IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v421y2015icp78-97.html
   My bibliography  Save this article

A stochastic SIS epidemic model with heterogeneous contacts

Author

Listed:
  • Economou, A.
  • Gómez-Corral, A.
  • López-García, M.

Abstract

A stochastic model for the spread of an SIS epidemic among a population consisting of N individuals, each having heterogeneous infectiousness and/or susceptibility, is considered and its behavior is analyzed under the practically relevant situation when N is small. The model is formulated as a finite time-homogeneous continuous-time Markov chain X. Based on an appropriate labeling of states, we first construct its infinitesimal rate matrix by using an iterative argument, and we then present an algorithmic procedure for computing steady-state measures, such as the number of infected individuals, the length of an outbreak, the maximum number of infectives, and the number of infections suffered by a marked individual during an outbreak. The time till the epidemic extinction is characterized as a phase-type random variable when there is no external source of infection, and its Laplace–Stieltjes transform and moments are derived in terms of a forward elimination backward substitution solution. The inverse iteration method is applied to the quasi-stationary distribution of X, which provides a good approximation of the process X at a certain time, conditional on non-extinction, after a suitable waiting time. The basic reproduction number R0 is defined here as a random variable, rather than an expected value.

Suggested Citation

  • Economou, A. & Gómez-Corral, A. & López-García, M., 2015. "A stochastic SIS epidemic model with heterogeneous contacts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 78-97.
    • Handle: RePEc:eee:phsmap:v:421:y:2015:i:c:p:78-97
    DOI: 10.1016/j.physa.2014.10.054
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437114008929
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2014.10.054?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. van Doorn, Erik A. & Pollett, Philip K., 2013. "Quasi-stationary distributions for discrete-state models," European Journal of Operational Research, Elsevier, vol. 230(1), pages 1-14.
    2. Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521674096.
    3. Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521857406.
    4. Farida Chamchod & Shigui Ruan, 2012. "Modeling the Spread of Methicillin-Resistant Staphylococcus aureus in Nursing Homes for Elderly," PLOS ONE, Public Library of Science, vol. 7(1), pages 1-9, January.
    5. Robert R Wilkinson & Kieran J Sharkey, 2013. "An Exact Relationship Between Invasion Probability and Endemic Prevalence for Markovian SIS Dynamics on Networks," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-8, July.
    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. Amador, J. & Gómez-Corral, A., 2020. "A stochastic epidemic model with two quarantine states and limited carrying capacity for quarantine," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    2. Teng, Zhidong & Wang, Lei, 2016. "Persistence and extinction for a class of stochastic SIS epidemic models with nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 507-518.
    3. Karen M Ong & Michael S Phillips & Charles S Peskin, 2020. "A mathematical model and inference method for bacterial colonization in hospital units applied to active surveillance data for carbapenem-resistant enterobacteriaceae," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-32, November.
    4. Maria Gamboa & Maria Jesus Lopez-Herrero, 2020. "The Effect of Setting a Warning Vaccination Level on a Stochastic SIVS Model with Imperfect Vaccine," Mathematics, MDPI, vol. 8(7), pages 1-23, July.
    5. Antonio Gómez-Corral & Martín López-García & Maria Jesus Lopez-Herrero & Diana Taipe, 2020. "On First-Passage Times and Sojourn Times in Finite QBD Processes and Their Applications in Epidemics," Mathematics, MDPI, vol. 8(10), pages 1-25, October.
    6. Polly-Anne Jeffrey & Martín López-García & Mario Castro & Grant Lythe & Carmen Molina-París, 2020. "On Exact and Approximate Approaches for Stochastic Receptor-Ligand Competition Dynamics—An Ecological Perspective," Mathematics, MDPI, vol. 8(6), pages 1-31, 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. De Masi, G. & Giovannetti, G. & Ricchiuti, G., 2013. "Network analysis to detect common strategies in Italian foreign direct investment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(5), pages 1202-1214.
    2. Andrea Galeotti & Brian W. Rogers, 2013. "Strategic Immunization and Group Structure," American Economic Journal: Microeconomics, American Economic Association, vol. 5(2), pages 1-32, May.
    3. Bargigli, Leonardo & Gallegati, Mauro, 2011. "Random digraphs with given expected degree sequences: A model for economic networks," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 396-411, May.
    4. Cabrales, Antonio & Calvó-Armengol, Antoni & Zenou, Yves, 2011. "Social interactions and spillovers," Games and Economic Behavior, Elsevier, vol. 72(2), pages 339-360, June.
    5. Zenou, Yves, 2007. "Social Interactions and Labour Market Outcomes in Cities," CEPR Discussion Papers 6129, C.E.P.R. Discussion Papers.
    6. Bravard, Christophe & Charroin, Liza & Touati, Corinne, 2017. "Optimal design and defense of networks under link attacks," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 62-79.
    7. Florian Blöchl & Fabian J. Theis & Fernando Vega-Redondo & Eric O'N. Fisher, 2010. "Which Sectors of a Modern Economy are most Central?," CESifo Working Paper Series 3175, CESifo.
    8. Sanjeev Goyal & Adrien Vigier, 2014. "Attack, Defence, and Contagion in Networks," Review of Economic Studies, Oxford University Press, vol. 81(4), pages 1518-1542.
    9. Levent V. Orman, 2016. "Information markets over trust networks," Electronic Commerce Research, Springer, vol. 16(4), pages 529-551, December.
    10. Michael D. König & Xiaodong Liu & Yves Zenou, 2019. "R&D Networks: Theory, Empirics, and Policy Implications," The Review of Economics and Statistics, MIT Press, vol. 101(3), pages 476-491, July.
    11. Galeotti, Andrea & Goyal, Sanjeev, 2007. "Network Multipliers and the Optimality of Indirect Communication," Economics Discussion Papers 2982, University of Essex, Department of Economics.
    12. Michael D König & Stefano Battiston & Mauro Napoletano & Frank Schweitzer, 2008. "The Efficiency and Evolution of R&D Networks," Working Papers hal-00973077, HAL.
    13. Chang, Chia-ling & Chen, Shu-heng, 2011. "Interactions in DSGE models: The Boltzmann-Gibbs machine and social networks approach," Economics Discussion Papers 2011-25, Kiel Institute for the World Economy (IfW Kiel).
    14. Cinara G. Ghedini & Carlos H. C. Ribeiro, 2014. "Improving Resilience Of Complex Networks Facing Attacks And Failures Through Adaptive Mechanisms," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 1-25.
    15. Cátia Batista & Marcel Fafchamps & Pedro C. Vicente, 2018. "Keep It Simple: A Field Experiment on Information Sharing in Social Networks," NBER Working Papers 24908, National Bureau of Economic Research, Inc.
    16. Kets, W., 2008. "Beliefs in Network Games (Revised version of CentER DP 2007-46)," Other publications TiSEM a08e38fd-6b00-4233-94ce-3, Tilburg University, School of Economics and Management.
    17. Fausto Bonacina & Marco D’Errico & Enrico Moretto & Silvana Stefani & Anna Torriero & Giovanni Zambruno, 2015. "A multiple network approach to corporate governance," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(4), pages 1585-1595, July.
    18. Solomon Sorin & Golo Natasa, 2013. "Minsky Financial Instability, Interscale Feedback, Percolation and Marshall–Walras Disequilibrium," Accounting, Economics, and Law: A Convivium, De Gruyter, vol. 3(3), pages 167-260, October.
    19. Olaizola Ortega, María Norma & Valenciano Llovera, Federico, 2015. "Efficiency vs. Stability in a Mixed Network Formation Model," IKERLANAK info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    20. Zenou, Yves, 2011. "Spatial versus Social Mismatch: The Strength of Weak Ties," Research Papers in Economics 2011:5, Stockholm University, Department of Economics.

    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:phsmap:v:421:y:2015:i:c:p:78-97. 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: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.