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([email protected]) ###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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