IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v167y2023ics0960077922011870.html
   My bibliography  Save this article

Stochastic simplicial contagion model

Author

Listed:
  • Serrano, Daniel Hernández
  • Villarroel, Javier
  • Hernández-Serrano, Juan
  • Tocino, Ángel

Abstract

We propose a stochastic model that describes of epidemics over simplicial complex networks (SSCM) in which higher-order unforeseen or random interactions may occur. Its dynamics obeys a stochastic differential equation (SDE) based on the mean field approach of the simplicial social contagion model. In this stochastic regime the only possible equilibrium state is the origin. We give conditions to guarantee global stability and hence that the disease dies out. We partition the parameter space into the instability, the bi-stability and the globally asymptotically stable regions described in terms of appropriate epidemiological parameters. These regimes codify whether the disease will, can or will not disappear. We also present empirical results obtained by running different simulations of the SSCM over several real-world simplicial networks and over a synthetically generated one, which validate the theoretical results presented.

Suggested Citation

  • Serrano, Daniel Hernández & Villarroel, Javier & Hernández-Serrano, Juan & Tocino, Ángel, 2023. "Stochastic simplicial contagion model," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:chsofr:v:167:y:2023:i:c:s0960077922011870
    DOI: 10.1016/j.chaos.2022.113008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922011870
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.113008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hernández Serrano, Daniel & Sánchez Gómez, Darío, 2020. "Centrality measures in simplicial complexes: Applications of topological data analysis to network science," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    2. Giovanni Petri & Martina Scolamiero & Irene Donato & Francesco Vaccarino, 2013. "Topological Strata of Weighted Complex Networks," PLOS ONE, Public Library of Science, vol. 8(6), pages 1-8, June.
    3. Cowan, Robin & Jonard, Nicolas, 2004. "Network structure and the diffusion of knowledge," Journal of Economic Dynamics and Control, Elsevier, vol. 28(8), pages 1557-1575, June.
    4. Iacopo Iacopini & Giovanni Petri & Alain Barrat & Vito Latora, 2019. "Simplicial models of social contagion," Nature Communications, Nature, vol. 10(1), pages 1-9, December.
    5. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    6. Hernández Serrano, Daniel & Hernández-Serrano, Juan & Sánchez Gómez, Darío, 2020. "Simplicial degree in complex networks. Applications of topological data analysis to network science," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    7. Zhao, Yanan & Jiang, Daqing & O’Regan, Donal, 2013. "The extinction and persistence of the stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4916-4927.
    8. Lu, Qiuying, 2009. "Stability of SIRS system with random perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(18), pages 3677-3686.
    9. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    10. Ruimin Xu & Rongwei Guo, 2020. "Pontryagin’s Maximum Principle for Optimal Control of Stochastic SEIR Models," Complexity, Hindawi, vol. 2020, pages 1-5, October.
    11. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    12. Tornatore, Elisabetta & Maria Buccellato, Stefania & Vetro, Pasquale, 2005. "Stability of a stochastic SIR system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 111-126.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li, Shuyu & Li, Xiang, 2023. "Influence maximization in hypergraphs: A self-optimizing algorithm based on electrostatic field," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Álvarez Echeverría Francisco & López Sarabia Pablo & Venegas Martínez Francisco, 2012. "Valuación financiera de proyectos de inversión en nuevas tecnologías con opciones reales," Contaduría y Administración, Accounting and Management, vol. 57(3), pages 115-145, julio-sep.
    2. Podolskij, Mark & Vetter, Mathias, 2009. "Bipower-type estimation in a noisy diffusion setting," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2803-2831, September.
    3. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742, Decembrie.
    4. Linnenluecke, Martina K. & Chen, Xiaoyan & Ling, Xin & Smith, Tom & Zhu, Yushu, 2017. "Research in finance: A review of influential publications and a research agenda," Pacific-Basin Finance Journal, Elsevier, vol. 43(C), pages 188-199.
    5. Chen, An-Sing & Chu, Hsiang-Hui & Hung, Pi-Hsia & Cheng, Miao-Sih, 2020. "Financial risk and acquirers' stockholder wealth in mergers and acquisitions," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    6. Zhou, Chunsheng, 2001. "The term structure of credit spreads with jump risk," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 2015-2040, November.
    7. Bu, Ruijun & Cheng, Jie & Hadri, Kaddour, 2016. "Reducible diffusions with time-varying transformations with application to short-term interest rates," Economic Modelling, Elsevier, vol. 52(PA), pages 266-277.
    8. Aït-Sahalia, Yacine & Park, Joon Y., 2016. "Bandwidth selection and asymptotic properties of local nonparametric estimators in possibly nonstationary continuous-time models," Journal of Econometrics, Elsevier, vol. 192(1), pages 119-138.
    9. Choi, Jaehyung, 2012. "Spontaneous symmetry breaking of arbitrage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3206-3218.
    10. Dong-Mei Zhu & Jiejun Lu & Wai-Ki Ching & Tak-Kuen Siu, 2019. "Option Pricing Under a Stochastic Interest Rate and Volatility Model with Hidden Markovian Regime-Switching," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 555-586, February.
    11. Yanhong Zhong & Guohe Deng, 2019. "Geometric Asian Options Pricing under the Double Heston Stochastic Volatility Model with Stochastic Interest Rate," Complexity, Hindawi, vol. 2019, pages 1-13, January.
    12. Antonio Mele, 2003. "Fundamental Properties of Bond Prices in Models of the Short-Term Rate," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 679-716, July.
    13. Emmanuel Coffie, 2021. "Delay stochastic interest rate model with jump and strong convergence in Monte Carlo simulations," Papers 2103.07651, arXiv.org, revised Jul 2021.
    14. Yu, Jun, 2014. "Econometric Analysis Of Continuous Time Models: A Survey Of Peter Phillips’S Work And Some New Results," Econometric Theory, Cambridge University Press, vol. 30(4), pages 737-774, August.
    15. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    16. Ako Doffou & Jimmy E. Hilliard, 2001. "Pricing Currency Options Under Stochastic Interest Rates And Jump-Diffusion Processes," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 24(4), pages 565-585, December.
    17. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    18. Jianqing Fan, 2004. "A selective overview of nonparametric methods in financial econometrics," Papers math/0411034, arXiv.org.
    19. Jorgensen, Peter Lochte, 2007. "Traffic light options," Journal of Banking & Finance, Elsevier, vol. 31(12), pages 3698-3719, December.
    20. Peter Hördahl & David Vestin, 2005. "Interpreting Implied Risk-Neutral Densities: The Role of Risk Premia," Review of Finance, European Finance Association, vol. 9(1), pages 97-137.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:167:y:2023:i:c:s0960077922011870. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.