == 1):
                earth[x, y] = 1 if random.rand() < prob_infect else earth[x, y]
            # healing
            earth[x, y] = -1 if random.rand() < prob_heal else earth[x, y]
            # random walk around
            x_next = min(max(x + random.randint(-1, 2), 0), 99)
            y_next = min(max(y + random.randint(-1, 2), 0), 99)
            if ((x_next, y_next) != (x, y)) & (earth[x_next, y_next] == 0):
                earth[x_next, y_next] = earth[x, y]
                earth[x, y] = 0
    time += 1
    infection_ratio[time] = np.sum(np.where(earth == 1, 1, 0)) / (10000 * density) * 100
    try:
        subplot0.cla()
        subplot1.cla()
    except:
        print('no need to refresh figure')
    plt.suptitle('time: {}'.format(time))
    subplot0 = sns.heatmap(earth, vmin=-1, vmax=1, center=0, cmap='coolwarm', ax=ax[0], cbar=False)
    ax[0].axis('off')
    ax[0].set_title('density: {}%'.format(int(density * 100)))
    subplot1 = sns.lineplot(data=infection_ratio)
    ax[1].set_title('time series of infection')
    ax[1].set_xlabel('time')
    ax[1].set_ylabel('infection ratio %')
    ax[1].set_ylim([0, 100])
    ax[1].set_xlim([0, time + 10])
    plt.tight_layout()
    plt.draw()
    plt.pause(0.01)