Graph Theory Applications to Comprehend Epidemics Spread of a Disease

Authors

  • Yegnanarayanan Venkatraman Member, Board of Advisors, RNB Global University, Bikaner, Rajasthan - 334601, India
  • Krithicaa Narayanaa Y Department of Biomedical Sciences, Sri Ramachandra Institute for Higher Education and Research (Deemed to be University), Chennai, Tamil Nadu - 600116, India
  • Valentina E. Balas Aurel Vlaicu University of Arad, Faculty of Engineering
  • Dana Rad Aurel Vlaicu University of Arad http://orcid.org/0000-0001-6754-3585

DOI:

https://doi.org/10.18662/brain/12.2/198

Keywords:

Virus, Epidemics, Pandemics, Graph, Regular Tree

Abstract

Theory of Graphs could offer a plenty to enrich the analysis and modeling to generate datasets out of the systems and processes regarding the spread of a disease that affects humans, animals, plants,  crops etc., In this paper first we show graphs can serve as a model for cattle movements from one farm to another. Second, we give a crisp explanation regarding disease transmission models on contact graphs/networks. It is possible to indicate how a regular tree exhibits relations among graph structure and the infectious disease spread and how certain properties of it akin to diameter and density of graph, affect the duration of an outbreak. Third, we elaborate on the presence of a suitable environment for exploiting several streams of data such as genetic temporal and spatial to locate case clusters one dependent on the other of a disease that is infectious. Here a graph for each stream of data joining all cases that are created with pairwise distance among them as edge weights and altered by omitting exceeding distances of a cutoff assigned that relies on already existing assumptions and rate of spread of a disease information. Fourth we provide an overview of epidemiology, disease transmission, fatality rate and clinical features of zoonotic viral infections of epidemic and pandemic magnitude since 2000. Fifth we indicate how the clinical data and virus spread data can be exploited for the creation of health knowledge graph. Graph Theory is an ideal tool to model, predict, form an opinion to devise strategies to quickly arrest the outbreak and minimize the devastating effect of zoonotic viral infections.

Author Biographies

Yegnanarayanan Venkatraman, Member, Board of Advisors, RNB Global University, Bikaner, Rajasthan - 334601, India

Yegnanarayanan Venkatraman (b. Nov 3, 1966) received his BSc in Mathematics (1986), MSc in Mathematics (1988), M. Phil in Mathematics (1989), M.Tech in Information Technology (2004), PhD in Mathematics (1997) from Annamalai University of India. Now he is acting as a Member of Board of Advisors of RNB Global University, Rajasthan, India.  He is a senior member of IEEE and a Life Member of various professional organizations. He has served senior Professor, Dean, Director and Research Chair of various Universities in India and his research interests include Graph Theory, Number Theory and their Applications. He has authored 170 research papers and completed funded research projects in India.

Krithicaa Narayanaa Y, Department of Biomedical Sciences, Sri Ramachandra Institute for Higher Education and Research (Deemed to be University), Chennai, Tamil Nadu - 600116, India

Krithicaa Narayanaa Y (b. Oct 12, 1995) received her B. Tech in Genetic Engineering (2017), M. Tech in Genetic Engineering (2019). Now she is a Ph.D Research Scholar in the Department of Biomedical Sciences,  Sri Ramachandra Institute of Higher Education and Research (Deemed to be University), Chennai, India. Her current interests are in Neuro-genetics and Cancer genetics.

Valentina E. Balas, Aurel Vlaicu University of Arad, Faculty of Engineering

Valentina E. Balas is currently Full Professor in the Department of Automatics and Applied Software at the Faculty of Engineering, “Aurel Vlaicu” University of Arad, Romania. She holds a Ph.D. in Applied Electronics and Telecommunications from Polytechnic University of Timisoara. Dr. Balas is author of more than 300 research papers in refereed journals and International Conferences. Her research interests are in Intelligent Systems, Fuzzy Control, Soft Computing, Smart Sensors, Information Fusion, Modeling and Simulation. She is the Editor-in Chief to International Journal of Advanced Intelligence Paradigms (IJAIP) and to International Journal of Computational Systems Engineering (IJCSysE). She is a Senior Member IEEE and is a Joint Secretary of the Governing Council of Forum for Interdisciplinary Mathematics (FIM), - A Multidisciplinary Academic Body, India.

