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## Contact networks and simple viral spreading.
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##
using Random
Random.seed!(0) # ensure repeatable results...
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## Generate a simple spatial graph model to look at.\
using NearestNeighbors, Distributions, SparseArrays
function spatial_graph_edges(n::Integer,d::Integer;degreedist=LogNormal(log(4),1))
xy = rand(d,n)
T = BallTree(xy)
# form the edges for sparse
ei = Int[]
ej = Int[]
for i=1:n
deg = min(ceil(Int,rand(degreedist)),n-1)
idxs, dists = knn(T, xy[:,i], deg+1)
for j in idxs
if i != j
push!(ei,i)
push!(ej,j)
end
end
end
return xy, ei, ej
end
function spatial_network(n::Integer, d::Integer; degreedist=LogNormal(log(3),1))
xy, ei, ej = spatial_graph_edges(n, d;degreedist=degreedist)
A = sparse(ei,ej,1,n,n)
return max.(A,A'), xy
end
A,xy = spatial_network(1000, 2)
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##
using Plots
function plotgraph(A::SparseMatrixCSC,xy::AbstractArray{T,2};kwargs...) where T
px,py = zeros(T,0),zeros(T,0)
P = [px,py]
rows = rowvals(A)
skip = NaN.*xy[:,begin] # first row
for j=1:size(A,2) # for each column
for nzi in nzrange(A, j)
i = rows[nzi]
if i > j
push!.(P, @view xy[:,i])
push!.(P, @view xy[:,j])
push!.(P, skip)
end
end
end
plot(px,py;framestyle=:none,legend=false,kwargs...)
end
plotgraph(A,xy,alpha=0.25); scatter!(xy[1,:],xy[2,:],
markersize=2, markerstrokewidth=0, color=1)
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## Run a contact simulation
p = 0.2 # probability of infection
# The result we use is that your probability of infection is
# 1 - probability of not being infected
# and your probability of not being infected is that you
# didn't get infected from any neighbor.
# https://www.khanacademy.org/math/ap-statistics/probability-ap/probability-multiplication-rule/a/probabilities-involving-at-least-one-success
function evolve(x::Vector, p::Real, A::AbstractMatrix)
log_not_infected = log.(1 .- p.*x)
y = 1 .- exp.(A*log_not_infected)
y = max.(y, x)
end
x = zeros(size(A,1))
x[2] = 1.0
anim = @animate for i=1:100
global x = evolve(x, p, A)
plotgraph(A,xy,alpha=0.25, size=(600,600))
scatter!(xy[1,:],xy[2,:],
markersize=5, markerstrokewidth=0,
color=1, marker_z = x, clim=(0,1))
title!("$i")
end
gif(anim, "viral-wrong.gif", fps=10)
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## Okay, fix one bug, you need to scale by the probability
# you weren't infected at the previous step.
# 1 - probability of not being infected
# and your probability of not being infected is that you
# didn't get infected from any neighbor.
# https://www.khanacademy.org/math/ap-statistics/probability-ap/probability-multiplication-rule/a/probabilities-involving-at-least-one-success
function evolve_self(x::Vector, p::Real, A::AbstractMatrix)
log_not_infected = log.(1 .- p.*x)
y = (1 .- exp.(A*log_not_infected).*(1 .- x))
y = max.(y, x)
end
p = 0.2
x = zeros(size(A,1))
x[2] = 1.0
anim = @animate for i=1:100
global x = evolve_self(x, p, A)
plotgraph(A,xy,alpha=0.25, size=(600,600))
scatter!(xy[1,:],xy[2,:],
markersize=5, markerstrokewidth=0,
color=1, marker_z = x, clim=(0,1))
title!("$i")
end
gif(anim, "viral-self.gif", fps=10)
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##
function evolve_self(x::Vector, p::Real, A::AbstractMatrix)
log_not_infected = log.(1 .- p.*x)
y = (1 .- exp.(A*log_not_infected).*(1 .- x))
y = max.(y, x)
end
p = 0.01
x = zeros(size(A,1))
x[2] = 1.0
anim = @animate for i=1:500
global x = evolve_self(x, p, A)
plotgraph(A,xy,alpha=0.25, size=(600,600))
scatter!(xy[1,:],xy[2,:],
markersize=5, markerstrokewidth=0,
color=1, marker_z = x, clim=(0,1))
title!("$i")
end
gif(anim, "viral-self-slow-long.gif", fps=10)
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