noah/CS-7863-Sci-Stat-Proj-3
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SIR Model

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Noah L. Schrick 2023-02-15 19:02:31 -06:00
parent aaddbc2ba9
commit f68c9b10fb
1 changed files with 47 additions and 8 deletions
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Schrick-Noah_Homework-3.R
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@ -233,9 +233,9 @@ my_euler2 <- function(f, y0, t0, tfinal, dt){
for (i in 2:npts){ # rows are time
for (j in 1:nvars){
y_vec_prev <- y[i-1,] # both y values at previous time point
dy <- f(t[i-1],y_vec_prev)*dt # f returns a vector, t not used
y[i,] <- y_vec_prev + dy
}
dy <- f(t[i-1],y_vec_prev)*dt # f returns a vector, t not used
y[i,] <- y_vec_prev + dy
}
return(list(t=tspan,y=y))
}
@ -250,12 +250,14 @@ my_rk4_2 <- function(f, y0, t0, tfinal, h){
for (i in 2:npts){ # rows are time
for (j in 1:nvars){
y_vec_prev <- y[i-1,] # both y values at previous time point
k1 <- f(t[i-1], y_vec_prev[i-1])
k2 <- f(t[i-1] + 0.5 * h, y_vec_prev[i-1] + 0.5 * k1 * h)
k3 <- f(t[i-1] + 0.5 * h, y_vec_prev[i-1] + 0.5 * k2 * h)
k4 <- f(t[i-1] + h, y_vec_prev[i-1] + k3*h)
y[i,] <- y_vec_prev[i-1] + (h/6)*(k1 + 2*k2 + 2*k3 + k4)
}
k1 <- f(t[i-1], y_vec_prev[i-1])
k2 <- f(t[i-1] + 0.5 * h, y_vec_prev[i-1] + 0.5 * k1 * h)
k3 <- f(t[i-1] + 0.5 * h, y_vec_prev[i-1] + 0.5 * k2 * h)
k4 <- f(t[i-1] + h, y_vec_prev[i-1] + k3*h)
y[i,] <- y_vec_prev[i-1] + (h/6)*(k1 + 2*k2 + 2*k3 + k4)
}
return(list(t=tspan,y=y))
}
@ -263,7 +265,6 @@ my_rk4_2 <- function(f, y0, t0, tfinal, h){
pp.euler.sol <- my_euler2(f = function(t,y){pp.f(t,y,k=pp.params)},
y = c(prey0, pred0),
t0 = tmin, tfinal = tmax, dt=h)
plot.pred.prey(pp.euler.sol, "Euler")
pp.rk4.sol <- my_rk4_2(f = function(t,y){pp.f(t,y,k=pp.params)},
@ -282,12 +283,50 @@ pp.sol.c <- ode45(f = function(t,y){pp.f(t,y,k=pp.params)},
plot.pred.prey(pp.sol.c, "ODE45 with k3=0.02")
## 5. Solve SIR model numerically from t=0 -> 20
sir.f <- function(t, y, k) {
dS <- -k[1] * y[1] * y[2]
dI <- k[1] * y[1] * y[2] - k[2] * y[2]
dR <- k[2] * y[2]
return(as.matrix(c(dS, dI, dR)))
}
# a) a=0.5, b=1, S(0)=0.9, I(0)=0.1, R(0)=0
sir.params <- c(0.5, 1)
S0 <- 0.9
I0 <- 0.1
R0 <- 0.0
tmin <- 0
tmax <- 20
sir.ode.sol <- ode45(f = function(t,y){sir.f(t,y,k=sir.params)},
y = c(S0, I0, R0),
t0 = tmin, tfinal = tmax)
# plot
plot.sir <- function(sol, method){
# - pred/prey columns melted to 1 column called "value"
sol.melted <- melt(data.frame(time=sol$t,
S=sol$y[,1],
I=sol$y[,2]),
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("SIR Model Using", method))
show(g)
}
plot.sir(sir.ode.sol, "ODE45")
# b) a=3
sir.params.b <- c(3, 1)
sir.ode.sol.b <- ode45(f = function(t,y){sir.f(t,y,k=sir.params.b)},
y = c(S0, I0, R0),
t0 = tmin, tfinal = tmax)
plot.sir(sir.ode.sol.b, "ODE45 with a=3")
## 6. Decomp of dinitrogen pentoxygen into nitrogen dioxide and molecular oxygen