ON THE EQUIVALENCE OF THE EFFECTIVE DEGREE NETWORK MODEL AND DYNAMICAL SURVIVAL ANALYSIS MODEL

Yue Wu; Shuixian Yan; Yueming Gu; Yan Zhang

doi:10.11948/20240466

2025 Volume 15 Issue 4

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Yue Wu, Shuixian Yan, Yueming Gu, Yan Zhang. ON THE EQUIVALENCE OF THE EFFECTIVE DEGREE NETWORK MODEL AND DYNAMICAL SURVIVAL ANALYSIS MODEL[J]. Journal of Applied Analysis & Computation, 2025, 15(4): 2340-2355. doi: 10.11948/20240466

Citation:

Yue Wu, Shuixian Yan, Yueming Gu, Yan Zhang. ON THE EQUIVALENCE OF THE EFFECTIVE DEGREE NETWORK MODEL AND DYNAMICAL SURVIVAL ANALYSIS MODEL[J]. Journal of Applied Analysis & Computation, 2025, 15(4): 2340-2355. doi: 10.11948/20240466

ON THE EQUIVALENCE OF THE EFFECTIVE DEGREE NETWORK MODEL AND DYNAMICAL SURVIVAL ANALYSIS MODEL

1.
School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China
2.
Rehabilitation College, Gannan Medical University, Ganzhou 341000, China

Author Bio: Email: 15979775648@163.com(Y. Wu); Email: 424172203@qq.com(Y. Gu); Email: 0700077@gnnu.edu.cn(Y. Zhang)
Corresponding author: Email: 0700046@gnnu.edu.cn(S. Yan)
Fund Project: This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 12161005, 12461098)

Abstract

Abstract

We delve into the existing effective degree model and dynamical survival analysis model for network epidemic dynamics. By employing the integrating factor method, we elaborate on the mutual derivation process between the two models, demonstrating their equivalence. Leveraging this result, the effective degree model is simplified to an equation that only involves susceptible individuals.
- Effective degree model /
- dynamical survival analysis model /
- equivalence
MSC: 92D30

