IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v353y2019icp265-273.html
   My bibliography  Save this article

Disease spreading on populations structured by groups

Author

Listed:
  • Ramos, A.B.M.
  • Schimit, P.H.T.

Abstract

Epidemiological modeling usually relies on contact between two individuals as the method for a contagious infection spread over the population. Although for some diseases the contact is indeed between only two individuals (HIV), many contagious diseases are favored to spread inside a group of individuals. For instance, consider flu: usually infected persons spread the disease on public transport, inside a room in their jobs or their homes. All these situations are related to groups of individuals that may get a disease due to the presence of an infected individual in the group. Here we use a population model structured by groups, where individuals move inside a neighborhood forming groups, where the disease may be transmitted. The population model is based on evolutionary graph theory and modeled by probabilistic cellular automata, and the disease is modeled by the classical SIR-model. A mean-field approach is presented in terms of ordinary differential equations, and population parameters are used to analyze the disease dynamic. The major results of this paper are: (1) the number of groups that an individual belongs and the lattice temperature can estimate the disease spread strength inside the population and; (2) when infected individuals do not move, this is not enough to control the disease spreading.

Suggested Citation

  • Ramos, A.B.M. & Schimit, P.H.T., 2019. "Disease spreading on populations structured by groups," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 265-273.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:265-273
    DOI: 10.1016/j.amc.2019.01.055
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319300700
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.01.055?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. Schimit, P.H.T. & Monteiro, L.H.A., 2010. "Who should wear mask against airborne infections? Altering the contact network for controlling the spread of contagious diseases," Ecological Modelling, Elsevier, vol. 221(9), pages 1329-1332.
    2. Cristopher Moore & M. E. J. Newman, 2000. "Epidemics and Percolation in Small-World Networks," Working Papers 00-01-002, Santa Fe Institute.
    3. Erez Lieberman & Christoph Hauert & Martin A. Nowak, 2005. "Evolutionary dynamics on graphs," Nature, Nature, vol. 433(7023), pages 312-316, January.
    4. Monteiro, L.H.A. & Sasso, J.B. & Chaui Berlinck, J.G., 2007. "Continuous and discrete approaches to the epidemiology of viral spreading in populations taking into account the delay of incubation time," Ecological Modelling, Elsevier, vol. 201(3), pages 553-557.
    5. Ilnytskyi, Jaroslav & Kozitsky, Yuri & Ilnytskyi, Hryhoriy & Haiduchok, Olena, 2016. "Stationary states and spatial patterning in an SIS epidemiology model with implicit mobility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 36-45.
    6. Joël Mossong & Niel Hens & Mark Jit & Philippe Beutels & Kari Auranen & Rafael Mikolajczyk & Marco Massari & Stefania Salmaso & Gianpaolo Scalia Tomba & Jacco Wallinga & Janneke Heijne & Malgorzata Sa, 2008. "Social Contacts and Mixing Patterns Relevant to the Spread of Infectious Diseases," PLOS Medicine, Public Library of Science, vol. 5(3), pages 1-1, March.
    7. Schimit, P.H.T. & Monteiro, L.H.A., 2009. "On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata," Ecological Modelling, Elsevier, vol. 220(7), pages 1034-1042.
    8. Ahmed, E. & Agiza, H.N., 1998. "On modeling epidemics Including latency, incubation and variable susceptibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 253(1), pages 347-352.
    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, Yinwei & Jiang, Guo-Ping & Wu, Meng & Song, Yu-Rong & Wang, Haiyan, 2021. "Undirected Congruence Model: Topological characteristics and epidemic spreading," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    2. Monteiro, L.H.A., 2020. "More guns, less crime? A dynamical systems approach," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    3. Bing Li & Ziye Xiang, 2023. "Evolutionary Game of Vaccination Considering Both Epidemic and Economic Factors by Infectious Network of Complex Nodes," Mathematics, MDPI, vol. 11(12), pages 1-26, June.

