binder/covid-19.ipynb

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    "## A Live [SEIR](https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SEIR_model) Model for Covid-19 with Error Bars in Julia\n",
    "\n",
    "#### Author: Dan Segal (@[djsegal](https://github.com/djsegal/))\n",
    "\n",
    "as requested by Prof. Alan Edelman, MIT\n",
    "\n",
    "----\n"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "using Measurements\n",
    "\n",
    "param_error = 0.05\n",
    "\n",
    "α = 0.2 ± param_error\n",
    "γ = 0.5 ± param_error\n",
    "\n",
    "# β = f(social distancing, masks, etc.)\n",
    "\n",
    "E₀ = 1e-4\n",
    "u₀ = [ 1 - E₀ ; E₀ ; 0 ; 0 ]\n",
    "\n",
    "tspan = (0.0, 200.0);  # 200 days\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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   "source": [
    "using DifferentialEquations\n",
    "\n",
    "function seir!(du,u,p,t)\n",
    "  S,E,I,_ = u\n",
    "  α,β,γ = p\n",
    "\n",
    "  dS = ( -β*I*S )\n",
    "  dE = ( +β*I*S ) - α*E\n",
    "  dI = ( -γ*I   ) + α*E\n",
    "  dR = ( +γ*I   )\n",
    "\n",
    "  du .= (dS, dE, dI, dR)\n",
    "end\n",
    "\n",
    "labels = [\n",
    "  \"Susceptible\", \"Exposed\", \n",
    "  \"Infected\", \"Recovered\"\n",
    "];\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
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       "      $(\"#js-interact__4a4e53eb-56fd-4403-a0eb-c48916e51673\").trigger(\"interact\");\n",
       "    })\n",
       "\n",
       "    var curCommand = 'Main.SimplePlots.interact_comms[\"interact-4a4e53eb-56fd-4403-a0eb-c48916e51673\"][] += 10';\n",
       "    Jupyter.notebook.kernel.execute(curCommand, {\"iopub\": {\"output\": function(tmpMessage) {\n",
       "      console.log(tmpMessage)\n",
       "    }}});\n",
       "\n",
       "    if ( typeof curCallback !== \"undefined\" ) { curCallback(); }\n",
       "  }\n",
       "\n",
       "  if ( typeof Jupyter === \"undefined\" ) {\n",
       "    customPlotLoader(function() {\n",
       "      $(\"#js-interact__4a4e53eb-56fd-4403-a0eb-c48916e51673\").trigger(\"interact\");\n",
       "    });\n",
       "  } else {\n",
       "    if (Jupyter.notebook.kernel) {\n",
       "      _guiBootup()\n",
       "    } else {\n",
       "      Jupyter.notebook.events.one('kernel_ready.Kernel', (e) => {\n",
       "        _guiBootup(function() {\n",
       "          customPlotLoader(function() {\n",
       "            $(\"#js-interact__4a4e53eb-56fd-4403-a0eb-c48916e51673\").trigger(\"interact\");\n",
       "          });\n",
       "        });\n",
       "      });\n",
       "    }\n",
       "  }\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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(Days)\",\"type\":\"linear\"},\"annotations\":[],\"title\":\"Covid-19 SEIR Model with Error Bars\",\"yaxis\":{\"autorange\":false,\"range\":[0,100],\"title\":\"%\",\"type\":\"linear\"},\"shapes\":[],\"legend\":{}}}}\n",
       "  $(\"#js-interact__4a4e53eb-56fd-4403-a0eb-c48916e51673\").trigger(\"interact\");\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using SimplePlots\n",
    "\n",
    "display(html\"\"\"\n",
    "  <h3> Sliding the β value reduces/increases infectivity </h3>\n",
    "  <p style=\"margin-top: 0.4em\">(social distancing, immunity, vaccines reduce β)</p>\n",
    "\"\"\")\n",
    "\n",
    "beta_slider = slider(0.25:0.25:2, value=1, label=\"β\") \n",
    "\n",
    "@demo for β in beta_slider\n",
    "  title!(\"Covid-19 SEIR Model with Error Bars\") ;\n",
    "  xlabel!(\"Time (Days)\") ; ylabel!(\"%\")  \n",
    "  \n",
    "  soln = solve(ODEProblem(\n",
    "    seir!, u₀, tspan, [α, β ± param_error, γ]\n",
    "  ), saveat=0.5)\n",
    "  \n",
    "  x, y = soln.t, 100*Array(soln)\n",
    "  ylims!(0, 100) # using percentages\n",
    "  \n",
    "  for (index, label) in enumerate(labels)\n",
    "    plot!(\n",
    "      x, y[index,:], label=label, \n",
    "      alpha=0.8, fillalpha=0.1\n",
    "    )\n",
    "  end\n",
    "end\n"
   ]
  }
 ],
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