{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5. Spatial SIR model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are now ready to build the spatial model. It will consist of walkers moving in a 2D box."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Confinement inside a box"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need the agents to live inside a box so that they don't disperse."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise\n",
    "\n",
    "1. Make a `ConfinedWalker2D` type. Its fields are a `Walker2D` object and a box size, `L`. \n",
    "\n",
    "\n",
    "2. Extend `move` to `ConfinedWalker2D`. If the walker tries to jump outside the box, i.e. outside the sites 1 to $L$, in either direction, then it remains where it is.\n",
    "\n",
    "\n",
    "3. Make a confined `Agent` and calculate and draw its trajectory to make sure it stays inside the box."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For simplicity we will impose in our model that there is at most one agent on each site at all times (i.e. there is \"hard-core exclusion\"). This models the fact that two people cannot be in the same place at the same time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Write a function `initialize` that takes parameters 𝐿, the box length, and 𝑁, the number of agents.\n",
    "It builds, one by one, a `Vector` of agents, by proposing a position for each one and checking if that position is already occupied. If it is occupied, it should generate another one, and so on until it finds a free spot.\n",
    "All of the agents should have state `S`, except for one infectious individual (`I`).\n",
    "\n",
    "    To do this you should write a function `check_occupied` that checks if a particular position is occupied."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Write a function `visualize_agents` that takes in a collection of agents as argument. It should plot a point for each agent, coloured according to its status.\n",
    "\n",
    "    Hint: You can use the keyword argument `c=cs` inside your call to the plotting function to set the colours of points to a vector of integers called `cs`. Don’t forget to use `ratio=1`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. Run these functions to visualize the initial condition."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dynamics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dynamics has parameters $p_I$ and $p_R$, the probabilities of infection and recovery at each time step, respectively.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise\n",
    "\n",
    "1. Make an immutable `struct` `SIRSimulation` containing fields `L`, `p_I`, `p_R` and a `Vector` `agents` of `Agent`s. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we will have many `Agent`s, stored in a `Vector`, we do not want to recreate the whole simulation at each time step. Instead we will now *modify* (*mutate*) the data structure, so our functions will now have `!` at the end of their names.\n",
    "\n",
    "Nonetheless, we can still use an *immutable* `struct`, since the only things we will modify are inside the `Vector`. That is, we will never reassign the fields of the `struct` itself."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Write a function `step!` that does one step of the dynamics of the model. The rules are as follows:\n",
    "\n",
    "    1. Choose a single agent at random; call it $i$.\n",
    "    \n",
    "    2. Propose a new position for that agent.\n",
    "\n",
    "    3. If that new position is not occupied, move agent $i$ there.\n",
    "\n",
    "    4. If the new position *is* occupied, by agent $j$, then *neither* of them move, but they interact as follows:\n",
    "\n",
    "        - If agent $i$ is infected and agent $j$ is susceptible then agent $j$ gets infected with probability $p_I$.\n",
    "\n",
    "    5. If  agent $i$ is infected, it recovers with probability $p_R$.\n",
    "    \n",
    "  You should write helper functions when necessary."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. Make an interactive visualization to display the agents after each step, to check visually that the implementation is correct. You will need to *pre-compute* the whole evolution of the system before visualizing it.\n",
    "Use the function `deepcopy` to copy the state of the whole system each time you store it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4. Add to your visualization the history of $S$, $I$ and $R$ from time $0$ up to time $n$. To do this, make two separate plot objects $p_1$ and $p_2$ and use the `hbox` or `vbox` function (from `Interact.jl`) to put them together horizontally or vertically into a single plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    " "
   ]
  }
 ],
 "metadata": {
  "@webio": {
   "lastCommId": null,
   "lastKernelId": null
  },
  "kernelspec": {
   "display_name": "Julia 1.4.2",
   "language": "julia",
   "name": "julia-1.4"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.4.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}