diff --git a/notebooks/sis_heterogeneous_compare_homogeneous.ipynb b/notebooks/sis_heterogeneous_compare_homogeneous.ipynb
index ba24ba79..3bc26d13 100644
--- a/notebooks/sis_heterogeneous_compare_homogeneous.ipynb
+++ b/notebooks/sis_heterogeneous_compare_homogeneous.ipynb
@@ -23,7 +23,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -70,63 +70,63 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "\u001b[32mRunning MPBP: iter 2    Time: 0:00:53\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 2    Time: 0:00:44\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 3    Time: 0:00:56\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 3    Time: 0:00:47\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 4    Time: 0:00:58\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 4    Time: 0:00:49\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 5    Time: 0:01:01\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 5    Time: 0:00:51\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 6    Time: 0:01:03\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 6    Time: 0:00:53\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 7    Time: 0:01:06\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 7    Time: 0:00:55\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 8    Time: 0:01:08\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 8    Time: 0:00:57\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 9    Time: 0:01:11\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 9    Time: 0:01:00\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 10    Time: 0:01:13\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 10    Time: 0:01:02\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 11    Time: 0:01:16\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 11    Time: 0:01:04\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 12    Time: 0:01:18\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 12    Time: 0:01:06\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 13    Time: 0:01:21\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 13    Time: 0:01:08\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 14    Time: 0:01:23\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 14    Time: 0:01:10\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 15    Time: 0:01:26\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 15    Time: 0:01:12\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 16    Time: 0:01:28\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 16    Time: 0:01:14\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 17    Time: 0:01:31\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 17    Time: 0:01:17\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 18    Time: 0:01:33\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 18    Time: 0:01:19\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 19    Time: 0:01:36\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 19    Time: 0:01:21\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 20    Time: 0:01:38\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 20    Time: 0:01:23\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 21    Time: 0:01:41\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 21    Time: 0:01:25\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 22    Time: 0:01:43\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 22    Time: 0:01:27\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 23    Time: 0:01:46\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 23    Time: 0:01:29\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 24    Time: 0:01:48\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 24    Time: 0:01:31\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 25    Time: 0:01:51\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 25    Time: 0:01:34\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 26    Time: 0:01:53\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 26    Time: 0:01:36\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 27    Time: 0:01:56\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 27    Time: 0:01:38\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 28    Time: 0:01:58\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 28    Time: 0:01:40\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 29    Time: 0:02:00\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 29    Time: 0:01:42\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 30    Time: 0:02:03\u001b[39m\u001b[K"
+      "\u001b[32mRunning MPBP: iter 30    Time: 0:01:44\u001b[39m\u001b[K"
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@@ -156,7 +156,7 @@
       "\n",
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       "\n",
-      "\u001b[32mRunning MPBP: iter 7    Time: 0:00:18\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 7    Time: 0:00:17\u001b[39m\u001b[K\n",
       "\n",
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@@ -164,39 +164,39 @@
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       "\n",
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+      "\u001b[32mRunning MPBP: iter 11    Time: 0:00:26\u001b[39m\u001b[K\n",
       "\n",
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       "\n",
       "\u001b[32mRunning MPBP: iter 13    Time: 0:00:31\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 14    Time: 0:00:34\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 14    Time: 0:00:33\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 15    Time: 0:00:36\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 15    Time: 0:00:35\u001b[39m\u001b[K\n",
       "\n",
       "\u001b[32mRunning MPBP: iter 16    Time: 0:00:38\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 17    Time: 0:00:41\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 17    Time: 0:00:40\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 18    Time: 0:00:43\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 18    Time: 0:00:42\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 19    Time: 0:00:45\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 19    Time: 0:00:44\u001b[39m\u001b[K\n",
       "\n",
       "\u001b[32mRunning MPBP: iter 20    Time: 0:00:47\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 21    Time: 0:00:50\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 21    Time: 0:00:49\u001b[39m\u001b[K\n",
       "\n",
       "\u001b[32mRunning MPBP: iter 22    Time: 0:00:52\u001b[39m\u001b[K\n",
       "\n",
       "\u001b[32mRunning MPBP: iter 23    Time: 0:00:54\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 24    Time: 0:00:57\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 24    Time: 0:00:56\u001b[39m\u001b[K\n",
       "\n",
       "\u001b[32mRunning MPBP: iter 25    Time: 0:00:59\u001b[39m\u001b[K\n",
       "\n",
       "\u001b[32mRunning MPBP: iter 26    Time: 0:01:01\u001b[39m\u001b[K\n",
       "\n",
-      "\u001b[32mRunning MPBP: iter 27    Time: 0:01:04\u001b[39m\u001b[K\n",
+      "\u001b[32mRunning MPBP: iter 27    Time: 0:01:03\u001b[39m\u001b[K\n",
       "\n",
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@@ -225,123 +225,123 @@
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@@ -8371,108 +8371,108 @@
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+       "<path clip-path=\"url(#clip262)\" d=\"M1126.69 437.904 L1118.2 434.388 L1114.69 425.904 L1118.2 417.42 L1126.69 413.904 L1135.17 417.42 L1138.69 425.904 L1135.17 434.388 Z\" fill=\"#f05f73\" fill-rule=\"evenodd\" fill-opacity=\"1\" stroke=\"none\"/>\n",
        "</svg>\n"
       ]
      },
diff --git a/src/MatrixProductBP.jl b/src/MatrixProductBP.jl
index a3327682..c7907399 100644
--- a/src/MatrixProductBP.jl
+++ b/src/MatrixProductBP.jl
@@ -2,7 +2,7 @@ module MatrixProductBP
 
