前言
前几天微博的一个热搜主题是**“计算机仿真程序告诉你为什么现在还没到出门的时候！！！”**，该视频用模拟的疫情数据告诉大家“不要随便出门（宅在家）”对战胜疫情很重要，生动形象，广受好评。
所用的程序叫VirusBroadcast，源码已经公开，是用Java写的。鉴于画图是R语言的优势，所以笔者在读过源码后，写了一个VirusBroadcast程序的R语言版本，暂且叫做RVirusBroadcast。与VirusBroadcast相比，RVirusBroadcast所用的模型和逻辑大体不变，只是在少许细节上做了修改。
（为了防止上面的超链接被过滤掉而打不开，文末也放上了明文链接）
效果展示
下面两段视频是RVirusBroadcast用模拟的数据展示的效果，由于笔者的电脑性能实在一般，所以暂时只模拟了30天的数据。请再次注意下面两段视频的数据是模拟生成的，纯属虚构，不具有现实意义，仅供电脑模拟实验所用。
其他条件不变，当人们随意移动时，病毒传播迅速，疫情很难控制
其他条件不变，当人们控制自己的移动时，病毒传播缓慢，疫情逐渐得到控制
小结
诚如VirusBroadcast的作者所说，现在的模型是一个很简单的模型，所用的数据也是模拟生成的，还需优化改进。朋友们如果有兴趣，可以自行查阅复制下文中的R代码，自由修改。
参考
[1] “计算机仿真程序告诉你为什么现在还没到出门的时候” 原视频地址：
https://www.bilibili.com/video/av86478875?spm_id_from=333.788.b_765f64657363.1
附录：RVirusBroadcast代码
###name:RVirusBroadcast
###author:hxj7(hxj5hxj5@126.com)
###version:202002010
###note:本程序是"VirusBroadcast (in Java)"的R版本
### VirusBroadcast (in Java) 项目链接：
### https://github.com/KikiLetGo/VirusBroadcast/tree/master/src
library(tibble)
library(dplyr)
########## 模拟参数 ##########
ORIGINAL_COUNT <- 50 # 初始感染数量
BROAD_RATE <- 0.8 # 传播率
SHADOW_TIME <- 140 # 潜伏时间，14天为140
HOSPITAL_RECEIVE_TIME <- 10 # 医院收治响应时间
BED_COUNT <- 1000 # 医院床位
MOVE_WISH_MU <- -0.99 # 流动意向平均值，建议调整范围：[-0.99,0.99];
# -0.99 人群流动最慢速率，甚至完全控制疫情传播;
# 0.99为人群流动最快速率, 可导致全城感染
CITY_PERSON_SIZE <- 5000 # 城市总人口数量
FATALITY_RATE <- 0.02 # 病死率，根据2月6日数据估算（病死数/确诊数）为0.02
SHADOW_TIME_SIGMA <- 25 # 潜伏时间方差
CURED_TIME <- 50 # 治愈时间均值，从入院开始计时
CURED_SIGMA <- 10 # 治愈时间标准差
DIE_TIME <- 300 # 死亡时间均值，30天，从发病（确诊）时开始计时
DIE_SIGMA <- 50 # 死亡时间标准差
CITY_WIDTH <- 700 # 城市大小即窗口边界，限制不允许出城
CITY_HEIGHT <- 800
MAX_TRY <- 300 # 最大模拟次数，300代表30天
########## 生成人群点，用不同颜色代表不同健康状态。 ##########
# 用正态分布刻画人群点的分布
CITY_CENTERX <- 400 # x轴的mu值
CITY_CENTERY <- 400
PERSON_DIST_X_SIGMA <- 100 # x轴的sigma值
PERSON_DIST_Y_SIGMA <- 100
# 市民状态应该需要细分，虽然有的状态暂未纳入模拟，但是细分状态应该保留
STATE_NORMAL <- 0 # 正常人，未感染的健康人
STATE_SUSPECTED <- STATE_NORMAL + 1 # 有暴露感染风险
STATE_SHADOW <- STATE_SUSPECTED + 1 # 潜伏期
STATE_CONFIRMED <- STATE_SHADOW + 1 # 发病且已确诊为感染病人
STATE_FREEZE <- STATE_CONFIRMED + 1 # 隔离治疗，禁止位移
STATE_DEATH <- STATE_FREEZE + 1 # 病死者
STATE_CURED <- STATE_DEATH + 1 # 治愈数量用于计算治愈出院后归还床位数量，该状态是否存续待定
worldtime <- 0
NTRY_PER_DAY <- 10 # 一天模拟几次
getday <- function(t) (t - 1) %/% NTRY_PER_DAY + 1
# 生成人群数据
format_coord <- function(coord, boundary) {
if (coord < 0) return(runif(1, 0, 10))
else if (coord > boundary) return(runif(1, boundary - 10, boundary))
else return(coord)
}
set.seed(123)
people <- tibble(
id = 1:CITY_PERSON_SIZE,
x = sapply(rnorm(CITY_PERSON_SIZE, CITY_CENTERX, PERSON_DIST_X_SIGMA),
format_coord, boundary = CITY_WIDTH), # (x, y) 为人群点坐标
y = sapply(rnorm(CITY_PERSON_SIZE, CITY_CENTERY, PERSON_DIST_Y_SIGMA),
format_coord, boundary = CITY_HEIGHT),
state = STATE_NORMAL, # 健康状态
infected_time = 0, # 感染时刻
confirmed_time = 0, # 确诊时刻
freeze_time = 0, # 隔离时刻
cured_moment = 0, # 痊愈时刻，为0代表不确定
die_moment = 0 # 死亡时刻，为0代表未确定，-1代表不会病死
) %>%
mutate(tx = rnorm(CITY_PERSON_SIZE, x, PERSON_DIST_X_SIGMA), # target x
ty = rnorm(CITY_PERSON_SIZE, y, PERSON_DIST_Y_SIGMA),
has_target = T, is_arrived = F)
# 随机选择初始感染者
peop_id <- sample(people$id, ORIGINAL_COUNT)
people$state[peop_id] <- STATE_SHADOW
people$infected_time[peop_id] <- worldtime
people$confirmed_time[peop_id] <- worldtime +
max(rnorm(length(peop_id), SHADOW_TIME / 2, SHADOW_TIME_SIGMA), 0)
########## 生成床位点 ##########
HOSPITAL_X <- 720 # 第一张床位的x坐标
HOSPITAL_Y <- 80 # 第一张床位的y坐标
NBED_PER_COLUMN <- 100 # 医院每一列有多少张床位
BED_ROW_SPACE <- 6 # 一行中床位的间距
BED_COLUMN_SPACE <- 6 # 一列中床位的间距
bed_ncolumn <- ceiling(BED_COUNT / NBED_PER_COLUMN)
hosp_beds <- tibble(id = 1, x = 0, y = 0, is_empty = T, state = STATE_NORMAL) %>%
slice(-1)
if (BED_COUNT > 0) {
hosp_beds <- tibble(
id = 1:BED_COUNT,
x = HOSPITAL_X + rep(((1:bed_ncolumn) - 1) * BED_ROW_SPACE,
each = NBED_PER_COLUMN)[1:BED_COUNT],
y = HOSPITAL_Y + 10 - BED_COLUMN_SPACE +
rep((1:NBED_PER_COLUMN) * BED_COLUMN_SPACE, bed_ncolumn)[1:BED_COUNT],
is_empty = T,
person_id = 0 # 占用床位的患者的序号，床位为空时为0
)
}
########## 准备画图的数据 ##########
npeople_total <- CITY_PERSON_SIZE
npeople_shadow <- ORIGINAL_COUNT
npeople_confirmed <- npeople_freeze <- npeople_cured <- npeople_death <- 0
nbed_need <- 0
########## 画出初始数据 ##########
# 设置画图参数
person_color <- data.frame( # 不同健康状态的颜色不同
label = c("健康", "潜伏", "确诊", "隔离", "治愈", "死亡"),
state = c(STATE_NORMAL, STATE_SHADOW, STATE_CONFIRMED, STATE_FREEZE,
STATE_CURED, STATE_DEATH),
color = c(
"lightgreen", # 健康
"#EEEE00", # 潜伏期
"red", # 确诊
"#FFC0CB", # 隔离
"green", # 治愈
"black" # 死亡
), stringsAsFactors = F
)
bed_color <- data.frame(
is_empty = c(T, F), color = c("#F8F8FF", "#FFC0CB"), stringsAsFactors = F
)
x11(width = 5, height = 7, xpos = 0, ypos = 0, title = "人群变化模拟")
window_hist <- dev.cur()
x11(width = 7, height = 7, xpos = 460, ypos = 0, title = "疫情传播模拟")
window_scatter <- dev.cur()
max_plot_x <- ifelse(BED_COUNT > 0, max(hosp_beds$x), CITY_WIDTH) + 10
# 疫情传播模拟散点图
dev.set(window_scatter)
plot(x = people$x, y = people$y, cex = .8, pch = 20, xlab = NA, ylab = NA,
xlim = c(5, max_plot_x), xaxt = "n", yaxt = "n", bty = "n", main = "疫情传播模拟",
sub = paste0("世界时间第 ", getday(worldtime), " 天"),
col = (people %>% left_join(person_color, by = "state") %>%
select(color))$color)
points(x = hosp_beds$x, y = hosp_beds$y, cex = .8, pch = 20,
col = (hosp_beds %>% left_join(bed_color, by = "is_empty") %>%
select(color))$color)
