library(deSolve)
library(ggplot2)

# Define the ODE system
ode_system <- function(t, y, parms) {
  with(as.list(c(y, parms)), {
    dydt <- r * y * (1 - y/K)
    return(list(dydt))
  })
}

# Define the initial conditions and parameters
y0 <- c(y = 1)
parms <- c(r = 0.1, K = 10)

# Define the time span
times <- seq(0, 50, by = 0.1)

# Solve the ODE system using the "ode" solver
out <- ode(y = y0, times = times, func = ode_system, parms = parms)

# Convert the output to a data frame
df <- as.data.frame(out)

# Create a plot using ggplot2
p <- ggplot(df, aes(times, y)) + 
  geom_line() + 
  labs(title = "Logistic Growth Model", x = "Time", y = "Population Size")

# Save the plot as a PDF file
ggsave("logistic_growth.pdf", p)