---
title: "Linear Chain System"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Linear Chain System}
  %\VignetteEncoding{UTF-8}
  %\VignetteEngine{knitr::rmarkdown}
editor_options: 
  chunk_output_type: console
bibliography: ../inst/REFERENCES.bib
---

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

```{r, setseed, echo=FALSE}
set.seed(1)
knitr::opts_chunk$set(fig.width = 6, fig.height = 4)
if("package:GillespieSSA" %in% search()) detach("package:GillespieSSA", unload=TRUE) 
```

The Linear Chain System [@Cao2004] consists of M chain reactions with M+1 species as follows:

```
  S_1 --c1--> S_2
  S_2 --c2--> S_3
       ...
  S_M --cM--> S_(M+1)
```

Define parameters
```{r}
library(GillespieSSA2)
sim_name <- "Linear Chain System"
M <- 50
params <- c(c = 1)
final_time <- 5
initial_state <- c(1000, rep(0, M)) 
names(initial_state) <- paste0("x", seq_len(M+1))
```

Define the reactions
```{r}
reactions <- lapply(
  seq_len(M),
  function(i) {
    effect <- c(-1, 1)
    names(effect) <- paste0("x", c(i, i + 1))
    
    reaction(paste0("c * x", i), effect)
  }
)
```

Run simulations with the Exact method
```{r exact}
set.seed(1)
out <- ssa(
  initial_state = initial_state,
  reactions = reactions,
  params = params,
  final_time = final_time,
  method = ssa_exact(),
  sim_name = sim_name
) 
plot_ssa(out)
```

Run simulations with the Explict tau-leap method
```{r etl}
set.seed(1)
out <- ssa(
  initial_state = initial_state,
  reactions = reactions,
  params = params,
  final_time = final_time,
  method = ssa_etl(tau = .1),
  sim_name = sim_name
) 
plot_ssa(out)
```

Run simulations with the Binomial tau-leap method
```{r btl}
set.seed(1)
out <- ssa(
  initial_state = initial_state,
  reactions = reactions,
  params = params,
  final_time = final_time,
  method = ssa_btl(mean_firings = 50),
  sim_name = sim_name
) 
plot_ssa(out)
```

## References