    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. Schimit, P.H.T. & Monteiro, L.H.A., 2011. "A vaccination game based on public health actions and personal decisions," Ecological Modelling, Elsevier, vol. 222(9), pages 1651-1655.
    2. Pereira, F.M.M. & Schimit, P.H.T., 2018. "Dengue fever spreading based on probabilistic cellular automata with two lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 75-87.
    3. Schimit, P.H.T. & Monteiro, L.H.A., 2012. "On estimating the basic reproduction number in distinct stages of a contagious disease spreading," Ecological Modelling, Elsevier, vol. 240(C), pages 156-160.
    4. Schimit, P.H.T. & Monteiro, L.H.A., 2010. "Who should wear mask against airborne infections? Altering the contact network for controlling the spread of contagious diseases," Ecological Modelling, Elsevier, vol. 221(9), pages 1329-1332.
    5. Ichino, Andrea & Favero, Carlo A. & Rustichini, Aldo, 2020. "Restarting the economy while saving lives under Covid-19," CEPR Discussion Papers 14664, C.E.P.R. Discussion Papers.
    6. M. Hashem Pesaran & Cynthia Fan Yang, 2022. "Matching theory and evidence on Covid‐19 using a stochastic network SIR model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(6), pages 1204-1229, September.
    7. Wei Zhong, 2017. "Simulating influenza pandemic dynamics with public risk communication and individual responsive behavior," Computational and Mathematical Organization Theory, Springer, vol. 23(4), pages 475-495, December.
    8. Konno, Tomohiko, 2013. "An imperfect competition on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5453-5460.
    9. Houštecká, Anna & Koh, Dongya & Santaeulàlia-Llopis, Raül, 2021. "Contagion at work: Occupations, industries and human contact," Journal of Public Economics, Elsevier, vol. 200(C).
    10. Kuchler, Theresa & Russel, Dominic & Stroebel, Johannes, 2022. "JUE Insight: The geographic spread of COVID-19 correlates with the structure of social networks as measured by Facebook," Journal of Urban Economics, Elsevier, vol. 127(C).
    11. R. Bentley & Michael O’Brien & Paul Ormerod, 2011. "Quality versus mere popularity: a conceptual map for understanding human behavior," Mind & Society: Cognitive Studies in Economics and Social Sciences, Springer;Fondazione Rosselli, vol. 10(2), pages 181-191, December.
    12. John M Drake & Tobias S Brett & Shiyang Chen & Bogdan I Epureanu & Matthew J Ferrari & Éric Marty & Paige B Miller & Eamon B O’Dea & Suzanne M O’Regan & Andrew W Park & Pejman Rohani, 2019. "The statistics of epidemic transitions," PLOS Computational Biology, Public Library of Science, vol. 15(5), pages 1-14, May.
    13. S. M. Niaz Arifin & Christoph Zimmer & Caroline Trotter & Anaïs Colombini & Fati Sidikou & F. Marc LaForce & Ted Cohen & Reza Yaesoubi, 2019. "Cost-Effectiveness of Alternative Uses of Polyvalent Meningococcal Vaccines in Niger: An Agent-Based Transmission Modeling Study," Medical Decision Making, , vol. 39(5), pages 553-567, July.
    14. Ganjeh-Ghazvini, Mostafa & Masihi, Mohsen & Ghaedi, Mojtaba, 2014. "Random walk–percolation-based modeling of two-phase flow in porous media: Breakthrough time and net to gross ratio estimation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 214-221.
    15. Bisin, Alberto & Moro, Andrea, 2022. "Spatial‐SIR with network structure and behavior: Lockdown rules and the Lucas critique," Journal of Economic Behavior & Organization, Elsevier, vol. 198(C), pages 370-388.
    16. Mirjam Kretzschmar & Rafael T Mikolajczyk, 2009. "Contact Profiles in Eight European Countries and Implications for Modelling the Spread of Airborne Infectious Diseases," PLOS ONE, Public Library of Science, vol. 4(6), pages 1-8, June.
    17. Andrei I. Vlad & Alexei A. Romanyukha & Tatiana E. Sannikova, 2024. "Parameter Tuning of Agent-Based Models: Metaheuristic Algorithms," Mathematics, MDPI, vol. 12(14), pages 1-21, July.
    18. Elisabetta De Cao & Alessia Melegaro & Rogier Klok & Maarten Postma, 2014. "Optimising Assessments of the Epidemiological Impact in the Netherlands of Paediatric Immunisation with 13-Valent Pneumococcal Conjugate Vaccine Using Dynamic Transmission Modelling," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-9, April.
    19. Jianhong Chen & Hongcai Ma & Shan Yang, 2023. "SEIOR Rumor Propagation Model Considering Hesitating Mechanism and Different Rumor-Refuting Ways in Complex Networks," Mathematics, MDPI, vol. 11(2), pages 1-22, January.
    20. Gillis, Melissa & Urban, Ryley & Saif, Ahmed & Kamal, Noreen & Murphy, Matthew, 2021. "A simulation–optimization framework for optimizing response strategies to epidemics," Operations Research Perspectives, Elsevier, vol. 8(C).

    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:apmaco:v:353:y:2019:i:c:p:265-273. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.