rect(HOSPITAL_X - BED_ROW_SPACE / 2, HOSPITAL_Y + 10 - BED_COLUMN_SPACE,
max(hosp_beds$x) + BED_ROW_SPACE / 2, max(hosp_beds$y + BED_COLUMN_SPACE))
legend(x = 150, y = -30, legend = person_color$label, col = person_color$color,
pch = 20, horiz = T, bty = "n", xpd = T)
# 人群变化模拟条形图
dev.set(window_hist)
bp_data <- c(npeople_death, npeople_cured, nbed_need, npeople_freeze,
npeople_confirmed, npeople_shadow)
bp_color <- c("black", "green", "#FFE4E1", "#FFC0CB", "red", "#EEEE00")
bp_labels <- c("死亡", "治愈", "不足\n床位", "隔离", "累计\n确诊", "潜伏")
bp <- barplot(bp_data, horiz = T, border = NA, col = bp_color,
xlim = c(0, CITY_PERSON_SIZE * 1), main = "人群变化模拟",
sub = paste0("世界时间第 ", getday(worldtime), " 天"))
abline(v = BED_COUNT, col = "gray", lty = 3)
abline(v = CITY_PERSON_SIZE, col = "gray", lty = 1)
text(x = -350, y = bp, labels = bp_labels, xpd = T)
text(x = bp_data + CITY_PERSON_SIZE / 15, y = bp, xpd = T,
labels = ifelse(bp_data > 0, bp_data, ""))
legend(x = 300, y = -.6, legend = c("总床位数", "城市总人口"), col = "gray",
lty = c(3, 1), bty = "n", horiz = T, xpd = T)
Sys.sleep(5) # 手动调整窗口大小
########## 更新人群数据 ##########
# 市民流动意愿以及移动位置参数174 MOVE_WISH_SIGMA <- 1
MOVE_DIST_SIGMA <- 50
SAFE_DIST <- 2 # 安全距离
worldtime <- worldtime + 1
get_min_dist <- function(person, peop) { # 一个人和一群人之间的最小距离
min(sqrt((person["x"] - peop$x) ^ 2 + (person["y"] - peop$y) ^ 2))
}
for (i in 1:MAX_TRY) {
# 如果已经隔离或者死亡了，就不需要处理了
#
# 处理已经确诊的感染者（即患者）
peop_id <- people$id[people$state == STATE_CONFIRMED &
people$die_moment == 0]
if ((npeop <- length(peop_id)) > 0) {
people$die_moment[peop_id] <- ifelse(
runif(npeop, 0, 1) < FATALITY_RATE, # 用均匀分布模拟确诊患者是否会死亡
people$confirmed_time + max(rnorm(npeop, DIE_TIME, DIE_SIGMA), 0), # 发病后确定死亡时刻
-1 # 逃过了死神的魔爪
)
}
# 如果患者已经确诊，且（世界时刻-确诊时刻）大于医院响应时间，
# 即医院准备好病床了，可以抬走了
peop_id <- people$id[people$state == STATE_CONFIRMED &
worldtime - people$confirmed_time >= HOSPITAL_RECEIVE_TIME]
if ((npeop <- length(peop_id)) > 0) {
if ((nbed_empty <- sum(hosp_beds$is_empty)) > 0) { # 有空余床位
nbed_use <- min(npeop, nbed_empty)
bed_id <- hosp_beds$id[hosp_beds$is_empty][1:nbed_use]
# 更新患者信息
peop_id2 <- sample(peop_id, nbed_use) # 这里是随机选择，理论上应该按症状轻重
people$x[peop_id2] <- hosp_beds$x[bed_id]
people$y[peop_id2] <- hosp_beds$y[bed_id]
people$state[peop_id2] <- STATE_FREEZE
people$freeze_time[peop_id2] <- worldtime
# 更新床位信息
hosp_beds$is_empty[bed_id] <- F
hosp_beds$person_id[bed_id] <- peop_id2
}
}
# TODO 需要确定一个变量用于治愈时长。
# 为了说明问题，暂时用一个正态分布模拟治愈时长并且假定治愈的人不会再被感染
peop_id <- people$id[people$state == STATE_FREEZE &
people$cured_moment == 0]
if ((npeop <- length(peop_id)) > 0) { # 正态分布模拟治愈时间
people$cured_moment[peop_id] <- people$freeze_time[peop_id] +
