Graph model: The spread of SARS-CoV-2#
Source from Agents.jl examples
Here we add one more category of individuals: those who are infected, but do not know it. Transmission rate for infected and diagnosed individuals is lower than infected and undetected.
using Agents, Random
using Agents.DataFrames, Agents.Graphs
using StatsBase: sample, Weights
using LinearAlgebra: diagind
using CairoMakie
CairoMakie.activate!(px_per_unit = 1.0)
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Define the Model#
@agent struct PoorSoul(GraphAgent)
days_infected::Int ## number of days since is infected
status::Symbol ## S/I/R
end
Initialize the model
function make_model(;
Ns,
migration_rates,
β_und,
β_det,
infection_period = 30,
reinfection_probability = 0.05,
detection_time = 14,
death_rate = 0.02,
Is = [zeros(Int, length(Ns) - 1)..., 1],
seed = 2024,
)
rng = Xoshiro(seed)
@assert length(Ns) ==
length(Is) ==
length(β_und) ==
length(β_det) ==
size(migration_rates, 1) "length of Ns, Is, and B, and number of rows/columns in migration_rates should be the same "
@assert size(migration_rates, 1) == size(migration_rates, 2) "migration_rates rates should be a square matrix"
C = length(Ns) ## Number of cities
# normalize migration_rates
migration_rates_sum = sum(migration_rates, dims = 2)
for c in 1:C
migration_rates[c, :] ./= migration_rates_sum[c]
end
properties = (;
Ns,
Is,
β_und,
β_det,
migration_rates,
infection_period,
reinfection_probability,
detection_time,
C,
death_rate
)
space = GraphSpace(complete_graph(C))
model = StandardABM(PoorSoul, space; agent_step!, properties, rng)
# Add initial individuals
for city in 1:C, n in 1:Ns[city]
ind = add_agent!(city, model, 0, :S) ## Susceptible
end
# add infected individuals
for city in 1:C
inds = ids_in_position(city, model)
for n in 1:Is[city]
agent = model[inds[n]]
agent.status = :I ## Set infected individual
agent.days_infected = 1
end
end
return model
end
make_model (generic function with 1 method)
Initialize parameters
function create_params(;
C,
max_travel_rate,
infection_period = 30,
reinfection_probability = 0.05,
detection_time = 14,
death_rate = 0.02,
Is = [zeros(Int, C - 1)..., 1],
seed = 2024,
)
rng = Xoshiro(seed)
Ns = rand(rng, 50:5000, C) ## City population
β_und = rand(rng, 0.3:0.02:0.6, C) ## Undetected transmission
β_det = β_und ./ 10 ## Detected transmission (set to 10% of undetected)
# Migrate from city i to city j
# People in small cities tend to migrate to bigger cities
migration_rates = zeros(C, C)
for c in 1:C
for c2 in 1:C
migration_rates[c, c2] = (Ns[c] + Ns[c2]) / Ns[c]
end
end
# Normalize migration rates
maxM = maximum(migration_rates)
migration_rates = (migration_rates .* max_travel_rate) ./ maxM
# Migrate to self = 1
migration_rates[diagind(migration_rates)] .= 1.0
params = (;
Ns,
β_und,
β_det,
migration_rates,
infection_period,
reinfection_probability,
detection_time,
death_rate,
Is
)
return params
end
create_params (generic function with 1 method)
Stepping functions#
function agent_step!(agent, model)
migrate!(agent, model)
transmit!(agent, model)
update!(agent, model)
recover_or_die!(agent, model)
return nothing
end
function migrate!(agent, model)
pid = agent.pos
m = sample(abmrng(model), 1:(model.C), Weights(model.migration_rates[pid, :]))
if m ≠ pid
move_agent!(agent, m, model)
end
return nothing
end
function transmit!(agent, model)
agent.status == :S && return
rate = if agent.days_infected < model.detection_time
model.β_und[agent.pos]
else
model.β_det[agent.pos]
end
rng = abmrng(model)
n = rate * abs(randn(rng))
n <= 0 && return
for contactID in ids_in_position(agent, model)
contact = model[contactID]
if contact.status == :S ||
(contact.status == :R && rand(rng) ≤ model.reinfection_probability)
contact.status = :I
n -= 1
n <= 0 && return
end
end
return nothing
end
update!(agent, model) = agent.status == :I && (agent.days_infected += 1)
function recover_or_die!(agent, model)
if agent.days_infected ≥ model.infection_period
if rand(abmrng(model)) ≤ model.death_rate
remove_agent!(agent, model)
else
agent.status = :R
agent.days_infected = 0
end
end
return nothing
end
recover_or_die! (generic function with 1 method)
Initialize the model
params = create_params(C = 10, max_travel_rate = 0.01)
model = make_model(; params...)
StandardABM with 24597 agents of type PoorSoul
agents container: Dict
space: GraphSpace with 10 positions and 45 edges
scheduler: fastest
properties: Ns, Is, β_und, β_det, migration_rates, infection_period, reinfection_probability, detection_time, C, death_rate
Animation#
Observable: The quantity that updates dynamically and interactively Makie plots.
abmobs = ABMObservable(model)
infected_fraction(m, x) = count(m[id].status == :I for id in x) / length(x)
infected_fractions(m) = [infected_fraction(m, ids_in_position(p, m)) for p in positions(m)]
infected_fractions (generic function with 1 method)
Connect (lift) observables to model states
fracs = lift(infected_fractions, abmobs.model)
color = lift(fs -> [cgrad(:inferno)[f] for f in fs], fracs)
title = lift(
(m) -> "step = $(abmtime(m)), infected = $(round(Int, 100infected_fraction(m, allids(m))))%",
abmobs.model
)
Observable("step = 0, infected = 0%")
Figure
fig = Figure(size = (600, 400))
ax = Axis(fig[1, 1]; title, xlabel = "City", ylabel = "Population")
barplot!(ax, model.Ns; strokecolor = :black, strokewidth = 1, color)
fig
Animation
vio = Makie.Record(fig; framerate = 5) do io
for j in 1:30
recordframe!(io)
Agents.step!(abmobs, 1)
end
recordframe!(io)
end
vio |> display
This notebook was generated using Literate.jl.