240115-fwd-back.Rmd

---
title: "Simulating forward and backwards generation intervals"
author: "Oliver Cheng"
date: "2024-01-15"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)

library(deSolve)

source("calculations.R")
source("solver.R")
source("model.R")
source("simulation.R")
source("plots.R")
```

## R Markdown

```{r}
parameters <- c(N = 100000, beta = 0.47857, sigma = 0.4, gamma = 0.17857)
state  <- c(S = 99999, E = 1, I = 0, R = 0)

state  <- c(S.AB = 99998, S.A = 0, S.B = 0, E.A = 1, E.B = 1, E.AA I = 0, R = 0)

dist <- simulate_seir(state, parameters, 0, 150, stochastic = FALSE)

plot_SEIR(dist, parameters, style="combined")
plot_SEIR(dist, parameters, style="exploded")
plot_SEIR(dist, parameters, style="incidence")

ggplot() +
  xlim(0, 50) +
  geom_function(fun = dist$F, n = 1000, aes(colour = "F")) +
  geom_function(fun = dist$L, n = 1000, aes(colour = "L"))
```

```{r}
times <- seq(0, 200, by=0.1)
gt <- data.frame(time = times)

gt$basic <- basic_mean_gt(dist)

gt$fwd <- sapply(times, \(x) forward_mean_gt(dist, x))
gt$back <- sapply(times, \(x) backward_mean_gt(dist, x))

ggplot(gt, aes(x=time)) + 
  xlim(0, 200) +
  geom_line(aes(y=basic, colour="basic"), linetype="dashed") +
  geom_line(aes(y=fwd, colour="forward")) + 
  geom_line(aes(y=back, colour="backward")) +
  geom_line(data=dist$overview,
            aes(y = incidence / 1500,
                colour="incidence (scaled)"
                ),
            linetype="dashed",
            na.rm=TRUE
            )
```