Dana Rad, Aurel Vlaicu University of Arad

Assoc.Prof. PhD

Faculty of Educational Sciences, Psychology and Social Sciences

References

Indian Swine Flu Outbreak (2020). Wikipedia. https://en.wikipedia.org/wiki/2015_Indian_swine_flu_outbreak

Ancel Meyers, L., Newman, M. E., Martin, M., & Schrag, S. (2003). Applying network theory to epidemics: control measures for Mycoplasma pneumoniae outbreaks. Emerging infectious diseases, 9(2), 204–210. https://doi.org/10.3201/eid0902.020188

Bauch, C. T., & Oraby, T. (2013). Assessing the pandemic potential of MERS-CoV. Lancet (London, England), 382(9893), 662–664. https://doi.org/10.1016/S0140-6736(13)61504-4

Beiu, V., Rohatinovici, N. C., Dăuş, L., & Balas, V. E. (2017). Transport reliability on axonal cytoskeleton. In 2017 14th International Conference on Engineering of Modern Electric Systems (EMES), (pp. 160-163). IEEE.

Bennett, N. J. & Domachowske, J. (2020, Feb 12). Avian Influenza (Bird Flu). Medscape. https://emedicine.medscape.com/article/2500029-overview#a4

Cauchemez, S., Fraser, C., Van Kerkhove, M. D., Donnelly, C. A., Riley, S., Rambaut, A., Enouf, V., Van der Werf, S., & Ferguson, N. M. (2014). Middle East respiratory syndrome coronavirus: quantification of the extent of the epidemic, surveillance biases, and transmissibility. The Lancet infectious diseases, 14(1), 50-56. https://doi.org/10.1016/S1473-3099(13)70304-9

Cauchemez, S., Nouvellet, P., Cori, A., Jombart, T., Garske, T., Clapham, H., Moore, S., Mills, H. L., Salje, H., Collins, C., & Rodriquez-Barraquer, I. (2016). Unraveling the drivers of MERS-CoV transmission. Proceedings of the national academy of sciences, 113(32), 9081-9086. https://doi.org/10.1073/pnas.1519235113

Cauchemez, S., Van Kerkhove, M. D., Riley, S., Donnelly, C. A., Fraser, C., & Ferguson, N. M. (2013). Transmission scenarios for Middle East Respiratory Syndrome Coronavirus (MERS-CoV) and how to tell them apart. Euro Surveillance: Bulletin Europeen Sur les Maladies Transmissibles = European Communicable Disease Bulletin, 18(24), 20503. https://doi.org/10.2807/ese.18.24.20503-en

Centers for Disease Control and Prevention, (2019 June 11). 2009 H1N1 Pandemic (H1N1pdm09 Virus). Cdc.gov http://www.cdc.gov/flu/pandemic-resources/2009-h1n1-pandemic.html

Chung The, H., Karkey, A., Pham Thanh, D., Boinett, C. J., Cain, A. K., Ellington, M., Baker, K. S., Dongol, S., Thompson, C., Harris, S. R., Jombart, T., Le Thi Phuong, T., Tran Do Hoang, N., Ha Thanh, T., Shretha, S., Joshi, S., Basnyat, B., Thwaites, G., Thomson, N. R., Rabaa, M. A., … Baker, S. (2015). A high-resolution genomic analysis of multidrug-resistant hospital outbreaks of Klebsiella pneumoniae. EMBO molecular medicine, 7(3), 227–239. https://doi.org/10.15252/emmm.201404767

Cori, A., Nouvellet, P., Garske, T., Bourhy, H., Nakouné, E., & Jombart, T. (2018). A graph-based evidence synthesis approach to detecting outbreak clusters: An application to dog rabies. PLoS computational biology, 14(12), e1006554. https://doi.org/10.1371/journal.pcbi.1006554

Donnelly, C. A., & Nouvellet, P. (2013). The contribution of badgers to confirmed tuberculosis in cattle in high-incidence areas in England. PLoS currents, 5. https://doi.org/10.1371/currents.outbreaks.097a904d3f3619db2fe78d24bc776098

