initial model fits done, bounded rationality too low or immunity loss too high

CovidAlertVaccinationModel/Project.toml

@@ -38,6 +38,7 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 RandomNumbers = "e6cf234a-135c-5ec9-84dd-332b85af5143"
 Serialization = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 ThreadsX = "ac1d9e8a-700a-412c-b207-f0111f4b6c0d"
 UnPack = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"

CovidAlertVaccinationModel/abm_fit_parameters.jl

@@ -2,65 +2,4 @@ using CovidAlertVaccinationModel
 using OnlineStats
 using Plots
 using StatsBase
-const parameters = (
-    sim_length = 600,
-    num_households = 5000,
-    I_0_fraction = 0.002,
-    base_transmission_probability = 0.001,
-    recovery_rate = 1/7,
-    immunization_loss_prob = 0.0055, #mean time of 6 months
-    π_base = -0.3,
-    η = 0.0,
-    κ = 0.8,
-    ω = 0.00005,
-    ρ_y = 0.0,
-    ρ_m = 0.0,
-    ρ_o = 0.0,
-    ω_en = 0.00,
-    ρ_en =  [0.0,0.0,0.0],
-    γ = 0.0,
-    β = 10.0,
-    notification_parameter = 0.001,
-    vaccinator_prob = 0.2,
-    app_user_fraction = 0.0,
-    notification_threshold = 17,
-    immunizing = true,
-    immunization_delay = 14,
-    immunization_begin_day = 30,
-    infection_introduction_day = 100
-)
-
-# seasonal_transmission_dist = CovidAlertVaccinationModel.fit_epi_parameters(parameters,0.073) ##seasonal
-# outbreak_transmission_dist = CovidAlertVaccinationModel.fit_epi_parameters(parameters,0.241) ##outbreak
-
-# function plot_max_posterior(fname,particles)
-#     samples = 5
-#     base_transmission = mode(particles.P.particles)
-#     p_tuple_without_vac = merge(parameters,
-#         (
-#             sim_length = 150,
-#             immunization_begin_day = 0,
-#             infection_introduction_day = 1,
-#             immunizing = false,
-#         )
-#     )
-#     new_params = merge(p_tuple_without_vac, (base_transmission_probability = base_transmission,))
-#     out = mean_solve(samples, new_params ,DebugRecorder)
-#     p = plot_model(nothing,[nothing],[out],new_params.infection_introduction_day,new_params.immunization_begin_day)
-#     savefig(p,"$fname.pdf")
-#     hist = fit(Histogram,particles.P.particles; nbins = 25)
-#     p = plot(hist;legend = false)
-#     savefig(p,"$(fname)_posterior.pdf")
-
-# end
-# plot_max_posterior("seasonal", seasonal_transmission_dist)
-# plot_max_posterior("outbreak", outbreak_transmission_dist)
-
-a = CovidAlertVaccinationModel.fit_behavioural_parameters(parameters,nothing)
-
-function solve_and_plot_parameters()
-    out = mean_solve(samples, parameters ,DebugRecorder)
-    p = plot_model(nothing,[nothing],[out],parameters.infection_introduction_day,parameters.immunization_begin_day)
-    savefig(p,"timeseries.pdf")
-    return out
-end
\ No newline at end of file
+CovidAlertVaccinationModel.fit_parameters(CovidAlertVaccinationModel.get_parameters())
\ No newline at end of file

CovidAlertVaccinationModel/abm_timeseries.jl

@@ -2,41 +2,13 @@ using CovidAlertVaccinationModel
 using OnlineStats
 using Plots
 const samples = 1
-const parameters = (
-    sim_length = 600,
-    num_households = 5000,
-    I_0_fraction = 0.0,
-    base_transmission_probability = 0.001,
-    recovery_rate = 1/7,
-    immunization_loss_prob = 0.0055, #mean time of 6 months
-    π_base = -0.8,
-    η = 0.0,
-    κ = 0.0,
-    ω = 0.00005,
-    ρ_y = 0.0,
-    ρ_m = 0.0,
-    ρ_o = 0.0,
-    ω_en = 0.00,
-    ρ_en =  [0.0,0.0,0.0],
-    γ = 0.0,
-    β = 10.0,
-    notification_parameter = 0.001,
-    vaccinator_prob = 0.2,
-    app_user_fraction = 0.2,
-    notification_threshold = 17,
-    immunizing = true,
-    immunization_delay = 14,
-    immunization_begin_day = 30,
-    infection_introduction_day = 100
-)
 function solve_and_plot_parameters()
-    out = mean_solve(samples, parameters ,DebugRecorder)
-    p = plot_model(nothing,[nothing],[out],parameters.infection_introduction_day,parameters.immunization_begin_day)
+    p =  CovidAlertVaccinationModel.get_parameters()
+    out = mean_solve(samples, p,DebugRecorder)
+    p = plot_model(nothing,[nothing],[out],p.infection_introduction_day,p.immunization_begin_day)
     savefig(p,"timeseries.pdf")
     return out
 end
 
 out = solve_and_plot_parameters()
-println(mean.(out.new_ymo_immunization.Y))
-println(mean.(out.new_ymo_immunization.M))
-println(mean.(out.new_ymo_immunization.O))
\ No newline at end of file
+println(sum.(eachrow(mean.(out.new_ymo_immunization))))
\ No newline at end of file

CovidAlertVaccinationModel/src/ABM/model_setup.jl

 
 function get_parameters()
     params = (
-        sim_length = 600,
+        sim_length = 120,
         num_households = 5000,
         I_0_fraction = 0.002,
         base_transmission_probability = 0.001,
         recovery_rate = 1/7,
-        immunization_loss_prob = 0.0055, #mean time of 6 months
-        π_base = -0.3,
+        immunization_loss_prob = 0.0001, #mean time of 6 months
+        π_base_y = -5.0,
+        π_base_m = -5.0,
+        π_base_o = 1.0,
         η = 0.0,
-        κ = 0.8,
+        κ = 0.0,
         ω = 0.00005,
-        ρ_y = 0.0,
-        ρ_m = 0.0,
-        ρ_o = 0.0,
         ω_en = 0.00,
-        ρ_en =  [0.0,0.0,0.0],
+        ρ_en = [0.0,0.0,0.0],
         γ = 0.0,
-        β = 10.0,
+        β = 5.0,
         notification_parameter = 0.001,
         vaccinator_prob = 0.2,
-        app_user_fraction = 0.2,
+        app_user_fraction = 0.0,
         notification_threshold = 2,
         immunizing = true,
         immunization_delay = 14,
-        immunization_begin_day = 30,
-        infection_introduction_day = 100
+        immunization_begin_day = 60,
+        infection_introduction_day = 120
     )
     return params
 end

