SIR model in Rstudio shiny

I´m trying to build the basic SIR model in Rstudio shiny. The model takes 2 parameters (beta = infection rate/day, gamma = recovery date/day), 3 initial values (S = numbers of susceptibles, I = infectious, R = recovered) and last variable is time (in days).

Here is the code of it just in R markdown:

library(deSolve)

sir_equations <- 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_values <- c(
  beta  = 0.05, # infectious rate/day
  gamma = 0.5    # recovery rate/day
)

initial_values <- c(
  S = 1000,  # susceptibles
  I =   1,  # infectious
  R =   0   # recovered (immune)
)

time_values <- seq(0, 10) #number of days (0-10)

sir_values_1 <- ode(
  y = initial_values,
  times = time_values,
  func = sir_equations,
  parms = parameters_values 
)

sir_values_1 <- as.data.frame(sir_values_1) # convert to data frame

with(sir_values_1, {
  plot(time, S, type = "l", col = "blue",
       xlab = "period (days)", ylab = "number of people")
  lines(time, I, col = "red")
  lines(time, R, col = "green")
})

legend("right", c("susceptibles", "infectious", "recovered"),
       col = c("blue", "red", "green"), lty = 1, bty = "n")

Now I want to add this into R shiny, where the user can input the beta, gamma and days value (sliderbar, or just input), then it will plot the result. I´m pretty new to R and tried some variations here, like putting the user input into ,,UI,, the calculating into ,,server,, then combine it in like this shinyApp(ui = ui, server = server). This code below I tried, but its not working. Can you guys help me, what I´m doing wrong, and what to follow to be able to put the code into R shiny?

library(deSolve)
library(shiny)


ui <- fluidPage(




  sliderInput(inputId = "time_values", label = "Dny", value = 10, min = 1, max = 100),
  sliderInput(inputId = "beta", label ="Míra nákazy", value = 0.05, min = 0.00, max = 1, step = 0.01),
  sliderInput(inputId = "gamma", label ="Míra uzdravení", value = 0.5, min = 0.00, max = 1, step = 0.1),

  plotOutput("plot")
)



server <- function(input, output) {
  sir_equations <- 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)))
  })
  }

  initial_values <- c(S = 1000, I = 1, R = 0)

  sir_values_1 <- ode(
  y = initial_values,
  times = time_values,
  func = sir_equations,
  parms = parameters_values 
)

  output$plot <- renderPlot({
    plot(rnorm(input$time_values))
    plot(rnorm(input$beta))
    plot(rnorm(input$gamma))
  })


}

shinyApp(ui = ui, server = server)

Thanks Michal