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pith:NP6QHBHL

pith:2026:NP6QHBHLC7WIDL63H6P3ADXCKK

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The interplay of network structure and correlated infectious traits in epidemic models

Abhay Gupta, Nicholas W. Landry

A framework with joint distributions of susceptibility and transmissibility across network subgroups yields analytical expressions for the basic reproduction number in SIR models.

arxiv:2605.12773 v1 · 2026-05-12 · q-bio.PE · physics.soc-ph

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Claims

C1strongest claim

We derive analytical expressions for the basic reproduction number, which, when reduced, corroborates prior results and validate these results with numerical simulations.

C2weakest assumption

The framework assumes that population subgroups can be defined with independent joint distributions of susceptibility and transmissibility that interact with network structure in a way that permits closed-form reproduction-number expressions; this may not hold if real correlations between traits and network position are more complex or data-driven.

C3one line summary

A new modeling framework for SIR epidemics incorporates joint distributions of susceptibility and transmissibility across network subgroups, producing analytical basic reproduction numbers that reduce to known results and are validated by simulations.

References

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[1] In the following, we analytically derive the eigenval- ues ofJfor several common network models to obtain an analytical expression forR 0. B. Random mixing Here, we assume a single subpopulation, i.e.

[2] In this case, N(g 1) =N(g 2) =N/2, P(g 1 |g 1) =P(g 2 |g 2) =p in, P(g 1 |g 2) =P(g 2 |g 1) =p out

[3] We specify that N(g 1) =rN, andN(g 2) = (1−r)N(whereris the fraction of individuals in community 1)

[4] Then, individual 8 values ofδandεwere sampled from this distribution, with different Σ values for each community

[5] W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Chara 1927

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Receipt and verification

First computed	2026-05-18T03:09:20.071379Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6bfd0384eb17ec81afdb3f9fb00ee2528817df608611a302d0ddeaa180580eb2

Aliases

arxiv: 2605.12773 · arxiv_version: 2605.12773v1 · doi: 10.48550/arxiv.2605.12773 · pith_short_12: NP6QHBHLC7WI · pith_short_16: NP6QHBHLC7WIDL63 · pith_short_8: NP6QHBHL

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/NP6QHBHLC7WIDL63H6P3ADXCKK \
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  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
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Canonical record JSON

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    "abstract_canon_sha256": "5a1ca2b498c9ac534e2970c31bf65f89013d6432771201f6e5e5b05cce71ac6b",
    "cross_cats_sorted": [
      "physics.soc-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "q-bio.PE",
    "submitted_at": "2026-05-12T21:35:43Z",
    "title_canon_sha256": "06c913d7585685c8883d8a5f737e869e899eb152be6800fadaa82c9bc67fd5a3"
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  "source": {
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    "kind": "arxiv",
    "version": 1
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}