CovidAlertVaccinationModel/src/ABM/output.jl

@@ -108,10 +108,29 @@ function OnlineStats.fit!(stat_type::R,pt) where {T,OS<:OnlineStat{T}, R<:Abstra
         end
     end
 end
+
 using Printf
+
 const ts_colors = cgrad(:PuBu_9)
+
 function plot_model(varname,univariate_series, output_list::Vector{T},infection_begin,vac_begin) where T<:DebugRecorder
-    plts = [plot() for i=1:7]
+    
+    sim_length = length(output_list[1].recorded_status_totals.S)
+    ts_list(data) = [
+        (data.recorded_status_totals.S, "Susceptible over time"),
+        (data.recorded_status_totals.I, "Infected over time"),
+        (data.recorded_status_totals.R, "Recovered over time"),
+        (data.recorded_status_totals.V, "Vaccinated over time"),
+        (data.total_vaccinators,  "No. vaccinators over time"),
+        (data.mean_time_since_last_notification, "Mean time since last notification"),
+        (data.daily_cases,"Daily (incident) cases"),
+        (data.new_ymo_immunization.Y, "new Y vaccinations each day"),
+        (data.new_ymo_immunization.M, "new M vaccinations each day"),
+        (data.new_ymo_immunization.O, "new O vaccinations each day"),
+    ]
+
+    l = length(ts_list(output_list[1]))
+    plts = [plot() for i=1:l]
     for (i,(p,data)) in enumerate(zip(univariate_series, output_list))
         # display(p[varname])
         if !isnothing(varname) 
@@ -120,65 +139,19 @@ function plot_model(varname,univariate_series, output_list::Vector{T},infection_
         else
             labelname = nothing
         end
-        # display(p_val)
-        plot!(plts[1], mean.(data.recorded_status_totals.S); ribbon = std.(data.recorded_status_totals.S),
-                label = labelname, line_z = i, color=:blues,
-                ylabel = "no. of people",
-                colorbar = false,
-                title = "Susceptible over time",
-                legend=:topright
-        )
-        plot!(plts[2], mean.(data.recorded_status_totals.I); ribbon = std.(data.recorded_status_totals.I),
-                label = labelname, line_z = i, color=:blues,
-                ylabel = "no. of people",
-                colorbar = false,
-                title = "Infected over time",
-                legend=false,
-        )
-        
-        plot!(plts[3], mean.(data.recorded_status_totals.R); ribbon = std.(data.recorded_status_totals.R),
-                label = labelname, line_z = i, color=:blues,
-                ylabel = "no. of people",
-                colorbar = false,
-                title = "Recovered over time",
-                legend=false
-        )
-        plot!(plts[4], mean.(data.recorded_status_totals.V); ribbon = std.(data.recorded_status_totals.V),
-                label = labelname, line_z = i, color=:blues,
-                ylabel = "no. of people",
-                colorbar = false,
-                title = "Vaccinated over time",
-                legend=false
-        )
-        plot!(plts[5], mean.(data.total_vaccinators); ribbon = std.(data.total_vaccinators),
-                label = labelname, line_z = i, color=:blues,
-                ylabel = "no. of people",
-                colorbar = false,
-                title = "No. vaccinators over time",
-                legend=false
-        )
-        plot!(plts[6], mean.(data.mean_time_since_last_notification); ribbon = std.(data.mean_time_since_last_notification),
-                label = labelname, line_z = i, color=:blues,
-                ylabel = "Days",
-                colorbar = false,
-                title = "Mean time since last notification",
-                legend=false
-        )
-
-
-        # ic,exp_growth_rate = exp_growth_rate_estimation(mean.(data.daily_cases[infection_begin,:]))
-
-        plot!(plts[7], mean.(data.daily_cases); ribbon = std.(data.daily_cases),
-                label = labelname, line_z = i, color=:blues,
-                ylabel = "Days",
-                colorbar = false,
-                title = "Daily (incident) cases",
-                legend= false
-        ) 
+        for (plt,(ts,title)) in zip(plts,ts_list(data))
+            plot!(plt, mean.(ts); ribbon = std.(ts),
+                    label = labelname, line_z = i, color=:blues,
+                    ylabel = "no. of people",
+                    colorbar = false,
+                    title = title,
+            ) 
+        end
     end
+    plot!(plts[begin]; legends = :topright)
     for p in plts
         vline!(p,[infection_begin]; label = "infection begin", line =:dot)
         vline!(p,[vac_begin]; label = "vaccination begin",line = :dot)
     end
-    return plot(plts...;layout = (7,1),size=(800,2900),leftmargin = 8Plots.mm)
+    return plot(plts...;layout = (l,1),size=(800,400*l),leftmargin = 12Plots.mm)
 end

CovidAlertVaccinationModel/src/ABM/parameter_optimization.jl

@@ -2,7 +2,16 @@ using KissABC
 using CurveFit
 using Loess
 
+const target_cumulative_vac_proportion = 0.33
+const vaccination_data = @SVector [0.0,0.043,0.385,0.424,0.115,0.03,0.005] #by month starting in august
+const ymo_vac = @SVector [0.255,0.278,0.602]
 
+function solve_w_parameters(default_p, p_names, new_p_list)
+    new_params = merge(default_p, NamedTuple{p_names}(ntuple(i -> new_p_list[i],length(p_names))))
+    out = DebugRecorder(0,default_p.sim_length)
+    model = abm(new_params,out)
+    return out, model
+end
 @views function exp_growth_rate_estimation(incident_cases)
     diff(l) = [l[i] - l[i-1] for i=2:length(l)]
     l = length(incident_cases)
@@ -14,13 +23,6 @@ using Loess
     return ic,exp_growth_rate
 end
 
