---
title: "Radioactive decay model (Gillespie, 1977)"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Radioactive decay model (Gillespie, 1977)}
  %\VignetteEncoding{UTF-8}
  %\VignetteEngine{knitr::rmarkdown}
editor_options: 
  chunk_output_type: console
---

<!-- github markdown built using 
rmarkdown::render("vignettes/radioactive_decay.Rmd", output_format = "github_document")
-->

```{r, setseed, echo=FALSE}
set.seed(1)
knitr::opts_chunk$set(fig.width = 8, fig.height = 6)
```

This model is also known as the irreversible isomerization reaction set.
It consists of a single species and single reaction channels,
```
X --c--> 0
```

Load package
```{r}
library(GillespieSSA)
```

Define parameters
```{r}
parms <- c(k = 0.5)
tf <- 20                                       # Final time
simName <- "Radioactive decay model"
```

Define initial state vector
```{r}
x0 <- c(N=1000)
```

Define state-change matrix
```{r}
nu <- matrix(c(-1),nrow=1,byrow=TRUE)
```

Define propensity functions
```{r}
a <- c("k*N")
```

Run simulations with the Direct method
```{r direct}
set.seed(1)
out <- ssa(
  x0 = x0,
  a = a,
  nu = nu,
  parms = parms,
  tf = tf,
  method = ssa.d(),
  simName = simName,
  verbose = FALSE,
  consoleInterval = 1
) 
ssa.plot(out, show.title = TRUE, show.legend = FALSE)
```

Run simulations with the Explict tau-leap method
```{r etl}
set.seed(1)
out <- ssa(
  x0 = x0,
  a = a,
  nu = nu,
  parms = parms,
  tf = tf,
  method = ssa.etl(tau = .003),
  simName = simName,
  verbose = FALSE,
  consoleInterval = 1
) 
ssa.plot(out, show.title = TRUE, show.legend = FALSE)
```

Run simulations with the Binomial tau-leap method
```{r btl}
set.seed(1)
out <- ssa(
  x0 = x0,
  a = a,
  nu = nu,
  parms = parms,
  tf = tf,
  method = ssa.btl(),
  simName = simName,
  verbose = FALSE,
  consoleInterval = 1
) 
ssa.plot(out, show.title = TRUE, show.legend = FALSE)
```

Run simulations with the Optimized tau-leap method
```{r otl}
set.seed(1)
out <- ssa(
  x0 = x0,
  a = a,
  nu = nu,
  parms = parms,
  tf = tf,
  method = ssa.otl(),
  simName = simName,
  verbose = FALSE,
  consoleInterval = 1
) 
ssa.plot(out, show.title = TRUE, show.legend = FALSE)
```