Enright, J., & Meeks, K. (2018). Deleting edges to restrict the size of an epidemic: a new application for treewidth. Algorithmica, 80(6), 1857-1889. https://doi.org/10.1007/s00453-017-0311-7

Ferguson, N. M., Fraser, C., Donnelly, C. A., Ghani, A. C., & Anderson, R. M. (2004). Public health risk from the avian H5N1 influenza epidemic. Science, 304(5673), 968-969. https://doi.org/10.1126/science.1096898

Fraser, C., Donnelly, C. A., Cauchemez, S., Hanage, W. P., Van Kerkhove, M. D., Hollingsworth, T. D., Griffin, J., Baggaley, R.F., Jenkins, H. E., Lyons, E. J., & Jombart, T. (2009). Pandemic potential of a strain of influenza A (H1N1): early findings. Science, 324(5934), 1557-1561. https://doi.org/10.1126/science.1176062

Gates, M. C., & Woolhouse, M. E. (2015). Controlling infectious disease through the targeted manipulation of contact network structure. Epidemics, 12, 11-19. https://doi.org/10.1016/j.epidem.2015.02.008

Hamidouche M. (2020, March 25). COVID-19 outbreak in Algeria: A mathematical Model to predict cumulative cases [Preprint]. Bull World Health Organ. http://dx.doi.org/10.2471/BLT.20.256065

Harris, S. R., Cartwright, E. J., Török, M. E., Holden, M. T., Brown, N. M., Ogilvy-Stuart, A. L., Ellington, M. J., Quail, M. A., Bentley, S. D., Parkhill, J., & Peacock, S. J. (2013). Whole-genome sequencing for analysis of an outbreak of meticillin-resistant Staphylococcus aureus: a descriptive study. The Lancet. Infectious diseases, 13(2), 130–136. https://doi.org/10.1016/S1473-3099(12)70268-2

Heath, M. F., Vernon, M. C., & Webb, C. R. (2008). Construction of networks with intrinsic temporal structure from UK cattle movement data. BMC Veterinary Research, 4(1), 11. https://doi.org/10.1186/1746-6148-4-11

Just, W., Callender, H., & LaMar, M. D. (2015). Disease Transmission Dynamics on Networks: Network Structure Versus Disease Dynamics. In R. S. Robeva (Ed.), Algebraic and Discrete Mathematical Methods for Modern Biology (pp. 217-235). Academic Press.

Keeling, M. J., & Eames, K. T. (2005). Networks and epidemic models. Journal of the Royal Society Interface, 2(4), 295-307. https://doi.org/10.1098/rsif.2005.0051

Kim, H., & Anderson, R. (2012). Temporal node centrality in complex networks. Physical Review E, 85(2), 026107.

Koopmans, M., Wilbrink, B., Conyn, M., Natrop, G., van der Nat, H., Vennema, H., Meijer, A., Van Steenbergen, J., Fouchier, R., Osterhaus, A., & Bosman, A. (2004). Transmission of H7N7 avian influenza A virus to human beings during a large outbreak in commercial poultry farms in the Netherlands. The Lancet, 363(9409), 587-593. https://doi.org/10.1016/S0140-6736(04)15589-X

Kreuels, B., Wichmann, D., Emmerich, P., Schmidt-Chanasit, J., de Heer, G., Kluge, S., Sow, A., Renné, T., Günther, S., Lohse, A. W. & Addo, M. M. (2014). A case of severe Ebola virus infection complicated by gram-negative septicemia. New england journal of medicine, 371(25), 2394-2401. https://doi.org/10.1056/NEJMoa1411677

Noor, R., & Ahmed, T. (2018). Zika virus: Epidemiological study and its association with public health risk. Journal of infection and public health, 11(5), 611-616. https://doi.org/10.1016/j.jiph.2018.04.007

Pan American Health Organization(PAHO), & World Health Orhanization (WHO) (2019, Jan 17). Weekly Report. Paho.org. https://www3.paho.org/data/index.php/en/?option=com_content&view=article&id=524:zika-weekly-en&Itemid=352

Riley, S., Fraser, C., Donnelly, C. A., Ghani, A. C., Abu-Raddad, L. J., Hedley, A. J., Leung, G.M., Ho, L.M., Lam, T.H., Thach, T.Q. & Chau, P. (2003). Transmission dynamics of the etiological agent of SARS in Hong Kong: impact of public health interventions. Science, 300(5627), 1961-1966. https://doi.org/10.1126/science.1086478

Rohatinovici, N. C., Proştean, O., & Balas, V. E. (2018). On Reliability of 3D Hammock Networks. In 2018 IEEE 12th International Symposium on Applied Computational Intelligence and Informatics (SACI), (pp: 000149-000154), IEEE. https://doi.org/10.1109/SACI.2018.8441003

Rotmensch, M., Halpern, Y., Tlimat, A., Horng, S., & Sontag, D. (2017). Learning a health knowledge graph from electronic medical records. Scientific reports, 7(1), 1-11. https://doi.org/10.1038/s41598-017-05778-z

Seibold, C., & Callender, H. L. (2016). Modeling epidemics on a regular tree graph. Letters in Biomathematics, 3(1), 59-74. https://doi.org/10.1080/23737867.2016.1185979

Vernon, M. C., & Keeling, M. J. (2008). Representing the UK's cattle herd as static and dynamic networks. Proceedings of the Royal Society B: Biological Sciences, 276(1656), 469-476. https://doi.org/10.1098/rspb.2008.1009

WHO Ebola Response Team (2015, July 24). Summary of probable SARS cases with onset of illness from 1 November 2002 to 31 July 2003. Summary of Probable SARS Cases with Onset of Illness from 1 November 2002 to 31 July 2003. Who.int. http://www.who.int/csr/sars/country/table2004_04_21/en/

WHO Ebola Response Team, Agua-Agum, J., Ariyarajah, A., Aylward, B., Blake, I. M., Brennan, R., Cori, A., Donnelly, C. A., Dorigatti, I., Dye, C., Eckmanns, T., Ferguson, N. M., Formenty, P., Fraser, C., Garcia, E., Garske, T., Hinsley, W., Holmes, D., Hugonnet, S., Iyengar, S., … Wijekoon Kannangarage, N. (2015). West African Ebola epidemic after one year--slowing but not yet under control. The New England journal of medicine, 372(6), 584–587. https://doi.org/10.1056/NEJMc1414992

World Health Orhanization (2017, Apr 12). Chikungunya. Who.int. http://www.who.int/news-room/fact-sheets/detail/chikungunya

World Health Orhanization (2018a, Aug 7). Nipah Virus – India. Who.int. http://www.who.int/csr/don/07-august-2018-nipah-virus-india/en/

World Health Orhanization (2018b, Aug 8). MERS-CoV Summary Updates. Who.int. http://www.who.int/csr/disease/coronavirus_infections/archive_updates/en/

World Health Orhanization (2018c, May 17). Marburg Virus Disease – Uganda and Kenya. Who.int. http://www.who.int/csr/don/15-november-2017-marburg-uganda-kenya/en/

World Health Orhanization (2020a, Feb 10). Ebola Virus Disease. Who.int. http://www.who.int/health-topics/ebola/#tab=tab_1

World Health Orhanization (2020b, Apr 9). Ebola Virus Disease – Democratic Republic of the Congo. Who.int. http://www.who.int/csr/don/09-April-2020-ebola-drc/en/

World Health Orhanization (2020c, Mar 2). Dengue and Severe Dengue. Who.int. http://www.who.int/news-room/fact-sheets/detail/dengue-and-severe-dengue

Downloads

Published

2021-07-19

How to Cite

Venkatraman, Y., Narayanaa Y, K., Balas, V. E., & Rad, D. (2021). Graph Theory Applications to Comprehend Epidemics Spread of a Disease. BRAIN. Broad Research in Artificial Intelligence and Neuroscience, 12(2), 161-177. https://doi.org/10.18662/brain/12.2/198

Most read articles by the same author(s)


Publish your work at the Scientific Publishing House LUMEN

It easy with us: publish now your work, novel, research, proceeding at Lumen Scientific Publishing House

Send your manuscript right now