-
-function vaccination_data()
-    ymo_total_vaccinated = [0.279,0.38,0.7]
-    total_vaccinated = 0.33
-
-end
-
 function fit_epi_parameters(p_tuple, target_growth_rate)
     p_tuple_without_vac = merge(p_tuple,
         (
@@ -30,71 +32,99 @@ function fit_epi_parameters(p_tuple, target_growth_rate)
             immunizing = false,
         )
     )
-    samples = 1
+    p_names = (:base_transmission_probability,)
     priors = Factored(Uniform(0.0001,0.005))    
-
     function cost(p)
-        new_params = merge(p_tuple_without_vac, (base_transmission_probability = p[1],))
-        out = mean_solve(samples, new_params ,DebugRecorder)
-        incident_cases = mean.(out.daily_cases)
+        output,model = solve_w_parameters(p_tuple_without_vac,p_names ,p)
+        incident_cases = output.daily_cases
         _,exp_growth_rate = exp_growth_rate_estimation(incident_cases)
         return (target_growth_rate - exp_growth_rate)^2
     end
 
-    out = ABCDE(priors,cost,0.01; verbose=true, nparticles=100,generations=20,  parallel = true) #this one has better NaN handling
-    return out
+    out = ABCDE(priors,cost,0.01; verbose=true, nparticles= 200,generations=20,  parallel = true) #this one has better NaN handling
+    return NamedTuple{p_names}((out.P.particles,))
 end
 
-
-function fit_behavioural_parameters(p_tuple, target_growth_rate)
+function fit_pre_inf_behavioural_parameters(p_tuple)
     samples = 1
-    p_names = (:π_base,:ρ_y,:ρ_m,:ρ_o)
-    priors = Factored(Uniform(-2.0,0.0),Uniform(0.0,1.0),Uniform(0.0,1.0),Uniform(0.0,1.0))
-    #simulation begins in august
-    #30 days for opinion dynamics to stabilize, then immunization begins in september,
-    #infection is introduced at the end of november 
-    sim_length = 120
+    p_names = (:π_base_y,:π_base_m,:π_base_o)
+    priors = Factored(
+        Uniform(-10.0,2.0),
+        Uniform(-10.0,2.0),
+        Uniform(-10.0,2.0)
+    )
+    
+    #simulation begins in july
+    #60 days for opinion dynamics to stabilize, then immunization begins in september,
+    #infection is not considered
+    
+    sim_length = 180
     p_tuple_adjust = merge(p_tuple,
         (
             sim_length = sim_length,
             I_0_fraction = 0.000,
             immunization_begin_day =60, 
-            infection_introduction_day = 91,
+            infection_introduction_day = 180,
             immunizing = true,
         )
     )
-    target_cumulative_vac_proportion = 0.33
-    vaccination_data = @SVector [0.0,0.043,0.385,0.424,0.115,0.03,0.005] #by month starting in august
-    ymo_vac = @SVector [0.255,0.278,0.602]
-    function cost(p)
-        new_params = merge(p_tuple_adjust, NamedTuple{p_names}(ntuple(i -> p[i],length(p_names))))
-        out = DebugRecorder(0,sim_length)
-        model = abm(new_params,out)
 
+    function cost(p)
+        output,model = solve_w_parameters(p_tuple_adjust, p_names,p)
         target_cumulative_vaccinations = target_cumulative_vac_proportion*model.nodes
         target_ymo_vac = ymo_vac .* sum(vaccination_data[1:4]) .* target_cumulative_vaccinations
-        ymo_vaccination_ts = out.new_ymo_immunization
+        ymo_vaccination_ts = output.new_ymo_immunization
         total_preinfection_vaccination = sum.(eachrow(ymo_vaccination_ts))
         # display(target_ymo_vac)
         # display(total_preinfection_vaccination)
         return sum((total_preinfection_vaccination .- target_ymo_vac).^2)    
     end
-#smc(priors,cost; verbose = true, nparticles = 100, parallel = true)#
-    out = ABCDE(priors,cost,1e6; verbose=true, nparticles=300,generations=100,  parallel = true) #this one has better NaN handling
-    return out
+    #smc(priors,cost; verbose = true, nparticles = 100, parallel = true)# smc(priors,cost; verbose = true, nparticles =300, parallel = true)#
+    out = smc(priors,cost; verbose = true, nparticles = 800, parallel = true)#
+    return NamedTuple{p_names}(ntuple(i -> out.P[i].particles,length(p_names)))
 end
 
+function fit_post_inf_behavioural_parameters(p_tuple)
+    samples = 1
+    p_names = (:ω,)
+    priors = Factored(Uniform(0.0,0.1))
+    #simulation begins in july
+    #60 days for opinion dynamics to stabilize, then immunization begins in september,
+    #infection introduced at beginning of december
+    sim_length = 300
+    p_tuple_adjust = merge(p_tuple,
+        (
+            sim_length = sim_length,
+            I_0_fraction = 0.002,
+            immunization_begin_day =60, 
+            infection_introduction_day = 180,
+            immunizing = true,
+        )
+    )
+    target_cumulative_vac_proportion = 0.33
+    vaccination_data = @SVector [0.0,0.043,0.385,0.424,0.115,0.03,0.005] #by month starting in august
+    ymo_vac = @SVector [0.255,0.278,0.602]
+    function cost(p)
+        output,model = solve_w_parameters(p_tuple_adjust, p_names,p)
+        target_cumulative_vaccinations = target_cumulative_vac_proportion*model.nodes
+        target_ymo_vac = ymo_vac .* sum(vaccination_data[5:end]) .* target_cumulative_vaccinations
+        ymo_vaccination_ts = output.new_ymo_immunization
+        total_vaccination = sum.(eachrow(ymo_vaccination_ts[:,180:end]))
+        return sum((total_vaccination .- target_ymo_vac).^2)    
+    end
+    out =smc(priors,cost; verbose = true, nparticles = 200, parallel = true)# ABCDE(priors,cost,1e6; verbose=true, nparticles=300,generations=1000,  parallel = true) #this one has better NaN handling
+    return NamedTuple{p_names}((out.P.particles,))
+end
 
 function plot_behavioural_fit(particles,p_tuple)
-    p_names = (:π_base, :ρ_y,:ρ_m,:ρ_o)
+    p_names = (:π_base_y,:π_base_m,:π_base_o)
     sim_length = 210
     samples = 1
     p_tuple_adjust = merge(p_tuple,
-    (
+        (
             sim_length = sim_length,
             I_0_fraction = 0.000,
             immunization_begin_day =60, 
-            infection_introduction_day = 91,
             immunizing = true,
         )
     )
@@ -108,10 +138,84 @@ function plot_behavioural_fit(particles,p_tuple)
     ymo_vaccination_ts = mean.(out.new_ymo_immunization)
     total_preinfection_vaccination = sum.(eachrow(ymo_vaccination_ts))
     display(total_preinfection_vaccination)
+    p = [plot(),plot(),plot()]
+
     p = plot_model(nothing,[nothing],[out],new_params.infection_introduction_day,new_params.immunization_begin_day)
     savefig(p,"behaviour_fit.pdf")
     return out
 end
+# outbreak_transmission_dist = CovidAlertVaccinationModel.fit_epi_parameters(default_parameters,0.241) ##outbreak
+# serialize(joinpath(PACKAGE_FOLDER,"abm_parameter_fits","outbreak_inf_parameters.dat"),outbreak_transmission_dist)
+# plot_max_posterior("outbreak", outbreak_transmission_dist,default_parameters)
+
+function fit_parameters(default_parameters)
+    seasonal_parameters_path = joinpath(PACKAGE_FOLDER,"abm_parameter_fits","outbreak_inf_parameters.dat")
+    pre_inf_behaviour_parameters_path =joinpath(PACKAGE_FOLDER,"abm_parameter_fits","pre_inf_behaviour_parameters.dat")
+    post_inf_behaviour_parameters_path = joinpath(PACKAGE_FOLDER,"abm_parameter_fits","post_inf_behaviour_parameters.dat")
+
+    seasonal_transmission_dist = CovidAlertVaccinationModel.fit_epi_parameters(default_parameters,0.073) ##seasonal
+    plot_max_posterior("seasonal", seasonal_transmission_dist,default_parameters)
+    pre_inf_behaviour_parameters = CovidAlertVaccinationModel.fit_pre_inf_behavioural_parameters(default_parameters)
+    fitted_parameters = map(mode,((;seasonal_transmission_dist...,pre_inf_behaviour_parameters...)))
+    fitted_parameter_tuple = merge(default_parameters,fitted_parameters)
+
+    serialize(seasonal_parameters_path,seasonal_transmission_dist)
+    serialize(pre_inf_behaviour_parameters_path, pre_inf_behaviour_parameters)
+
+    post_inf_behaviour_parameters = fit_post_inf_behavioural_parameters(fitted_parameter_tuple) 
+    serialize(post_inf_behaviour_parameters_path, post_inf_behaviour_parameters)
+    
+    
+
+    fitted_parameters_with_post_inf_behaviour = (;
+        deserialize(seasonal_parameters_path)...,
+        deserialize(pre_inf_behaviour_parameters_path)...,
+        deserialize(post_inf_behaviour_parameters_path)...
+    )
+    display(map(mode,fitted_parameters_with_post_inf_behaviour))
+    return plot_fitting_posteriors("post_inf_fitting",fitted_parameters_with_post_inf_behaviour,default_parameters)
+end 
+
+function plot_max_posterior(fname,particles,parameters)
+    samples = 5
+    base_transmission = mode(particles.base_transmission_probability)
+    p_tuple_without_vac = merge(parameters,
+        (
+            sim_length = 150,
+            immunization_begin_day = 0,
+            infection_introduction_day = 1,
+            immunizing = false,
+        )
+    )
+    new_params = merge(p_tuple_without_vac, (base_transmission_probability = base_transmission,))
+    out = mean_solve(samples, new_params ,DebugRecorder)
+    p = plot_model(nothing,[nothing],[out],new_params.infection_introduction_day,new_params.immunization_begin_day)
+    savefig(p,"$fname.pdf")
+    hist = StatsBase.fit(Histogram,particles.base_transmission_probability; nbins = 25)
+    p = plot(hist;legend = false)
+    savefig(p,"$(fname)_posterior.pdf")
+end
 
