using Measurements

param_error = 0.05

α = 0.2 ± param_error
γ = 0.5 ± param_error

# β = f(social distancing, masks, etc.)

E₀ = 1e-4
u₀ = [ 1 - E₀ ; E₀ ; 0 ; 0 ]

tspan = (0.0, 200.0);  # 200 days


using DifferentialEquations

function seir!(du,u,p,t)
  S,E,I,_ = u
  α,β,γ = p

  dS = ( -β*I*S )
  dE = ( +β*I*S ) - α*E
  dI = ( -γ*I   ) + α*E
  dR = ( +γ*I   )

  du .= (dS, dE, dI, dR)
end

labels = [
  "Susceptible", "Exposed", 
  "Infected", "Recovered"
];


using SimplePlots

display(html"""
  <h3> Sliding the β value reduces/increases infectivity </h3>
  <p style="margin-top: 0.4em">(social distancing, immunity, vaccines reduce β)</p>
""")

beta_slider = slider(0.25:0.25:2, value=1, label="β") 

@demo for β in beta_slider
  title!("Covid-19 SEIR Model with Error Bars") ;
  xlabel!("Time (Days)") ; ylabel!("%")  
  
  soln = solve(ODEProblem(
    seir!, u₀, tspan, [α, β ± param_error, γ]
  ), saveat=0.5)
  
  x, y = soln.t, 100*Array(soln)
  ylims!(0, 100) # using percentages
  
  for (index, label) in enumerate(labels)
    plot!(
      x, y[index,:], label=label, 
      alpha=0.8, fillalpha=0.1
    )
  end
end