max(rnorm(npeop, CURED_TIME, CURED_SIGMA), 0)
}
peop_id <- people$id[people$state == STATE_FREEZE & people$cured_moment > 0 &
worldtime >= people$cured_moment]
if ((npeop <- length(peop_id)) > 0) { # 归还床位
people$state[peop_id] <- STATE_CURED
hosp_beds$is_empty[! hosp_beds$is_empty & hosp_beds$person_id %in% peop_id] <- T
people$x[peop_id] <- sapply(rnorm(npeop, CITY_CENTERX, PERSON_DIST_X_SIGMA),
format_coord, boundary = CITY_WIDTH) # (x, y) 为人群点坐标
people$y[peop_id] <- sapply(rnorm(npeop, CITY_CENTERY, PERSON_DIST_Y_SIGMA),
format_coord, boundary = CITY_HEIGHT)
people$tx[peop_id] <- rnorm(npeop, people$x[peop_id], PERSON_DIST_X_SIGMA)
people$ty[peop_id] <- rnorm(npeop, people$y[peop_id], PERSON_DIST_Y_SIGMA)
people$has_target[peop_id] <- T
people$is_arrived[peop_id] <- F
}
# 处理病死者
peop_id <- people$id[people$state %in% c(STATE_CONFIRMED, STATE_FREEZE) &
worldtime >= people$die_moment & people$die_moment > 0]
if (length(peop_id) > 0) { # 归还床位
people$state[peop_id] <- STATE_DEATH
hosp_beds$is_empty[! hosp_beds$is_empty & hosp_beds$person_id %in% peop_id] <- T
}
# 处理发病的潜伏期感染者
peop_id <- people$id[people$state == STATE_SHADOW &
worldtime >= people$confirmed_time]
if ((npeop <- length(peop_id)) > 0) {
people$state[peop_id] <- STATE_CONFIRMED # 潜伏者发病
}
# 处理未隔离者的移动问题
peop_id <- people$id[
! people$state %in% c(STATE_FREEZE, STATE_DEATH) &
rnorm(CITY_PERSON_SIZE, MOVE_WISH_MU, MOVE_WISH_SIGMA) > 0] # 流动意愿
if ((npeop <- length(peop_id)) > 0) { # 正态分布模拟要移动到的目标点
pp_id <- peop_id[! people$has_target[peop_id] | people$is_arrived[peop_id]]
if ((npp <- length(pp_id)) > 0) {
people$tx[pp_id] <- rnorm(npp, people$tx[pp_id], PERSON_DIST_X_SIGMA)
people$ty[pp_id] <- rnorm(npp, people$ty[pp_id], PERSON_DIST_Y_SIGMA)
people$has_target[pp_id] <- T
people$is_arrived[pp_id] <- F
}
# 计算运动位移262 dx <- people$tx[peop_id] - people$x[peop_id]
dy <- people$ty[peop_id] - people$y[peop_id]
move_dist <- sqrt(dx ^ 2 + dy ^ 2)
people$is_arrived[peop_id][move_dist < 1] <- T # 判断是否到达目标点266 pp_id <- peop_id[move_dist >= 1]
if ((npp <- length(pp_id)) > 0) {
udx <- sign(dx[move_dist >= 1]) # x轴运动方向269 udy <- sign(dy[move_dist >= 1])
# 是否到了边界
pid_x <- (1:npp)[people$x[pp_id] + udx < 0 | people$x[pp_id] + udx > CITY_WIDTH]
pid_y <- (1:npp)[people$y[pp_id] + udy < 0 | people$y[pp_id] + udy > CITY_HEIGHT]
# 更新到了边界的点的信息
people$x[pp_id[pid_x]] <- people$x[pp_id[pid_x]] - udx[pid_x]
people$y[pp_id[pid_y]] <- people$y[pp_id[pid_y]] - udy[pid_y]
people$has_target[unique(c(pp_id[pid_x], pp_id[pid_y]))] <- F
# 更新没有到边界的点的信息278 people$x[pp_id[! pp_id %in% pid_x]] <- people$x[pp_id[! pp_id %in% pid_x]] +
udx[! pp_id %in% pid_x]
people$y[pp_id[! pp_id %in% pid_y]] <- people$y[pp_id[! pp_id %in% pid_y]] +
