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