-#once we have vaccine parameters, with seasonal, look at cumulative infections
-#
+function plot_fitting_posteriors(fname,particles_tuple,parameters)
+    p_tuple_adjust = merge(parameters,
+        (
+            sim_length = 500,
+            I_0_fraction = 0.002,
+            immunization_begin_day =60, 
+            infection_introduction_day = 180,
+            immunizing = true,
+        )
+    )
+    out = mean_solve(5, merge(p_tuple_adjust,map(mode,particles_tuple)) ,DebugRecorder)
+    p = plot_model(nothing,[nothing],[out],parameters.infection_introduction_day,parameters.immunization_begin_day)
+    savefig(p, "$fname.pdf")
+    
+    plts = [plot() for i in 1:length(particles_tuple)]
+    for (plt,(k,v)) in zip(plts,pairs(particles_tuple))
+        hist = StatsBase.fit(Histogram,v; nbins = 40)
+        plot!(plt,hist;legend = false,xlabel = k)            
+    end
+    p = plot(plts...; size = (1000,600))
+    savefig(p,"$(fname)_posteriors.pdf")
+    return out
+end

CovidAlertVaccinationModel/src/ABM/solve.jl

@@ -146,11 +146,9 @@ Base.@propagate_inbounds @views function update_vaccination_opinion_state!(t,mod
         vac_payoff = 0
         num_soc_nbrs = 0
         random_soc_network = sample(Random.default_rng(Threads.threadid()), soc_network.graph_list[t])
-        # display(random_soc_network)
 
         if !isempty(neighbors(random_soc_network.g,i))
             random_neighbour = sample(Random.default_rng(Threads.threadid()), neighbors(random_soc_network.g,i))
-
             if u_vac[random_neighbour] == u_vac[i]
                 vac_payoff += π_base[Int(demographics[i])] + total_infections*ω             
                 if app_user[i] && time_of_last_alert[app_user_list[i]]>=0
@@ -169,7 +167,9 @@ Base.@propagate_inbounds @views function update_vaccination_opinion_state!(t,mod
             end
         end
     end
+
     modelsol.daily_vaccinators = count(==(true),u_vac) #could maybe make this more efficient
+
 end
 
 

CovidAlertVaccinationModel/src/CovidAlertVaccinationModel.jl

@@ -24,7 +24,6 @@ using KissABC
 using CSV
 import Pandas: read_csv
 using DataFrames
-using VectorizedRNG
 using StaticArrays
 import LightGraphs.neighbors