udy[! pp_id %in% pid_y]
}
}
# 处理健康人被感染的问题
# 通过一个随机幸运值和安全距离决定感染其他人286 normal_peop_id <- people$id[people$state == STATE_NORMAL]
other_peop_id <- people$id[! people$state %in% c(STATE_NORMAL, STATE_CURED)]
if (length(normal_peop_id) > 0) {
normal_other_dist <- apply(people[normal_peop_id, ], 1, get_min_dist,
peop = people[other_peop_id, ])
normal2other_id <- normal_peop_id[normal_other_dist < SAFE_DIST &
runif(length(normal_peop_id), 0, 1) < BROAD_RATE]
if ((n2other <- length(normal2other_id)) > 0) {
people$state[normal2other_id] <- STATE_SHADOW
people$infected_time[normal2other_id] <- worldtime
people$confirmed_time[normal2other_id] <- worldtime +
max(rnorm(n2other, SHADOW_TIME / 2, SHADOW_TIME_SIGMA), 0)
}
}
# 画出更新后的数据
npeople_confirmed <- sum(people$state >= STATE_CONFIRMED)
npeople_death <- sum(people$state == STATE_DEATH)
npeople_freeze <- sum(people$state == STATE_FREEZE)
npeople_shadow <- sum(people$state == STATE_SHADOW)
npeople_cured <- sum(people$state == STATE_CURED)
nbed_need <- npeople_confirmed - npeople_cured - npeople_death - BED_COUNT
nbed_need <- ifelse(nbed_need > 0, nbed_need, 0) # 不足病床数
# 疫情传播模拟散点图
dev.set(window_scatter)
plot(x = people$x, y = people$y, cex = .8, pch = 20, xlab = NA, ylab = NA,
xlim = c(5, max_plot_x), xaxt = "n", yaxt = "n", bty = "n", main = "疫情传播模拟",
sub = paste0("世界时间第 ", getday(worldtime), " 天"),
col = (people %>% left_join(person_color, by = "state") %>%
select(color))$color)
points(x = hosp_beds$x, y = hosp_beds$y, cex = .8, pch = 20,
col = (hosp_beds %>% left_join(bed_color, by = "is_empty") %>%
select(color))$color)
rect(HOSPITAL_X - BED_ROW_SPACE / 2, HOSPITAL_Y + 10 - BED_COLUMN_SPACE,
max(hosp_beds$x) + BED_ROW_SPACE / 2, max(hosp_beds$y + BED_COLUMN_SPACE))
legend(x = 150, y = -30, legend = person_color$label, col = person_color$color,
pch = 20, horiz = T, bty = "n", xpd = T)
# 人群变化模拟条形图
dev.set(window_hist)
bp_data <- c(npeople_death, npeople_cured, nbed_need, npeople_freeze,
npeople_confirmed, npeople_shadow)
bp <- barplot(bp_data, horiz = T, border = NA, col = bp_color,
xlim = c(0, CITY_PERSON_SIZE * 1), main = "人群变化模拟",
sub = paste0("世界时间第 ", getday(worldtime), " 天"))
abline(v = BED_COUNT, col = "gray", lty = 3)
abline(v = CITY_PERSON_SIZE, col = "gray", lty = 1)
text(x = -350, y = bp, labels = bp_labels, xpd = T)
text(x = bp_data + CITY_PERSON_SIZE / 15, y = bp, xpd = T,
labels = ifelse(bp_data > 0, bp_data, ""))
legend(x = 300, y = -.6, legend = c("总床位数", "城市总人口"), col = "gray",
lty = c(3, 1), bty = "n", horiz = T, xpd = T)
# 更新世界时间
worldtime <- worldtime + 1
}
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