Analysis of Multi-Interacting Networks and Their Application to HIV Transmission Among Men Who Have Sex with Men
Abstract
1. Introduction
2. Methods
2.1. Structure of Complex Network
2.2. Complex Network Centrality
2.3. Model of HIV Transmission Among MSM
2.4. Algorithm Implementation
2.4.1. Symmetric Degree Distribution Network
2.4.2. Asymmetric Degree Distribution Network
2.4.3. Simulation Procedure
3. Results
3.1. Stochasticity in the Network
3.1.1. Stochasticity in the Symmetric Degree Distribution Network
3.1.2. Stochasticity in the Asymmetric Degree Distribution Network
3.2. Analysis of Centrality
3.2.1. Centrality of the Symmetric Degree Distribution Network
3.2.2. Centrality of the Asymmetric Degree Distribution Network
4. Discussion
4.1. Stochasticity of Complex Networks
4.2. Analysis of the Degree Vector and the Centrality Eigenvectors
4.3. Comparison Between Symmetric and Asymmetric Distribution Networks
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Boccaletti, S.; Latora, V.; Moreno, Y.; Chavez, M.; Hwang, D.U. Complex networks: Structure and dynamics. Phys. Rep. 2006, 424, 175–308. [Google Scholar] [CrossRef]
- Boccaletti, S.; Almendral, J.A.; Guan, S.; Leyva, I.; Liu, Z.; Sendina-Nadal, I.; Wang, Z.; Zou, Y. Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization. Phys. Rep. 2016, 660, 1–94. [Google Scholar] [CrossRef]
- Estrada, E. Introduction to Complex Networks: Structure and Dynamics. Evol. Equ. Appl. Nat. Sci. 2015, 2126, 93–131. [Google Scholar] [CrossRef]
- Watts, D.J.; Strogatz, S.H. Collective dynamics of ‘small-world’ networks. Nature 1998, 393, 440–442. [Google Scholar] [CrossRef] [PubMed]
- Barabasi, A.L.; Albert, R. Emergence of scaling in random networks. Science 1999, 286, 509–512. [Google Scholar] [CrossRef] [PubMed]
- Yan, C. Network Model with Scale-Free, High Clustering Coefficients, and Small-World Properties. J. Appl. Math. 2023, 2023, 5533260. [Google Scholar] [CrossRef]
- Liljeros, F.; Edling, C.R.; Amaral, L.; Stanley, H.E.; Åberg, Y. The web of human sexual contacts. Nature 2001, 411, 907–908. [Google Scholar] [CrossRef] [PubMed]
- Restrepo, J.G.; Ott, E.; Hunt, B.R. Characterizing the dynamical importance of network nodes and links. Phys. Rev. Lett. 2006, 97, 94102. [Google Scholar] [CrossRef] [PubMed]
- Bonacich, P. Some unique properties of eigenvector centrality. Soc. Netw. 2007, 29, 555–564. [Google Scholar] [CrossRef]
- Zheng, Q.; Shen, J.; Pandey, V.; Guan, L.; Guo, Y. Turing instability in a network-organized epidemic model with delay. Chaos Solitons Fractals 2023, 168, 113205. [Google Scholar] [CrossRef]
- Shen, D.; Li, J.H.; Zhang, Q.; Zhu, R. Interlacing layered complex networks. Acta Phys. Sin.-Chin. Ed. 2014, 63, 190201. [Google Scholar] [CrossRef]
- Kurant, M.; Thiran, P. Layered complex networks. Phys. Rev. Lett. 2006, 96, 138701. [Google Scholar] [CrossRef]
- Tyloo, M. Layered complex networks as fluctuation amplifiers. J. Phys.-Complex. 2022, 3, 3. [Google Scholar] [CrossRef]
- Zhou, Y. Numerical Study of the Effective Degree Theory on Two- Layered Complex Networks. In Proceedings of the Iecon 2017—43rd Annual Conference of the IEEE Industrial Electronics Society, Beijing, China, 29 October–1 November 2017; pp. 5912–5917. [Google Scholar]
- Jeffries, W.T. The number of recent sex partners among bisexual men in the United States. Perspect. Sex. Reprod. Health 2011, 43, 151–157. [Google Scholar] [CrossRef]
- Wang, G.; Yao, W. An application of complex networks on predicting the behavior of infectious disease on campus. Math. Methods Appl. Sci. 2024, 48, 189–206. [Google Scholar] [CrossRef]
- Wang, G.; Yao, W. An application of small-world network on predicting the behavior of infectious disease on campus. Infect. Dis. Model. 2024, 9, 177–184. [Google Scholar] [CrossRef]
- Yang, J.; Cao, Z.; Lu, Y. Contagion dynamics on a compound model. Appl. Math. Comput. 2024, 460, 128293. [Google Scholar] [CrossRef]
- Saumell-Mendiola, A.; Serrano, M.A.; Boguna, M. Epidemic spreading on interconnected networks. Phys. Rev. E 2012, 86, 026106. [Google Scholar] [CrossRef]
- Saha, S.; Samanta, G.P. Modelling and optimal control of HIV / AIDS prevention through PrEP and limited treatment. Phys. A 2019, 516, 280–307. [Google Scholar] [CrossRef]
- Vieira, I.T.; Cheng, R.C.H.; Harper, P.R.; de Senna, V. Small world network models of the dynamics of HIV infection. Ann. Oper. Res. 2010, 178, 173–200. [Google Scholar] [CrossRef]
- Lou, J.; Wu, J.; Chen, L.; Ruan, Y.; Shao, Y. A sex-role-preference model for HIV transmission among men who have sex with men in China. BMC Public Health 2009, 9, S10. [Google Scholar] [CrossRef] [PubMed]
- Shen, Z.; Li, Y.; Yao, W. A scale-free network model for HIV transmission among men who have sex with men in China. Math. Methods Appl. Sci. 2016, 39, 5131–5139. [Google Scholar] [CrossRef]
- Zhong, C.; Sun, M.; Yao, W. A hybrid model for HIV transmission among men who have sex with men. Infect. Dis. Model. 2020, 5, 814–826. [Google Scholar] [CrossRef]
- Bonacich, P. Power and centrality—A family of measures. Am. J. Sociol. 1987, 92, 1170–1182. [Google Scholar] [CrossRef]
- Xie, L.; Yao, W. A network-based study on HIV spreading among men who have sex with men. Chin. Sci. Bull. (Chin. Ver.) 2013, 58, 1731–1738. [Google Scholar]
- Yee, N. Beyond Tops and Bottoms: Correlations between Sex-Role Preferences and Physical Preferences for Partners among Gay Men. 2002. Available online: http://www.nickyee.com/ponder/topbottom.pdf (accessed on 16 January 2025).