 using InvertedIndices: Not
 using ProgressMeter: Progress, ProgressUnknown, next!
-using TensorCast: @reduce, @cast, TensorCast 
+using TensorCast: @reduce, @cast, TensorCast
 using LoopVectorization
 using Tullio: @tullio
 using IndexedGraphs: IndexedGraphs, AbstractIndexedDiGraph, IndexedGraph, IndexedBiDiGraph,
@@ -10,7 +10,7 @@ using IndexedGraphs: IndexedGraphs, AbstractIndexedDiGraph, IndexedGraph, Indexe
     issymmetric
 using UnPack: @unpack
 using Random: shuffle!, AbstractRNG, GLOBAL_RNG
-using SparseArrays: rowvals, nonzeros, nzrange
+using SparseArrays: rowvals, nonzeros, nzrange, sparse
 using Distributions: Distributions, sample, sample!
 using Measurements: Measurement, ±
 using Statistics: mean, std
diff --git a/src/Models/Models.jl b/src/Models/Models.jl
index e025bb5e..b6f6096b 100644
--- a/src/Models/Models.jl
+++ b/src/Models/Models.jl
@@ -11,7 +11,7 @@ using MatrixProductBP
 import IndexedGraphs: IndexedGraph, IndexedBiDiGraph, AbstractIndexedDiGraph, ne, nv, 
     outedges, idx, src, dst, inedges, neighbors, edges, vertices, IndexedEdge
 import UnPack: @unpack
-import SparseArrays: nonzeros, nzrange, rowvals, Symmetric, SparseMatrixCSC
+import SparseArrays: nonzeros, nzrange, rowvals, Symmetric, SparseMatrixCSC, sparse
 import TensorCast: @reduce, @cast, TensorCast 
 import ProgressMeter: Progress, next!, ProgressUnknown
 import LogExpFunctions: xlogx, xlogy
diff --git a/src/Models/epidemics/sis_heterogeneous.jl b/src/Models/epidemics/sis_heterogeneous.jl
index 9f21a9b0..6917f536 100644
--- a/src/Models/epidemics/sis_heterogeneous.jl
+++ b/src/Models/epidemics/sis_heterogeneous.jl
@@ -1,6 +1,6 @@
 struct SIS_heterogeneous{T, N, F<:Real}
     g  :: IndexedGraph
-    λ  :: SparseMatrixCSC{F,Int64}
+    λ  :: Vector{F}
     ρ  :: Vector{F}
     ϕ  :: Vector{Vector{Vector{F}}}  # site observations
     ψ  :: Vector{Vector{Matrix{F}}}  # edge observations
@@ -17,7 +17,7 @@ struct SIS_heterogeneous{T, N, F<:Real}
         @assert all(length(ϕᵢ) == T + 1 for ϕᵢ in ϕ)
         @assert length(ψ) == 2*ne(g)
         @assert all(length(ψᵢⱼ) == T + 1 for ψᵢⱼ in ψ)
-        new{T,N,F}(g, λ, ρ, ϕ, ψ)
+        new{T,N,F}(g, nonzeros(λ), ρ, ϕ, ψ)
     end
 end
 
@@ -37,5 +37,5 @@ function SIS_heterogeneous(λ::SparseMatrixCSC{F,Int64}, ρ::Vector{F}, T::Int;
 end
 
 function sis_heterogeneous_factors(sis::SIS_heterogeneous{T,N,F}) where {T,N,F}
-    [fill(SIS_heterogeneousFactor([sis.λ[j,i] for j in sis.λ.rowval[nzrange(sis.λ,i)]], sis.ρ[i]), T + 1) for i in vertices(sis.g)]
+    [fill(SIS_heterogeneousFactor(sis.λ[nzrange(sis.g.A,i)], sis.ρ[i]), T + 1) for i in vertices(sis.g)]
 end
\ No newline at end of file
diff --git a/test/Project.toml b/test/Project.toml
index 56738865..d27a58f0 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -4,5 +4,6 @@ Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 IndexedGraphs = "8a731c18-cfb7-4915-927e-cc26b56b67cd"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 TensorTrains = "89893e69-996d-40b1-ba32-8ff5f34c0dd5"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff --git a/test/runtests.jl b/test/runtests.jl
index 9edc7f27..4dc3c466 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,6 +1,6 @@
 using Test, MatrixProductBP
 using MatrixProductBP.Models
-using Graphs, IndexedGraphs, Random, Distributions
+using Graphs, IndexedGraphs, Random, Distributions, SparseArrays
 using TensorTrains
 using Aqua
 
@@ -19,6 +19,7 @@ include("pair_observations.jl")
 include("periodic.jl")
 include("sampling.jl")
 include("sirs_small_tree.jl")
+include("sis_heterogeneous_compare_homogeneous.jl")
 include("sis_infinite_graph.jl")
 include("sis_small_tree.jl")