THERMAL SCIENCE

International Scientific Journal

EPIDEMIC SPREAD MODELING IN HETEROGENEOUS NETWORKS INTEGRATING BARABASI-ALBERT NETWORK AND SIRS MODEL WITH METHODOLOGICAL EXPLORATION AND FUTURE PROSPECTS

ABSTRACT
This paper integrates the Barabasi-Albert network model and the Susceptible-infectious-recovered-susceptible (SIRS) model to explore epidemic spread modeling in heterogeneous networks. Notwithstanding the simplifying assumptions inherent in the model and the absence of empirical verification, the proposed approach provides a theoretical foundation for comprehending multi-scale epidemic transmission. The Barabasi-Albert subnetworks and SIRS-based simulation method are described in detail, and they can be used to create a realistic network environment for further analysis. Subsequent research endeavors will center on the implementation of this framework in relation to authentic data and the integration of more intricate elements, such as human behavior and environmental factors.
KEYWORDS
PAPER SUBMITTED: 2024-12-15
PAPER REVISED: 2025-03-21
PAPER ACCEPTED: 2025-03-23
PUBLISHED ONLINE: 2026-04-12
DOI REFERENCE: https://doi.org/10.2298/TSCI2602899L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2026, VOLUME 30, ISSUE No. 2, PAGES [899 - 906]
REFERENCES
[1] Dietz, K., Heesterbeek, J. A. P., Daniel Bernoulli's Epidemiological Model Revisited, Mathematical Biosciences, 180 (2002), 1, pp. 1-21
[2] Kermack, W. O., McKendrick, A. G., Contributions to the Mathematical Theory of Epidemics - II. The Problem of Endemicity, Bulletin of Mathematical Biology, 53 (1991), 1, pp. 57-87
[3] Furushima, D., et al., Estimation of the Basic Reproduction Numbers of Novel Influenza a (H1N1) pdm09 in Elementary Schools Using the SIR Model, TONURSJ-11-64, The Open Nursing Journal, 11 (2017), pp. 64-72
[4] Zhang, Y., et al., Unraveling Atherosclerosis: A Nonlinear Coupled Mathematical Model with Dual Free Boundaries - Solution and Numerical Insights. Journal of Applied and Computational Mechanics, 11 (2025), 4, pp. 1162-1171
[5] Alshomrani, N. A., et al., Homotopy Perturbation Method for Solving a Nonlinear System for an Epidemic0 Advances in Differential Equations and Control Processes, 31 (2024), 3, pp. 347-355
[6] Alsubaie, A. A., et al., Adomian's Method for Solving a Nonlinear Epidemic Model, Advances in Differential Equations and Control Processes, 31 (2024), 1, pp. 95-107
[7] Basnarkov, L., et al., Non-Markovian SIR Epidemic Spreading Model of COVID-19, Chaos, Solitons & Fractals, 160 (2022), 112286
[8] Ahmed, M., et al., Bifurcation Analysis and Optimal Control of Discrete SIR Model for COVID-19, Chaos, Solitons & Fractals, 174 (2023), 113899
[9] Yagasaki, K., Nonintegrability of the SEIR Epidemic Model, Physica D: Nonlinear Phenomena, 453 (2023), 133820
[10] Erdos, P., Renyi, A., On Random Graphs I, Publicationes Mathematicae, 6 (1959), pp. 290-297
[11] Watts, D. J., Strogatz, S. H., Collective Dynamics of ‘Small-World' Networks, Nature, 393 (1998), 6684, pp. 440-442
[12] Barabasi, A. L., Albert, R., Emergence of Scaling in Random Networks, Science, 286 (1999), 5439, pp. 509-512
[13] Kitsak, M., et al., Identification of Influential Spreaders in Complex Networks, Nature Physics, 6 (2010), 11, pp. 888-893
[14] He, J.-H., Transforming Frontiers: The Next Decade of Differential Equations and Control Processes, Advances in Differential Equations and Control Processes, 32 (2025), 1, 2589
[15] Li, H. B., et al., Correlation Analysis Based on Neural Network Copula Function, Thermal Science, 27 (2023) , 3A, pp. 2081-2089
[16] Nosonovsky, M., Aglikov, A. S. Triboinformatics: Machine Learning Methods for Frictional Instabilities, Facta Universitatis: Series Mechanical Engineering, 22 (2024), 3, pp. 423-433

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence