SEIRDS model

.gitignore

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+.Rproj.user
+.Rhistory
+.RData
+.Ruserdata

Analysis/ode.R

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+seirds.f <- function(t, y, k) {
+  S <- y[1]
+  E <- y[2]
+  I_R <- y[3]
+  I_D <- y[4]
+  R <- y[5]
+  D <- y[6]
+  N <- y[7]
+
+  beta = k[1]
+  delta = k[2]
+  gamma_r = k[3]
+  gamma_d = k[4]
+  mu = k[5]
+  epsilon = k[6]
+  waning = k[7]
+
+  dS <- S - beta*(I_R+I_D)/N + waning*R
+  dE <- E + beta*S*(I_R+I_D)/N - delta*E + epsilon
+  dI_R <- I_R + delta*(1-mu)*E - gamma_r*I_R + epsilon
+  dI_D <- I_D + delta*mu*E - gamma_d*I_D + epsilon
+  dR <- R + gamma_r*I_R - waning*R
+  dD <- D + gamma_d*I_D
+  return(as.matrix(c(dS, dE, dI_R, dI_D, dR, dD, N)))
+}
+
+# a) a=0.5, b=1, S(0)=0.9, I(0)=0.1, R(0)=0
+seirds.params <- c(0.7316455696202532,    # beta
+                   0.020253164556962026,  # delta
+                   0.09113924050632911,   # gamma_r
+                   0.002531645569620253,  # gamma_d
+                   0.0034602076124567475, # mu
+                   0.0)                   #epsilon
+
+seirds.params <- c(1,    # beta
+                   1,  # delta
+                   1,   # gamma_r
+                   1,  # gamma_d
+                   1, # mu
+                   1)                   #epsilon
+
+
+S <- 62
+E <- 8
+I_R <- 288
+I_D <- 1
+R <- 36
+D <- 1
+
+N <- S+E+I_R+I_D+R+D
+S <- S/N
+E <- E/N
+I_R <- I_R/N
+I_D <- I_D/N
+R <- R/N
+D <- D/N
+
+tmin <- 0
+tmax <- 20
+
+install.packages("pracma")
+library(pracma)
+seirds.ode.sol <- ode45(f = function(t,y){seirds.f(t,y,k=seirds.params)},
+                     y = c(S, E, I_R, I_D, R, D, N),
+                     t0 = tmin, tfinal = tmax)
+# plot
+plot.seirds <- function(sol, method){
+  # - pred/prey columns melted to 1 column called "value"
+  sol.melted <- melt(data.frame(time=sol$t,
+                                S=sol$y[,1],
+                                E=sol$y[,2],
+                                I_R=sol$y[,3],
+                                I_D=sol$y[,4],
+                                R=sol$y[,5],
+                                D=sol$y[,6],),
+                     id = "time") # melt based on time
+  # New column created with variable names, called “variable”
+  colnames(sol.melted)[2] <- "Group" # used in legend
+  g <- ggplot(data = sol.melted,
+              aes(x = time, y = value, color = Group))
+  g <- g + geom_point(size=2)
+  g <- g + xlab("time") + ylab("Population")
+  g <- g + ggtitle(paste("SEIRDS Model Using", method))
+  show(g)
+}
+
+plot.seirds(seirds.ode.sol, "ODE45")

CS-7863-Sci-Stat-Final.Rproj

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+AlwaysSaveHistory: Default
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