R语言模拟疫情传播图RVirusBroadcast展示疫情数据

目录

• 前言
• 效果展示
• 小结
• 参考
• 附录：RVirusBroadcast代码

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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