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References

[1]	L. Cai, J. Liu, G. Fan and H. Chen, Lobal dynamics of a cholera model with age-of-immunity structure and reinfection, Journal of Applied Analysis & Computation, 2019, 9(5), 1731–1749. Google Scholar
[2]	L. Decreusefond, J. S. Dhersin, P. Moyal and V. C. Tran, Large graph limit for an SIR process in random network with heterogeneous connectivity, Annals of Applied Probability, 2012, 22(2), 541–575. Google Scholar
[3]	K. T. D. Eames and M. J. Keeling, Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases, Proceedings of the National Academy of Sciences, 2008, 99(20), 13330–13335. Google Scholar
[4]	J. Ge, Z. Lin and H. Zhu, Modeling the spread of west nile virus in a spa-tially heterogeneous and advective environment, Journal of Applied Analysis & Computation, 2021, 11(4), 1868–1897. Google Scholar
[5]	K. A. Jacobsen, M. G. Burch, J. H. Tien and G. A. Rempala, The large graph limit of a stochastic epidemic model on a dynamic multilayer network, Journal of Biological Dynamics, 2018, 12(1), 746–788. doi: 10.1080/17513758.2018.1515993 CrossRef Google Scholar
[6]	Z. Jin, S. Li, X. Zhang, J. Zhang and X. Peng, Epidemiological modeling on complex networks, Complex Systems and Networks: Dynamics, Controls and Applications, 2016, 51–77. Google Scholar
[7]	M. J. Keeling, The effects of local spatial structure on epidemiological invasions, Proceedings of the Royal Society of London. Series B: Biological Sciences, 1999, 266(1421), 859–867. doi: 10.1098/rspb.1999.0716 CrossRef Google Scholar
[8]	W. R. KhudaBukhsh, C. D. Bastian, M. Wascher, C. Klaus, S. Y. Sahai, M. Weir, E. Kenah, E. Root, J. H. Tien and G. Rem-Pala, Projecting COVID-19 cases and subsequent hospital burden in Ohio, Journal of Theoretical Biology, 2023, 561, 111404. doi: 10.1016/j.jtbi.2022.111404 CrossRef Google Scholar
[9]	W. R. KhudaBukhsh, B. Choi, E. Kenah and G. A. Rempala, Survival dynamical systems: Individual-level survival analysis from population-level epidemic models, Interface Focus, 2020, 10(1). DOI: 10.1098/rsfs.2019.0048. CrossRef Google Scholar
[10]	I. Z. Kiss, L. Berthouze and W. R. KhudaBukhsh, Towards inferring network properties from epidemic data, Bulletin of Mathematical Biology, 2024, 86(1), 6. doi: 10.1007/s11538-023-01235-3 CrossRef Google Scholar
[11]	I. Z. Kiss, I. Iacopini, P. L. Simon and N. Georgiou, Insights from exact social contagion dynamics on networks with higher-order structures, Journal of Complex Networks, 2023, 11(6), 044. Google Scholar
[12]	I. Z. Kiss, E. Kenah and G. A. Rempala, Necessary and sufficient conditions for exact closures of epidemic equations on configuration model networks, Journal of Mathematical Biology, 2023, 87(2), 36. doi: 10.1007/s00285-023-01967-9 CrossRef Google Scholar
[13]	I. Z. Kiss, J. C. Miller and P. L. Simon, Mathematics of Epidemics on Networks, Springer, 2017. Google Scholar
[14]	F. D. Lauro, W. R. KhudaBukhsh, I. Z. Kiss, E. Kenah, M. Jensen and G. A. Rempala, Dynamic survival analysis for non-Markovian epidemic models, Journal of The Royal Society Interface, 2022, 19(191), 20220124. doi: 10.1098/rsif.2022.0124 CrossRef Google Scholar
[15]	J. Lindquist, J. Ma, P. V. Driessche and F. H. Willeboordse, Effective degree network disease models, Journal of Mathematical Biology, 2011, 62, 143–164. doi: 10.1007/s00285-010-0331-2 CrossRef Google Scholar
[16]	J. C. Miller, A primer on the use of probability generating functions in infectious disease modeling, Infectious Disease Modelling, 2018, 3, 192–248. doi: 10.1016/j.idm.2018.08.001 CrossRef Google Scholar
[17]	J. C. Miller and I. Z. Kiss, Epidemic spread in networks: Existing methods and current challenges, Mathematical Modelling of Natural Phenomena, 2014, 9(2), 4–42. doi: 10.1051/mmnp/20149202 CrossRef Google Scholar
[18]	M. Molloy and B. Reed, A critical point for random graphs with a given degree sequence, Random Structures & Algorithms, 1995, 6(2–3), 161–180. Google Scholar
[19]	M. E. J. Newman, Spread of epidemic disease on networks, Physical Review E, 2002, 66(1), 016128. doi: 10.1103/PhysRevE.66.016128 CrossRef Google Scholar
[20]	M. E. J. Newman, S. H. Strogatz and D. J. Watts, Random graphs with arbitrary degree distributions and their applications, Physical Review E, 2001, 64(2), 026118. doi: 10.1103/PhysRevE.64.026118 CrossRef Google Scholar
[21]	R. Pastor-Satorras and A. Vespignani, Epidemic spreading in scale-free networks, Physical Review Letters, 2001, 86(14), 3200. doi: 10.1103/PhysRevLett.86.3200 CrossRef Google Scholar
[22]	D. A. Rand, Correlation Equations and Pair Approximations for Spatial Ecologies, Blackwell Publishing Ltd, 2009. Google Scholar
[23]	E. Volz, SIR dynamics in random networks with heterogeneous connectivity, Journal of Mathematical Biology, 2008, 56, 293–310. doi: 10.1007/s00285-007-0116-4 CrossRef Google Scholar
[24]	Y. Yang, T. Q. S. Abdullah, G. Huang and Y. Dong, Mathematical analysis of SIR epidemic model with piecewise infection rate and control strategies, Journal of Nonlinear Modeling and Analysis, 2023, 5(3), 524–539. Google Scholar