SIR Model: JumpProcesses.jl vs Gillespie.jl External Library Comparison

This benchmark compares JumpProcesses.jl's SSA aggregators against Gillespie.jl, a standalone implementation of Gillespie's direct method, on the standard SIR epidemic model. This addresses SciMLBenchmarks.jl#27, which requested comparisons against other Gillespie SSA libraries in addition to the existing aggregator-vs-aggregator benchmarks in this folder.

using JumpProcesses, Gillespie
using Random, Statistics, DataFrames, StatsPlots
fmt = :png

:png

Model and setup

The susceptible-infected-recovered (SIR) model has state (S, I, R) and two reactions

\[S + I \overset{\beta}{\rightarrow} 2I, \qquad I \overset{\gamma}{\rightarrow} R\]

The same initial condition, rates, and end time are used for both libraries, taken from the SIR example in the Gillespie.jl README.

u0 = [999, 1, 0]
p = (β = 0.1 / 1000.0, γ = 0.01)
tf = 250.0

250.0

Gillespie.jl

function F(x, params)
    (S, I, R) = x
    (β, γ) = params
    infection = β * S * I
    recovery = γ * I
    [infection, recovery]
end

nu = [[-1 1 0]; [0 -1 1]]
gillespie_params = [p.β, p.γ]

Random.seed!(1234)
result = ssa(u0, F, nu, gillespie_params, tf)
data = ssa_data(result)
first(data, 5)

5×4 DataFrame
 Row │ time      x1     x2     x3
     │ Float64   Int64  Int64  Int64
─────┼───────────────────────────────
   1 │  0.0        999      1      0
   2 │  5.06671    998      2      0
   3 │  6.45689    997      3      0
   4 │  8.62597    996      4      0
   5 │ 13.0211     995      5      0

JumpProcesses.jl

rate1(u, p, t) = p.β * u[1] * u[2]
function affect1!(integrator)
    integrator.u[1] -= 1
    integrator.u[2] += 1
end
jump1 = ConstantRateJump(rate1, affect1!)

rate2(u, p, t) = p.γ * u[2]
function affect2!(integrator)
    integrator.u[2] -= 1
    integrator.u[3] += 1
end
jump2 = ConstantRateJump(rate2, affect2!)

dprob = DiscreteProblem(u0, (0.0, tf), p)

DiscreteProblem with uType Vector{Int64} and tType Float64. In-place: true
timespan: (0.0, 250.0)
u0: 3-element Vector{Int64}:
 999
   1
   0

Benchmarking performance of the methods

We compare Gillespie.jl's ssa (Gillespie's direct method) against the JumpProcesses.jl aggregators that work directly on ConstantRateJumps without requiring a precomputed dependency graph.

methods = (Direct(), FRM())
shortlabels = [string(nameof(typeof(leg))) for leg in methods]
labels = vcat(["Gillespie.jl"], shortlabels)

3-element Vector{String}:
 "Gillespie.jl"
 "Direct"
 "FRM"

function run_benchmark!(t, f)
    f()
    @inbounds for i in 1:length(t)
        t[i] = @elapsed f()
    end
end

run_benchmark! (generic function with 1 method)

nsims = 2000
benchmarks = Vector{Vector{Float64}}()

t = Vector{Float64}(undef, nsims)
run_benchmark!(t, () -> ssa(u0, F, nu, gillespie_params, tf))
push!(benchmarks, t)

for method in methods
    local t
    jump_prob = JumpProblem(
        dprob, method, jump1, jump2; save_positions = (false, false))
    stepper = SSAStepper()
    t = Vector{Float64}(undef, nsims)
    run_benchmark!(t, () -> solve(jump_prob, stepper))
    push!(benchmarks, t)
end

medtimes = Vector{Float64}(undef, length(labels))
stdtimes = Vector{Float64}(undef, length(labels))
avgtimes = Vector{Float64}(undef, length(labels))
for i in 1:length(labels)
    medtimes[i] = median(benchmarks[i])
    avgtimes[i] = mean(benchmarks[i])
    stdtimes[i] = std(benchmarks[i])
end
medtimes / medtimes[1]

