seir模型数学建模python_R示例：SEIR模型代码
说明：本例对常见的SEIR模型作了改变，由于DDE模型始终存在缺陷，故仍采用ODE建模。
实现环境：R 3.6.3+deSolve+ggplot2。
#-------------------------------------
#基于微分方程组建模
#dS/dt=-b_1*S*I/N-b_2*S*E/N
#dE/dt=b_1*S*I/N+b_2*S*E/N-k*E
#dI/dt=k*E-z*I
#dH/dt=z*I-d*H-m*H
#dR/dt=m*H
#dD/dt=d*H
#变量
#S易感人群
#E暴露潜伏
#I发病
#H入院
#R治愈
#D病故
#参数
#b_1,b_2接触感染概率
#k潜伏到发病的转化率
#z发病入院比例
#m治愈率
#d感染期死亡率
#--------------------------------------
library(deSolve)
library(ggplot2)
#模型
seir
with(as.list(c(state, pars)), {
dS
dE
dI
dH
dR
dD
dN
list(c(dS, dE, dI, dH, dR, dD, dN))
})
}
#参数
N
I_0
H_0
E_0
R_0
D_0
S_0
init
S = S_0,
E = E_0,
I = I_0,
H = H_0,
R = R_0,
D = D_0,
N = N
)
time
pars
b_1 = 0.16,
#发病者接触感染概率0.1575
b_2 = 0.79,
#潜伏期接触感染概率0.7875
k = 0.2,
#潜伏到发病的转化率
z = 0.25,
#发病入院比例
m = 0.04,
#治愈率
d = 0.0025
#感染期死亡率
)
#触发事件,S降低,10t至100%,20t至100%,90t维持控制
eventdat
var = c("S", "S", "S"),
time = c(10, 20, 90),
value = c(1, 1, 1),
method = c("mult", "mult", "mult")
)
#微分计算
res.seir
as.data.frame(lsoda(
y = init,
times = time,
func = seir,
parms = pars,
events = list(data = eventdat)
))
#可视化
ggplot(res.seir) +
geom_line(aes(x = time, y = N, col = "人口"), size = 1) +
geom_line(aes(x = time, y = S, col = "易感"), size = 1) +
geom_line(aes(x = time, y = E, col = "潜伏"), size = 2) +
geom_line(aes(x = time, y = I, col = "发病"), size = 2) +
geom_line(aes(x = time, y = H, col = "入院"), size = 2) +
geom_line(aes(x = time, y = R, col = "治愈"), size = 2) +
geom_line(aes(x = time, y = D, col = "病故"), size = 2) +
scale_color_manual(
name = "图例",
values = c(
"人口" = "purple",
"易感" = "blue",
"潜伏" = "orange",
"发病" = "red",
"入院" = "darkred",
"治愈" = "green",
"病故" = "black"
)
) +
scale_y_continuous("") +
labs(caption = "Note:All Hypothesis Reflecting No Reality")
结果：
2020-7-15 12:37:40 上传
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