examples.qmd

---
title: Examples
---

This R package includes several popular epidemiological models, including SIS ([wiki](https://en.wikipedia.org/w/index.php?title=Compartmental_models_in_epidemiology&oldid=1155757336#Variations_on_the_basic_SIR_model)), SIR ([wiki](https://en.wikipedia.org/w/index.php?title=Compartmental_models_in_epidemiology&oldid=1155757336#The_SIR_model)), and SEIR ([wiki](https://en.wikipedia.org/w/index.php?title=Compartmental_models_in_epidemiology&oldid=1155757336#The_SEIR_model)) using either a fully connected graph (similar to a compartmental model) or a user-defined network. Here are some examples:

## SIR Model Using a Random Graph

This Susceptible-Infected-Recovered model features a population of 100,000 agents simulated in a small-world network. Each agent is connected to ten other agents. One percent of the population has the virus, with a 70% chance of transmission. Infected individuals recover at a 0.3 rate:

```{r}
library(epiworldR)

## Creating a SIR model
sir <- ModelSIR(
  name           = "COVID-19",
  prevalence     = .01,
  transmission_rate  = .7,
  recovery_rate =  .3
  ) |>
  # Adding a Small world population 
  agents_smallworld(n = 100000, k = 10, d = FALSE, p = .01) |>
  # Running the model for 50 days
  run(ndays = 50, seed = 1912)

sir
```

Visualizing the outputs

```{r}
plot(sir)
```

## SEIR Model With a Fully Connected Graph

```{r}
model_seirconn <- ModelSEIRCONN(
  name                = "COVID-19",
  prevalence          = 0.01, 
  n                   = 10000,
  contact_rate        = 4, 
  incubation_days     = 7, 
  transmission_rate   = 0.6,
  recovery_rate       = 0.5
)

set.seed(132)
run(model_seirconn, ndays = 100)
model_seirconn
```

Computing some key statistics: plotting and reproductive number ([wiki](https://en.wikipedia.org/w/index.php?title=Basic_reproduction_number&oldid=1155282807))

```{r}
plot(model_seirconn)

repnum <- get_reproductive_number(model_seirconn)
plot(repnum, type = "b")
```

## SIR Logit

```{r}
set.seed(2223)
n <- 100000

X <- cbind(
  Intercept = 1,
  Female    = sample.int(2, n, replace = TRUE) - 1
  )

coef_infect  <- c(.1, -2, 2)
coef_recover <- rnorm(2)

model_logit <- ModelSIRLogit(
  "covid2",
  data = X,
  coefs_infect      = coef_infect,
  coefs_recover     = coef_recover, 
  coef_infect_cols  = 1L:ncol(X),
  coef_recover_cols = 1L:ncol(X), 
  prob_infection = .8,
  recovery_rate = .3,
  prevalence = .01
)

agents_smallworld(model_logit, n, 8, FALSE, .01)

run(model_logit, 50)

plot(model_logit)

## Females are supposed to be more likely to become infected
rn <- get_reproductive_number(model_logit)

(table(
  X[, "Female"],
  (1:n %in% rn$source)
) |> prop.table())[,2]

## Looking into the agents
get_agents(model_logit)
```

## Transmission Network

```{r}
sir <- ModelSIR(
  name              = "COVID-19",
  prevalence        = .01,
  transmission_rate = .5,
  recovery_rate     = .5
  ) |>
    # Adding a Small world population 
    agents_smallworld(n = 500, k = 10, d = FALSE, p = .01) |>
    # Running the model for 50 days
    run(ndays = 50, seed = 1912)

## Transmission network
net <- get_transmissions(sir)

## Plotting
library(netplot)
library(igraph)
x <- graph_from_edgelist(as.matrix(net[,2:3]) + 1)

nplot(x, edge.curvature = 0, edge.color = "gray", skip.vertex=TRUE)
```

## Multiple Simulations

```{r}
model_sir <- ModelSIRCONN(
  name              = "COVID-19",
  prevalence        = 0.01,
  n                 = 1000,
  contact_rate      = 2,
  transmission_rate = 0.9,
  recovery_rate     = 0.1
  )

## Generating a saver
saver <- make_saver("total_hist", "reproductive")

## Running and printing
run_multiple(model_sir, ndays = 100, nsims = 50, saver = saver, nthread = 2)

## Retrieving the results
ans <- run_multiple_get_results(model_sir)

head(ans$total_hist)
head(ans$reproductive)

plot(ans$reproductive)
```