3-element Vector{Float64}:
 1.0
 0.3770166630608188
 0.3832443329215253

df = DataFrame(
    names = labels, medtimes = medtimes, relmedtimes = (medtimes / medtimes[1]),
    avgtimes = avgtimes, std = stdtimes, cv = stdtimes ./ avgtimes)
sa = [text(string(round(mt * 1000, sigdigits = 3), "ms"), :center, 10) for mt in df.medtimes]
bar(df.names, df.medtimes * 1000, legend = false, fmt = fmt)
scatter!(df.names, 0.05 .+ df.medtimes * 1000, markeralpha = 0,
    series_annotations = sa, fmt = fmt)
ylabel!("median time (ms)")
title!("SIR Model: JumpProcesses.jl vs Gillespie.jl")

Appendix

These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: https://github.com/SciML/SciMLBenchmarks.jl. For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization https://sciml.ai.

To locally run this benchmark, do the following commands:

using SciMLBenchmarks
SciMLBenchmarks.weave_file("benchmarks/Jumps","SIR_GillespieComparison.jmd")

Computer Information:

Julia Version 1.10.12
Commit d93beab124c (2026-08-15 10:29 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 128 × AMD EPYC 7502 32-Core Processor
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
Threads: 128 default, 0 interactive, 64 GC (on 128 virtual cores)
Environment:
  JULIA_NUM_THREADS = auto

Package Information:

Status `~/github-runners/amdci3-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/Jumps/Project.toml`
  [6e4b80f9] BenchmarkTools v1.8.0
  [479239e8] Catalyst v16.4.0
  [8f4d0f93] Conda v1.10.3
  [a93c6f00] DataFrames v1.8.2
  [0c46a032] DifferentialEquations v8.1.1
⌃ [31c24e10] Distributions v0.25.127
  [523d8e89] Gillespie v0.2.0
⌃ [86223c79] Graphs v1.14.0
  [faf0f6d7] JumpProblemLibrary v2.0.3
⌃ [ccbc3e58] JumpProcesses v9.32.0
⌃ [961ee093] ModelingToolkit v11.41.0
  [1dea7af3] OrdinaryDiffEq v7.8.1
  [86206cdf] PiecewiseDeterministicMarkovProcesses v0.0.12
  [91a5bcdd] Plots v1.41.7
  [438e738f] PyCall v1.96.4
  [b4db0fb7] ReactionNetworkImporters v1.5.0
⌃ [31c91b34] SciMLBenchmarks v0.1.3
  [860ef19b] StableRNGs v1.0.4
  [f3b207a7] StatsPlots v0.15.8
⌃ [c3572dad] Sundials v6.6.0
  [2efcf032] SymbolicIndexingInterface v0.3.55
  [37e2e46d] LinearAlgebra
  [9a3f8284] Random
  [10745b16] Statistics v1.10.0
Info Packages marked with ⌃ have new versions available and may be upgradable.

And the full manifest:

Status `~/github-runners/amdci3-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/Jumps/Manifest.toml`
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  [f151be2c] EnzymeCore v0.8.21
  [e2ba6199] ExprTools v0.1.11
  [55351af7] ExproniconLite v0.10.14
  [c87230d0] FFMPEG v0.4.5
  [b86e33f2] FFTA v0.3.1
  [7034ab61] FastBroadcast v1.4.0
  [9aa1b823] FastClosures v0.3.2
  [a4df4552] FastPower v1.5.0
  [1a297f60] FillArrays v1.17.0
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⌅ [53c48c17] FixedPointNumbers v0.8.6
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  [523d8e89] Gillespie v0.2.0
  [d7ba0133] Git v1.5.0
⌃ [86223c79] Graphs v1.14.0
⌅ [eafb193a] Highlights v0.5.3
  [34004b35] HypergeometricFunctions v0.3.30
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⌃ [3263718b] ImplicitDiscreteSolve v2.2.1
  [d25df0c9] Inflate v0.1.5
⌅ [842dd82b] InlineStrings v1.4.6
  [18e54dd8] IntegerMathUtils v0.1.4
  [a98d9a8b] Interpolations v0.16.3
  [8197267c] IntervalSets v0.7.14
  [3587e190] InverseFunctions v0.1.17
  [41ab1584] InvertedIndices v1.3.1
  [92d709cd] IrrationalConstants v0.2.6
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  [1019f520] JLFzf v0.1.11
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⌅ [682c06a0] JSON v0.21.4
  [ae98c720] Jieko v0.2.1
  [faf0f6d7] JumpProblemLibrary v2.0.3
⌃ [ccbc3e58] JumpProcesses v9.32.0
  [5ab0869b] KernelDensity v0.6.12
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  [b964fa9f] LaTeXStrings v1.4.1
  [23fbe1c1] Latexify v0.16.12
  [87fe0de2] LineSearch v0.1.16
⌃ [7ed4a6bd] LinearSolve v5.15.1
  [2ab3a3ac] LogExpFunctions v1.0.1
  [e6f89c97] LoggingExtras v1.2.0
  [1914dd2f] MacroTools v0.5.16
  [bb5d69b7] MaybeInplace v0.1.8
  [442fdcdd] Measures v0.3.3
  [e1d29d7a] Missings v1.2.0
⌃ [961ee093] ModelingToolkit v11.41.0
⌃ [7771a370] ModelingToolkitBase v1.68.2
  [6bb917b9] ModelingToolkitTearing v1.20.6
  [2e0e35c7] Moshi v0.3.12
  [46d2c3a1] MuladdMacro v0.2.7
  [102ac46a] MultivariatePolynomials v0.5.19
  [6f286f6a] MultivariateStats v0.10.5
  [ffc61752] Mustache v1.0.21
  [d8a4904e] MutableArithmetics v1.8.0
  [77ba4419] NaNMath v1.1.4
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  [a2964d1f] Wayland_jll v1.24.0+0
  [ffd25f8a] XZ_jll v5.8.3+0
  [f67eecfb] Xorg_libICE_jll v1.1.2+0
  [c834827a] Xorg_libSM_jll v1.2.6+0
  [4f6342f7] Xorg_libX11_jll v1.8.13+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.13+0
  [935fb764] Xorg_libXcursor_jll v1.2.4+0
  [a3789734] Xorg_libXdmcp_jll v1.1.6+0
  [1082639a] Xorg_libXext_jll v1.3.8+0
  [d091e8ba] Xorg_libXfixes_jll v6.0.2+0
  [a51aa0fd] Xorg_libXi_jll v1.8.4+0
  [d1454406] Xorg_libXinerama_jll v1.1.7+0
  [ec84b674] Xorg_libXrandr_jll v1.5.6+0
  [ea2f1a96] Xorg_libXrender_jll v0.9.12+0
  [a65dc6b1] Xorg_libpciaccess_jll v0.19.0+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.1+0
  [cc61e674] Xorg_libxkbfile_jll v1.2.0+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.6+0
  [12413925] Xorg_xcb_util_image_jll v0.4.1+0
  [2def613f] Xorg_xcb_util_jll v0.4.1+0
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.1+0
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.10+0
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.2+0
  [35661453] Xorg_xkbcomp_jll v1.4.7+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.47.0+2
  [c5fb5394] Xorg_xtrans_jll v1.6.0+0
  [8f1865be] ZeroMQ_jll v4.3.6+0
  [3161d3a3] Zstd_jll v1.5.7+1
  [35ca27e7] eudev_jll v3.2.14+0
⌅ [214eeab7] fzf_jll v0.61.1+0
  [a4ae2306] libaom_jll v3.14.1+0
  [0ac62f75] libass_jll v0.17.5+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [8e53e030] libdrm_jll v2.4.134+0
  [2db6ffa8] libevdev_jll v1.13.4+0
  [f638f0a6] libfdk_aac_jll v2.0.4+0
  [36db933b] libinput_jll v1.28.1+0
  [b53b4c65] libpng_jll v1.6.58+0
  [a9144af2] libsodium_jll v1.0.21+0
  [9a156e7d] libva_jll v2.23.0+0
  [f27f6e37] libvorbis_jll v1.3.8+0
  [009596ad] mtdev_jll v1.1.7+0
  [1317d2d5] oneTBB_jll v2022.3.0+0
⌅ [1270edf5] x264_jll v10164.0.1+0
  [dfaa095f] x265_jll v4.1.0+0
  [d8fb68d0] xkbcommon_jll v1.13.0+0
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.10.0
  [de0858da] Printf
  [9abbd945] Profile
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.1.2+1
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.1010+0
  [14a3606d] MozillaCACerts_jll v2025.12.2
  [4536629a] OpenBLAS_jll v0.3.23+5
  [05823500] OpenLibm_jll v0.8.5+0
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.6.1+0
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`