temporal-simulation.qmd

---
title: "Simulation"
---

::: {.callout-note appearance="simple"}
This is a work in progress that is currently undergoing heavy technical editing and copy-editing
:::

```{r warning=FALSE, message=FALSE}
library(tidyverse) # essential packages 
library(cowplot) # for themes 
library(deSolve)
theme_set(theme_bw(base_size = 16)) # set global theme
```

## HLIR function

```{r}
HLIR_fun <- function(t, y, par) {
  # Variables
  H <- y[1]
  L <- y[2]
  I <- y[3]
  R <- y[4]
  beta <- par$beta
  gama <- par$gama
  mu <- par$mu

  # Right hand side of the model
  dH <- -beta * H * I
  dL <- beta * H * I - gama * L
  dI <- gama * L - mu * I
  dR <- mu * I
  return(list(c(dH, dL, dI, dR)))
}
```

## Setting up

```{r}
# Set up parameters
beta <- 0.002 # Per capita rate of infection of susceptible hosts
gama <- 1 / 5 #  Rate at which exposed (i.e., latently infected) hosts become infectious
delta <- 15 # infectious period
mu <- 1 / delta
InitCond <- c(1000, 1, 0, 0)
```

## Solving equation

```{r}
steps <- seq(1, 60, by = 1)
parms <- list(beta = beta, gama = gama, mu = mu)
HLIR <- ode(InitCond, steps, HLIR_fun, parms)
epidemics <- data.frame(time = HLIR[, 1], H = HLIR[, 2], L = HLIR[, 3], I = HLIR[, 4], R = HLIR[, 5])
```

## Visualizing HLIR output

```{r}
library(ggthemes)
p1 <- epidemics %>%
  ggplot() +
  r4pde::theme_r4pde()+
  geom_line(aes(time, H, color = "H"), size = 2) +
  geom_line(aes(time, L, color = "L"), size = 2) +
  geom_line(aes(time, I, color = "I"), size = 2) +
  geom_line(aes(time, R, color = "R"), size = 2) +
  geom_line(aes(time, I+R, color = "DIS"), size =2, linetype = 2)+
  labs(y = "Population size (count)", x = "Time (days)", color = "Sites") 
 p1
```