How to plot several curves of the same variable for different values of a parameter using R?

Question

I am working with an SIR model using R. I need to plot multiple curves of I on the same figure for different values of beta, say for the values of 0.001, 0.002, 0.003, 0.004, and 0.005. Given below is the code that I have been working with so far. I know this might be a very simple problem, but I am new to R and couldn't find anything helpful yet.

library(deSolve)
sir_model <- function(time, variables, parameters) {
  with(as.list(c(variables, parameters)), {
    dS <- -beta * I * S
    dI <-  beta * I * S - gamma * I
    dR <-  gamma * I
    return(list(c(dS, dI, dR)))
  })
}
parameters <- c(beta  = 0.001, gamma = 0.3)
initial_values <- c(S = 999, I = 1, R = 0)
time_series <- seq(0, 100)

sir_model_1 <- ode(
  y = initial_values,
  times = time_series,
  func = sir_model,
  parms = parameters
)

sir_model_1 <- as.data.frame(sir_model_1)


with(sir_model_1, { 
  plot(time, I, type = "l", col = "black",
       xlab = "time (days)", ylab = "Number of infections")     
})

I tried to use a for loop, but I think I am not doing it right.

Answer 1

We could wrap the code in a function and loop over the sequence of beta values, and plot . If we need to do this in a single plot window, modify the par

par(mfrow = c(5, 1))
lapply(seq(0.001, length.out = 5, by = 0.001), f1)

where

f1 <- function(beta) {

parameters <- c(beta  = beta, gamma = 0.3)
initial_values <- c(S = 999, I = 1, R = 0)
time_series <- seq(0, 100)

sir_model_1 <- ode(
  y = initial_values,
  times = time_series,
  func = sir_model,
  parms = parameters
)

sir_model_1 <- as.data.frame(sir_model_1)


with(sir_model_1, { 
  plot(time, I, type = "l", col = "black",
       xlab = "time (days)", main = beta, ylab = "Number of infections")     
})

}

-output

---

In case we want to loop over the column names, use the formula method

par(mfrow = c(3, 1))
lapply(names(sir_model_1)[-1], function(nm) 
   plot(reformulate("time", response = nm), data = sir_model_1, main = nm,
      type = "l", col = "black",
        xlab = "time (days)", ylab = "Number of infections"))

-output

Answer 2

Package deSolve contains a plotting function that supports to add multiple scenarios. It works directly with the output of ode that is a matrix of class deSolve . The first argument of the plot function needs to be such a deSolve object and the second can be a list of such objects.

This way, it can be run and plotted as follows:

library(deSolve)
sir_model <- function(time, variables, parameters) {
  with(as.list(c(variables, parameters)), {
    dS <- -beta * I * S
    dI <-  beta * I * S - gamma * I
    dR <-  gamma * I
    return(list(c(dS, dI, dR)))
  })
}
parameters <- c(beta  = 0.001, gamma = 0.3)
initial_values <- c(S = 999, I = 1, R = 0)
time_series <- seq(0, 100)

run_sir <- function(beta) {
  parameters["beta"] <- beta
  ode(y = initial_values, times = time_series,func = sir_model, parms = parameters)
}

## define scenarios
beta <- 0.001 * 1:5

## run default scenario
run0 <- run_sir(beta = beta[1])
plot(run0)

## run other 4 scenarios
## [-1] means all except the first, that we already have
runs <- lapply(beta[-1], run_sir)

plot(run0, runs, las=1)
legend("bottomright", legend = paste("beta = ", beta), lty=1:5, col=1:5)

The plot.deSolve function is highly configurable with respect to layout, colors, line types, selection of variables, etc., see help page ?plot.deSolve .

To plot only selected state variables, one can use the which argument, eg which="I" to plot only the infected.

plot(run0, runs, which="I")

Some examples about plotting deSolve outputs can be found in the tutorial slides in section "Plotting".