MODELING EPIDEMIC SPREAD USING TIME-DEPENDENT GRAPH DIFFUSION EQUATIONS ON COMPLEX NETWORKS

G. Sarmitha; S. Vidyanandini; M. B. Sanjay; Anushree Shrivastava; Ravinder Singh Kuntal

MODELING EPIDEMIC SPREAD USING TIME-DEPENDENT GRAPH DIFFUSION EQUATIONS ON COMPLEX NETWORKS

Abstract

Epidemic spread in real populations is shaped by changing contact patterns, uneven connectivity, and localized transmission, so static and uniformly mixed models are often not sufficient. Complex networks provide a stronger mathematical basis for representing these evolving interactions because they capture both structural heterogeneity and temporal variation. Existing research has examined temporal networks, multilayer epidemic systems, and graph-based transmission models, but many formulations still do not fully unify node-wise epidemic states, weighted graph diffusion, and time-dependent transmission in one solvable framework. A clear gap therefore remains in developing a mathematically consistent model that can represent epidemic propagation on evolving complex networks with both analytical and numerical clarity. This study addresses that gap by proposing a time-dependent graph diffusion model for epidemic spread. The paper focuses on developing the graph-mathematical formulation, deriving the governing equations, implementing an explicit numerical solution method, and testing the model on various network types, diffusion strengths, temporal transmission patterns, and intervention scenarios. Results demonstrate the significant impact of structure and time on epidemic spread, showing faster initial spread in scale-free networks, shifts in peak timing in evolving-contact graphs, and reduced outbreak severity under early intervention. The proposed framework offers a solid and practical basis for predicting epidemics on changing networks.

Keywords

References

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Details

Primary Language

English

Subjects

Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)

Journal Section

Research Article

Authors

G. Sarmitha This is me
0009-0004-3362-2751
India

S. Vidyanandini ^* This is me
0000-0002-4812-3259
India

M. B. Sanjay This is me
0009-0009-1035-3268
India

Anushree Shrivastava This is me
0009-0004-1474-5190
India

Ravinder Singh Kuntal This is me
0000-0003-1225-8108
India

Publication Date

July 4, 2026

Submission Date

April 24, 2025

Acceptance Date

September 17, 2025

Published in Issue

Year 2026 Volume: 16 Number: 7

IZ

https://izlik.org/JA25ZP92CF

Cite

RIS / Bibtex

APA

Sarmitha, G., Vidyanandini, S., Sanjay, M. B., Shrivastava, A., & Kuntal, R. S. (2026). MODELING EPIDEMIC SPREAD USING TIME-DEPENDENT GRAPH DIFFUSION EQUATIONS ON COMPLEX NETWORKS. TWMS Journal of Applied and Engineering Mathematics, 16(7), 901-918. https://izlik.org/JA25ZP92CF

AMA

1.Sarmitha G, Vidyanandini S, Sanjay MB, Shrivastava A, Kuntal RS. MODELING EPIDEMIC SPREAD USING TIME-DEPENDENT GRAPH DIFFUSION EQUATIONS ON COMPLEX NETWORKS. JAEM. 2026;16(7):901-918. https://izlik.org/JA25ZP92CF

Chicago

Sarmitha, G., S. Vidyanandini, M. B. Sanjay, Anushree Shrivastava, and Ravinder Singh Kuntal. 2026. “MODELING EPIDEMIC SPREAD USING TIME-DEPENDENT GRAPH DIFFUSION EQUATIONS ON COMPLEX NETWORKS”. TWMS Journal of Applied and Engineering Mathematics 16 (7): 901-18. https://izlik.org/JA25ZP92CF.

EndNote

Sarmitha G, Vidyanandini S, Sanjay MB, Shrivastava A, Kuntal RS (July 1, 2026) MODELING EPIDEMIC SPREAD USING TIME-DEPENDENT GRAPH DIFFUSION EQUATIONS ON COMPLEX NETWORKS. TWMS Journal of Applied and Engineering Mathematics 16 7 901–918.

IEEE

[1]G. Sarmitha, S. Vidyanandini, M. B. Sanjay, A. Shrivastava, and R. S. Kuntal, “MODELING EPIDEMIC SPREAD USING TIME-DEPENDENT GRAPH DIFFUSION EQUATIONS ON COMPLEX NETWORKS”, JAEM, vol. 16, no. 7, pp. 901–918, July 2026, [Online]. Available: https://izlik.org/JA25ZP92CF

ISNAD

Sarmitha, G. - Vidyanandini, S. - Sanjay, M. B. - Shrivastava, Anushree - Kuntal, Ravinder Singh. “MODELING EPIDEMIC SPREAD USING TIME-DEPENDENT GRAPH DIFFUSION EQUATIONS ON COMPLEX NETWORKS”. TWMS Journal of Applied and Engineering Mathematics 16/7 (July 1, 2026): 901-918. https://izlik.org/JA25ZP92CF.

JAMA

1.Sarmitha G, Vidyanandini S, Sanjay MB, Shrivastava A, Kuntal RS. MODELING EPIDEMIC SPREAD USING TIME-DEPENDENT GRAPH DIFFUSION EQUATIONS ON COMPLEX NETWORKS. JAEM. 2026;16:901–918.

MLA

Sarmitha, G., et al. “MODELING EPIDEMIC SPREAD USING TIME-DEPENDENT GRAPH DIFFUSION EQUATIONS ON COMPLEX NETWORKS”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 7, July 2026, pp. 901-18, https://izlik.org/JA25ZP92CF.

Vancouver

1.G. Sarmitha, S. Vidyanandini, M. B. Sanjay, Anushree Shrivastava, Ravinder Singh Kuntal. MODELING EPIDEMIC SPREAD USING TIME-DEPENDENT GRAPH DIFFUSION EQUATIONS ON COMPLEX NETWORKS. JAEM [Internet]. 2026 Jul. 1;16(7):901-18. Available from: https://izlik.org/JA25ZP92CF