# How?

## Predicting health burden...

### How much sickness is experienced by a pop. of 1000 people?

Number Flu = Pop. * Flu Probability = 100
$Number Flu = Pop. * Flu Probability = 100$
Flu Burden = Number Flu * Flu Disability = 5
$Flu Burden = Number Flu * Flu Disability = 5$

## Predicting health burden...

### Flu is .05 disabling, pneumonia is .1 disabling

Disability = 1000 * (Flu Prob * Flu Disability + Pneu. Prob. * Pneu. Disability)
$Disability = 1000 * (Flu Prob * Flu Disability + Pneu. Prob. * Pneu. Disability)$

### How much sickness is experienced by a pop. of 1000 people?

Disability = 25
$Disability = 25$

### Pneu.

DW(combined) = 1 - (1 - flu) * (1 - pneu)
$DW(combined) = 1 - (1 - flu) * (1 - pneu)$
DW(combined) = .145
$DW(combined) = .145$

# Simulation!

## Random number generators

### Randomly sample out of a vector

# Given a 10% probability, simulate 1000 people getting the flu
people <- rbinom(n = 1000, size = 1, prob = .2)
# Generate a normal distribution of grades for 20 students
grades <- rnorm(20, mean = 80, sd = 10)
# Get the eye color for 100 people: blue, green, or hazel
colors <- c('blue', 'green', 'hazel')
eye_colors <- sample(colors, 100, replace = TRUE)

There is a very long, straight highway with some number of cars (N) placed somewhere along it, randomly. The highway is only one lane, so the cars can’t pass each other. Each car is going in the same direction, and each driver has a distinct positive speed at which she prefers to travel. Each preferred speed is chosen at random. Each driver travels at her preferred speed unless she gets stuck behind a slower car, in which case she remains stuck behind the slower car. On average, how many groups of cars will eventually form? (A group is one or more cars traveling at the same speed.)

For example, if the car in the very front happens to be slowest, there will be exactly one group — everybody will eventually pile up behind the slowpoke. If the cars happen to end up in order, fastest to slowest, there will be groups — no car ever gets stuck behind a slower car.

## Initial Steps

### Write a function to test if a car creates a new group

# Simulate 100 cars w/mean speed 50
cars <- rnorm(n = 100, mean = 50, sd = 5)
# A function to determine if a car is slower than all of the cars
# in front of it (which createa a new group of cars **behind** it)
slower_than <- function(index) {
return(cars[index] < min(cars[1:index - 1]))
}

### Apply the function to the list of indicies

# Apply the slower_than function to all of the cars
new_group <- lapply(2:length(cars), slower_than)


## Initial Steps

# Simulate 100 cars w/mean speed 50
cars <- rnorm(n = 1000, mean = 50, sd = 5)

# A function to determine if a car is slower than all of the cars
# in front of it (which createa a new group of cars **behind** it)
slower_than <- function(index) {
return(cars[index] < min(cars[1:index - 1]))
}

# Apply the slower_than function to all of the cars
new_group <- lapply(2:length(cars), slower_than)

# Determine number of groups created
groups <- length(new_group[new_group == TRUE]) + 1

## Better yet....

simulate_groups <- function() {
# Simulate 100 cars w/mean speed 50
cars <- rnorm(n = 1000, mean = 50, sd = 5)

# A function to determine if a car is slower than all of the cars
# in front of it (which createa a new group of cars **behind** it)
slower_than <- function(index) {
return(cars[index] < min(cars[1:index - 1]))
}

# Apply the slower_than function to all of the cars
new_group <- lapply(2:length(cars), slower_than)

# Determine number of groups created
groups <- length(new_group[new_group == TRUE]) + 1
return(groups)
}

## Loops

### Pass a different element into the block of code in each iteration

items <- 1:10

# Loop through each element in your vector items
for(i in items) {
print(2*i) # i takes on the identity of each element in the vector items
}

## Repeating your simulation

repeat_simulation <- function(num_sims) {
# Create an empty vector to store your results
results <- vector()

# Run your simulation 100 times, and track your results
for(i in 1:num_sims) {
results <- c(results, simulate_groups())
}
# Work with your results
hist(results)
return(mean(results))
}

## Parameterizing your simulation

simulate_groups <- function(mean, sd, num_cars) {
# Simulate 100 cars w/mean speed 50
cars <- rnorm(n = num_cars, mean = mean, sd = sd)

# A function to determine if a car is slower than all of the cars
# in front of it (which createa a new group of cars **behind** it)
slower_than <- function(index) {
return(cars[index] < min(cars[1:index - 1]))
}

# Apply the slower_than function to all of the cars
new_group <- lapply(2:length(cars), slower_than)

# Determine number of groups created
groups <- length(new_group[new_group == TRUE]) + 1
return(groups)
}

## Create an interface: ui.R

# Create UI
shinyUI(fluidPage(
# UI for the traffic simulation
titlePanel('Traffic Simulation'),

# Controls
sidebarLayout(
sidebarPanel(
sliderInput("num_cars", "Number of Cars:",
min = 10, max = 1000, value = 100, step = 10),
sliderInput("num_sims", "Iterations of Simulation",
min = 10, max = 1000, value = 100, step= 10),
sliderInput("speed", "Average Speed",
min = 10, max = 150, value = 40, step= 5),
sliderInput("deviation", "Speed Deviation",
min = 1, max = 20, value = 5, step= 1)
),
# Render plot
mainPanel(
plotOutput("histogram")
)
)
))


## Run your simulation: server.R

# Run the traffic simulation
source('traffic_sim.R')
shinyServer(function(input, output) {
output$histogram <- renderPlot({ repeat_simulation( num_sims = input$num_sims,
mean = input$speed, sd = input$deviation,
num_cars = input\$num_cars
)
})
})

## Assignments

### Keep working on your final projects!

#### simulation

By Michael Freeman

# simulation

• 590
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