Identifying the complex underlying transmission network of COVID-19 in México from 2020 to 2024
DOI:
https://doi.org/10.31349/RevMexFis.72.021701Abstract
Has been demonstrated that the interaction of individuals in a social network can be modeled using the complex networks theory. In this sense, we believe that knowing at least approximately the underlying network of interaction among the individuals in a society could help to understand the dynamic of diseases transmission among the individuals and elucidate the most effective mechanisms to contain the spread and minimize negative effects like the over-saturation of health systems, such as hospitals and medical clinics. In this work, we study the spread of COVID-19 in Mexico from 2020 to 2024 using the statistical data available in the public health departments of Mexico. Through stochastic simulations we found a complex network that could represent a simplification of the real underlying network of interaction among the Mexican population, in particular we found that the network has degree distribution following a power law P(k) ∼ k −γ with exponent close to γ ≈ 2.5. As mentioned before it could help to understand the spread of future diseases through stochastic simulations using a network structure closer to reality and consequently implement best healthy policies.
References
Okabe Y. and Shudo A., “Microscopic Numerical Simulations of Epidemic Models on Networks”. Mathematics 9, 932 (2021).
Sun L., He Q., Teng Y., Zhao Q., Yan X. and Wang X., “A complex network-based vaccination strategy for infectious diseases”. Applied Soft Computing 136, 932 (2023).
Szapudi I., “Heterogeneity in SIR epidemics modeling: superspreaders and herd immunity”. Appl Netw Sci 5, 93 (2020).
Herrmann H.A. and Schwartz J.M., “Why COVID19 models should incorporate the network of social interactions”. Phys. Biol. 17, 75-83 (2020).
Rafiq M., Nizami A.R., Baleanu D. and Ahmad N., “Numerical simulations on scale-free and random networks for the spread of COVID-19 in Pakistan”. Alexandria Engineering Journal 62, 75-83 (2023).
Li J., Yan H. and Jin Z., “SIR dynamics with infection age in complex heterogeneous networks”. Communications in Nonlinear Science and Numerical Simulation 121, 107183 (2023).
Erdös P. and Rényi A., “On random graphs 1”. Publicationes Mathematicae Debrecen 6, 290-297 (1959).
Erdös P. and Rényi A., “On the evolution of random graphs”. Publication of the Mathematical Institute of the Hungarian Academy of Sciences 5, 17-61 (1960).
Barabási A.L. and Albert R., “Emergence of Scaling in Random Networks”. Science 286, 509-512 (1999).
Kunegis J., KONECT-The Koblenz Network Collection. Proc. Int. Conf. on World Wide Web Companion, 1343-1350, (2013).
Albert R. and Barabási A.L., Topology of evolving networks: local events and universality. Phys. Rev. Lett. 85, 5234-5237 (2000).
Jeong H., Tombor B., Albert R., Oltvai Z.N. and Barabási A.L., The large-scale organization of metabolic networks. Nature 407, 651-654 (2000).
Garlaschelli D. and Loffredo M.I., Structure and evolution of the world trade network. Physica A: Statistical Mechanics and its Applications 355, 138–144, (2005).
Albert R. and Barabási A.L., Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47-97 (2002).
Timár G., Dorogovtsev S.N. and Mendes J.F.F., Scale-free networks with exponent one. Phys. Rev. E. 94, 022302 (2016).
Esquivel-Gómez J. and Barajas-Ramírez J.G., Emergence of dense scale-free networks and simplicial complexes by random degree-copying. Journal of Complex Networks, 11, 6 (2023). https://doi.org/10.1093/comnet/cnad045
Forien R., Pang G. and Pardoux É., Estimating the state of the COVID-19 epidemic in France using a model with memory. R. Soc. Open Sci. 8: 202327 (2021) https://doi.org/10.1098/rsos.202327
Buonomo B, Della Marca R., Effects of informationinduced behavioural changes during the COVID-19 lockdowns: the case of Italy. R. Soc. Open Sci. 7: 201635 (2020) http://dx.doi.org/10.1098/rsos.201635
Binny RN, Baker MG, Hendy SC, James A, Lustig A, Plank MJ, Ridings KM, Steyn N. Early intervention is the key to success in COVID-19
control. R. Soc. Open Sci. 8: 210488 (2021). https://doi.org/10.1098/rsos.210488
Yang W, Shaff J, Shaman J., Effectiveness of nonpharmaceutical interventions to contain COVID-19: a case study of the 2020 spring pandemic wave in New York City. J. R. Soc. Interface 18: 20200822 (2021) https://doi.org/10.1098/rsif.2020.0822
Instituto Nacional de Estadística y Geografía. Principales resultados del Censo de Población y Vivienda 2020 Estados Unidos Mexicanos. https://www.inegi.org.mx
Gobierno de México, CONAHCYT - CentroGeo - GeoInt. https://datos.covid-19.conacyt.mx
Moreno Y., Pastor-Satorras R., Vespignani A., Epidemic outbreaks in complex heterogeneous networks. Eur. Phys. J. B 26, 521–529 (2002).
Alimohamadi Y., Taghdir M., Sepandi M., Estimate of the Basic Reproduction Number for COVID19: A Systematic Review and Meta-analysis. J Prev Med Public Health, 53, 151-157 (2020). https://doi.org/10.3961/jpmph.20.076
Raveendran A.V., Jayadevan R., Sashidharan S., Long COVID: An overview. Diabetes & Metabolic Syndrome: Clinical Research & Reviews, 15, 869-875 (2021). https://doi.org/10.1016/j.dsx.2021.04.007
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 J. Esquivel-Gomez, E. E. Rodríguez Martínez, J. G. Barajas Ramírez
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