- Wang, S.T.; News, S.D. China’s Gay Men’s HIV Infection Rate Reaches 4.9%, Becoming a Key Population Group for Transmission. Available online: https://www.chinanews.com/jk/kong/news/2008/12-02/1470137.shtml (accessed on 14 January 2025). (In Chinese).
- Tocino, A.; Serrano, D.H.; Hernandez-Serrano, J.; Villarroel, J. A stochastic simplicial SIS model for complex networks. Commun. Nonlinear Sci. 2023, 120, 107161. [Google Scholar] [CrossRef]
- Li, Z.; Jiang, M.Y.; Liu, X.; Cai, Y.; Wang, C.; Cao, F.; Liu, J. Research trends of acupressure from 2004 to 2024: A bibliometric and visualization analysis. Heliyon 2024, 10, e38675. [Google Scholar] [CrossRef] [PubMed]
- Zhang, Y.; Wang, M.; Saberi, M.; Chang, E. Analysing academic paper ranking algorithms using test data and benchmarks: An investigation. Scientometrics 2022, 127, 4045–4074. [Google Scholar] [CrossRef]
- Buldyrev, S.V.; Parshani, R.; Paul, G.; Stanley, H.E.; Havlin, S. Catastrophic cascade of failures in interdependent networks. Nature 2010, 464, 1025–1028. [Google Scholar] [CrossRef] [PubMed]
Connection Type | Between Vs | From T to Others | From B to Others | From Others to T | From Others to B |
---|---|---|---|---|---|
ω | 1.5 | 2 | 1 | 1 | 2 |
Parameter | Description | Value |
---|---|---|
β | The infection rate of each connection | 0.025 [16] |
<kv> | The average degree of the V group | 8 [26] |
<k> | The average degree of the B or T group | 6 |
p0 | The initial proportion of infected nodes | 0.05 [28] |
Order | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|
degree | 15 | 15 | 15 | 15 | 14 | 13 | 13 | 13 | 13 | 12 |
nk | 88 | 42 | 96 | 6 | 79 | 70 | 65 | 63 | 24 | 69 |
nx | 88 | 79 | 96 | 275 | 172 | 6 | 69 | 20 | 42 | 65 |
order | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
degree | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 |
nk | 20 | 275 | 248 | 226 | 170 | 172 | 49 | 18 | 32 | 284 |
nx | 70 | 24 | 238 | 226 | 170 | 259 | 49 | 18 | 247 | 284 |
Order | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|
Weighted degree | 24 | 24 | 23.5 | 23 | 22.5 | 22 | 22 | 22 | 21.5 | 21.5 |
172 | 170 | 79 | 70 | 96 | 183 | 181 | 169 | 88 | 6 | |
172 | 88 | 170 | 79 | 96 | 183 | 173 | 118 | 184 | 125 | |
order | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Weighted degree | 21 | 20.5 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 |
42 | 65 | 197 | 195 | 184 | 176 | 155 | 132 | 125 | 18 | |
70 | 138 | 6 | 176 | 69 | 103 | 42 | 65 | 181 | 169 |
Order | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|
Weighted degree | 75.5 | 65.5 | 60 | 51.5 | 45 | 42 | 41.5 | 40 | 37 | 37 |
3 | 8 | 241 | 5 | 11 | 4 | 27 | 24 | 197 | 1 | |
3 | 97 | 5 | 8 | 241 | 4 | 165 | 11 | 229 | 12 | |
order | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Weighted degree | 36.5 | 34 | 32 | 30 | 28.5 | 28 | 28 | 28 | 27.5 | 24 |
2 | 20 | 291 | 229 | 17 | 294 | 239 | 18 | 12 | 289 | |
2 | 1 | 20 | 24 | 27 | 231 | 291 | 219 | 289 | 113 |
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Wang, G.; Yao, W. Analysis of Multi-Interacting Networks and Their Application to HIV Transmission Among Men Who Have Sex with Men. Symmetry 2025, 17, 165. https://doi.org/10.3390/sym17020165
Wang G, Yao W. Analysis of Multi-Interacting Networks and Their Application to HIV Transmission Among Men Who Have Sex with Men. Symmetry. 2025; 17(2):165. https://doi.org/10.3390/sym17020165
Chicago/Turabian StyleWang, Guojin, and Wei Yao. 2025. "Analysis of Multi-Interacting Networks and Their Application to HIV Transmission Among Men Who Have Sex with Men" Symmetry 17, no. 2: 165. https://doi.org/10.3390/sym17020165
APA StyleWang, G., & Yao, W. (2025). Analysis of Multi-Interacting Networks and Their Application to HIV Transmission Among Men Who Have Sex with Men. Symmetry, 17(2), 165. https://doi.org/10.3390/sym17020165