{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,27]],"date-time":"2026-09-27T23:29:34Z","timestamp":1790551774762,"version":"4.1.0"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,10,22]],"date-time":"2021-10-22T00:00:00Z","timestamp":1634860800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,10,22]],"date-time":"2021-10-22T00:00:00Z","timestamp":1634860800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soc. Netw. Anal. Min."],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s13278-021-00814-3","type":"journal-article","created":{"date-parts":[[2021,10,22]],"date-time":"2021-10-22T13:05:24Z","timestamp":1634907924000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Mobility-based SIR model for complex networks: with case study Of COVID-19"],"prefix":"10.1007","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2330-7369","authenticated-orcid":false,"given":"Rahul","family":"Goel","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lo\u00efc","family":"Bonnetain","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rajesh","family":"Sharma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Angelo","family":"Furno","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,10,22]]},"reference":[{"issue":"1","key":"814_CR1","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1103\/RevModPhys.74.47","volume":"74","author":"R Albert","year":"2002","unstructured":"Albert R, Barab\u00e1si AL (2002) Statistical mechanics of complex networks. Rev Modern Phys 74(1):47","journal-title":"Rev Modern Phys"},{"issue":"5721","key":"814_CR2","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1038\/280361a0","volume":"280","author":"RM Anderson","year":"1979","unstructured":"Anderson RM, May RM (1979) Population biology of infectious diseases: part i. Nature 280(5721):361","journal-title":"Nature"},{"key":"814_CR3","volume-title":"Infectious diseases of humans: dynamics and control","author":"RM Anderson","year":"1992","unstructured":"Anderson RM, May RM, Anderson B (1992) Infectious diseases of humans: dynamics and control, vol 28. Wiley, Hoboken"},{"issue":"4","key":"814_CR4","first-page":"041055","volume":"10","author":"A Arenas","year":"2020","unstructured":"Arenas A, Cota W, G\u00f3mez-Garde\u00f1es J, G\u00f3mez S, Granell C, Matamalas JT, Soriano-Pa\u00f1os D, Steinegger B (2020) Modeling the spatiotemporal epidemic spreading of covid-19 and the impact of mobility and social distancing interventions. Phys Rev X 10(4):041055","journal-title":"Phys Rev X"},{"key":"814_CR5","doi-asserted-by":"crossref","unstructured":"Arquam M, Singh A, Sharma R (2018) Modelling and analysis of delayed sir model on complex network. In: International conference on complex networks and their applications. Springer, pp 418\u2013430","DOI":"10.1007\/978-3-030-05411-3_34"},{"issue":"2","key":"814_CR6","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/j.jtbi.2005.01.011","volume":"235","author":"M Barth\u00e9lemy","year":"2005","unstructured":"Barth\u00e9lemy M, Barrat A, Pastor-Satorras R, Vespignani A (2005) Dynamical patterns of epidemic outbreaks in complex heterogeneous networks. J Theor Biol 235(2):275\u2013288","journal-title":"J Theor Biol"},{"issue":"suppl 3","key":"814_CR7","doi-asserted-by":"publisher","first-page":"7280","DOI":"10.1073\/pnas.082080899","volume":"99","author":"E Bonabeau","year":"2002","unstructured":"Bonabeau E (2002) Agent-based modeling: methods and techniques for simulating human systems. Proc Natl Acad Sci 99(suppl 3):7280\u20137287","journal-title":"Proc Natl Acad Sci"},{"issue":"11","key":"814_CR8","doi-asserted-by":"publisher","first-page":"1142","DOI":"10.1197\/j.aem.2006.07.017","volume":"13","author":"DS Burke","year":"2006","unstructured":"Burke DS, Epstein JM, Cummings DA, Parker JI, Cline KC, Singa RM, Chakravarty S (2006) Individual-based computational modeling of smallpox epidemic control strategies. Acad Emerg Med 13(11):1142\u20131149","journal-title":"Acad Emerg Med"},{"key":"814_CR9","doi-asserted-by":"crossref","unstructured":"Chinazzi M, Davis JT, Ajelli M, Gioannini C, Litvinova M, Merler S, YPiontti AP, Mu K, Rossi L, Sun K, et al. (2020). The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak. Science, 368(6489), 395-400.","DOI":"10.1126\/science.aba9757"},{"key":"814_CR10","unstructured":"CSSE, J. COVID-19 Dashboard by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University. 2020."},{"key":"814_CR11","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1016\/j.envsoft.2014.08.027","volume":"62","author":"AT Crooks","year":"2014","unstructured":"Crooks AT, Hailegiorgis AB (2014) An agent-based modeling approach applied to the spread of cholera. Environ Model Softw 62:164\u2013177","journal-title":"Environ Model Softw"},{"key":"814_CR12","unstructured":"CSSE J (2020) Coronavirus covid-19 global cases by the center for systems science and engineering (csse) at johns hopkins university (jhu)"},{"key":"814_CR13","unstructured":"Centers for Disease\u00a0Control C, Prevention et\u00a0al. (2012) First global estimates of 2009 h1n1 pandemic mortality released by cdc-led collaboration"},{"issue":"7256","key":"814_CR14","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1038\/460687a","volume":"460","author":"JM Epstein","year":"2009","unstructured":"Epstein JM (2009) Modelling to contain pandemics. Nature 460(7256):687\u2013687","journal-title":"Nature"},{"key":"814_CR15","doi-asserted-by":"crossref","unstructured":"Estonia S (2018) Quarterly bulletin of statistics Estonia. An overview of social and economic developments in Estonia. Statistics Estonia, Tallinn 25","DOI":"10.1787\/int_trade-v2018-1-10-en"},{"issue":"6988","key":"814_CR16","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1038\/nature02541","volume":"429","author":"S Eubank","year":"2004","unstructured":"Eubank S, Guclu H, Kumar VA, Marathe MV, Srinivasan A, Toroczkai Z, Wang N (2004) Modelling disease outbreaks in realistic urban social networks. Nature 429(6988):180\u2013184","journal-title":"Nature"},{"key":"814_CR17","doi-asserted-by":"crossref","unstructured":"Fekih M, Bellemans T, Smoreda Z, Bonnel P, Furno A, Galland S (2020) A data-driven approach for origin\u2013destination matrix construction from cellular network signalling data: a case study of Lyon region (France). Transportation, pp 1\u201332","DOI":"10.1007\/s11116-020-10108-w"},{"key":"814_CR18","doi-asserted-by":"publisher","unstructured":"Goel R, Sharma R (2020) Mobility based sir model for pandemics\u2014with case study of covid-19. In: 2020 IEEE\/ACM international conference on advances in social networks analysis and mining (ASONAM), pp 110\u2013117. https:\/\/doi.org\/10.1109\/ASONAM49781.2020.9381457","DOI":"10.1109\/ASONAM49781.2020.9381457"},{"issue":"3","key":"814_CR19","doi-asserted-by":"publisher","first-page":"e0248212","DOI":"10.1371\/journal.pone.0248212","volume":"16","author":"R Goel","year":"2021","unstructured":"Goel R, Sharma R, Aasa A (2021) Understanding gender segregation through call data records: an Estonian case study. PLoS ONE 16(3):e0248212","journal-title":"PLoS ONE"},{"key":"814_CR20","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1016\/j.physa.2018.11.035","volume":"518","author":"R Goel","year":"2019","unstructured":"Goel R, Singh A, Ghanbarnejad F (2019) Modeling competitive marketing strategies in social networks. Phys A Stat Mech Appl 518:50\u201370","journal-title":"Phys A Stat Mech Appl"},{"issue":"10","key":"814_CR21","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1503\/cmaj.091641","volume":"181","author":"MZ Gojovic","year":"2009","unstructured":"Gojovic MZ, Sander B, Fisman D, Krahn MD, Bauch CT (2009) Modelling mitigation strategies for pandemic (h1n1). CMAJ 181(10):673\u2013680","journal-title":"CMAJ"},{"key":"814_CR22","unstructured":"Hagberg A, Swart P, Chult SD (2008) Exploring network structure, dynamics, and function using networkx. Tech. rep., Los Alamos National Lab.(LANL), Los Alamos, NM (United States)"},{"issue":"4","key":"814_CR23","doi-asserted-by":"publisher","first-page":"599","DOI":"10.1137\/S0036144500371907","volume":"42","author":"HW Hethcote","year":"2000","unstructured":"Hethcote HW (2000) The mathematics of infectious diseases. SIAM Rev 42(4):599\u2013653","journal-title":"SIAM Rev"},{"key":"814_CR24","doi-asserted-by":"crossref","unstructured":"Hiir H, Sharma R, Aasa A, Saluveer E (2019) Impact of natural and social events on mobile call data records\u2013an estonian case study. In: International conference on complex networks and their applications, pp 415\u2013426. Springer","DOI":"10.1007\/978-3-030-36683-4_34"},{"key":"814_CR25","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1016\/j.envres.2016.01.013","volume":"146","author":"X Huang","year":"2016","unstructured":"Huang X, Clements AC, Williams G, Mengersen K, Tong S, Hu W (2016) Bayesian estimation of the dynamics of pandemic (h1n1) 2009 influenza transmission in queensland: a space-time sir-based model. Environ Res 146:308\u2013314","journal-title":"Environ Res"},{"issue":"106","key":"814_CR26","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1002\/tl.229","volume":"2006","author":"M Hurley","year":"2006","unstructured":"Hurley M, Jacobs G, Gilbert M (2006) The basic si model. New Directions Teach Learn 2006(106):11\u201322","journal-title":"New Directions Teach Learn"},{"issue":"5","key":"814_CR27","doi-asserted-by":"publisher","first-page":"1482","DOI":"10.1016\/j.chaos.2006.04.022","volume":"34","author":"Y Jin","year":"2007","unstructured":"Jin Y, Wang W, Xiao S (2007) An sirs model with a nonlinear incidence rate. Chaos Solitons Fractals 34(5):1482\u20131497","journal-title":"Chaos Solitons Fractals"},{"key":"814_CR28","doi-asserted-by":"crossref","unstructured":"Kermack WO, McKendrick AG (1927) A contribution to the mathematical theory of epidemics. In: Proceedings of the royal society of London a: mathematical, physical and engineering sciences, vol 115, pp 700\u2013721. The Royal Society","DOI":"10.1098\/rspa.1927.0118"},{"key":"814_CR29","doi-asserted-by":"crossref","unstructured":"Khalil KM, Abdel-Aziz M, Nazmy TT, Salem ABM (2012) An agent-based modeling for pandemic influenza in Egypt. In: Handbook on decision making, pp 205\u2013218. Springer","DOI":"10.1007\/978-3-642-25755-1_11"},{"key":"814_CR30","doi-asserted-by":"crossref","unstructured":"Kiskowski MA (2014) A three-scale network model for the early growth dynamics of 2014 west Africa Ebola epidemic. PLoS Curr 6","DOI":"10.1371\/currents.outbreaks.c6efe8274dc55274f05cbcb62bbe6070"},{"issue":"3","key":"814_CR31","doi-asserted-by":"publisher","first-page":"534","DOI":"10.1109\/TAC.2005.864203","volume":"51","author":"X Li","year":"2006","unstructured":"Li X, Wang X (2006) Controlling the spreading in small-world evolving networks: stability, oscillation, and topology. IEEE Trans Autom Control 51(3):534\u2013540","journal-title":"IEEE Trans Autom Control"},{"issue":"1","key":"814_CR32","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1186\/s13662-015-0619-z","volume":"2015","author":"L Liu","year":"2015","unstructured":"Liu L (2015) A delayed sir model with general nonlinear incidence rate. Adv Differ Equ 2015(1):329","journal-title":"Adv Differ Equ"},{"issue":"4","key":"814_CR33","first-page":"521","volume":"26","author":"Y Moreno","year":"2002","unstructured":"Moreno Y, Pastor-Satorras R, Vespignani A (2002) Epidemic outbreaks in complex heterogeneous networks. Eur Phys J B-Condens Matter Complex Syst 26(4):521\u2013529","journal-title":"Eur Phys J B-Condens Matter Complex Syst"},{"issue":"3","key":"814_CR34","doi-asserted-by":"publisher","first-page":"895","DOI":"10.2307\/1428186","volume":"28","author":"I N\u00e5sell","year":"1996","unstructured":"N\u00e5sell I (1996) The quasi-stationary distribution of the closed endemic sis model. Adv Appl Probab 28(3):895\u2013932","journal-title":"Adv Appl Probab"},{"issue":"2","key":"814_CR35","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1137\/S003614450342480","volume":"45","author":"ME Newman","year":"2003","unstructured":"Newman ME (2003) The structure and function of complex networks. SIAM Rev 45(2):167\u2013256","journal-title":"SIAM Rev"},{"key":"814_CR36","unstructured":"Organization WH, et al. (2009) Pandemic h1n1 2009. Tech. rep, WHO Regional Office for South-East Asia"},{"key":"814_CR37","unstructured":"Organization WH, et\u00a0al. (2020) Coronavirus disease 2019 (covid-19): situation report 46"},{"issue":"3","key":"814_CR38","doi-asserted-by":"publisher","first-page":"925","DOI":"10.1103\/RevModPhys.87.925","volume":"87","author":"R Pastor-Satorras","year":"2015","unstructured":"Pastor-Satorras R, Castellano C, Van Mieghem P, Vespignani A (2015) Epidemic processes in complex networks. Rev Modern Phys 87(3):925","journal-title":"Rev Modern Phys"},{"issue":"2","key":"814_CR39","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1080\/0022250X.1971.9989794","volume":"1","author":"TC Schelling","year":"1971","unstructured":"Schelling TC (1971) Dynamic models of segregation. J Math Sociol 1(2):143\u2013186","journal-title":"J Math Sociol"},{"issue":"8\u20139","key":"814_CR40","doi-asserted-by":"publisher","first-page":"2133","DOI":"10.1016\/j.physa.2007.11.048","volume":"387","author":"H Shi","year":"2008","unstructured":"Shi H, Duan Z, Chen G (2008) An sis model with infective medium on complex networks. Phys A Stat Mech Appl 387(8\u20139):2133\u20132144","journal-title":"Phys A Stat Mech Appl"},{"key":"814_CR41","unstructured":"Singh A, Singh YN (22012) Nonlinear spread of rumor and inoculation strategies in the nodes with degree dependent tie strength in complex networks. arXiv:1208.6063"},{"key":"814_CR42","volume-title":"Cognition and multi-agent interaction: from cognitive modeling to social simulation","author":"R Sun","year":"2006","unstructured":"Sun R et al (2006) Cognition and multi-agent interaction: from cognitive modeling to social simulation. Cambridge University Press, Cambridge"},{"key":"814_CR43","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/j.jtbi.2011.08.011","volume":"289","author":"S Towers","year":"2011","unstructured":"Towers S, Geisse KV, Zheng Y, Feng Z (2011) Antiviral treatment for pandemic influenza: assessing potential repercussions using a seasonally forced sir model. J Theor Biol 289:259\u2013268","journal-title":"J Theor Biol"},{"key":"814_CR44","doi-asserted-by":"crossref","unstructured":"Tuomisto JT, Yrj\u00f6l\u00e4 J, Kolehmainen M, Bonsdorff J, Pekkanen J, Tikkanen T (2020) An agent-based epidemic model reina for covid-19 to identify destructive policies. medRxiv","DOI":"10.1101\/2020.04.09.20047498"},{"issue":"1","key":"814_CR45","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1038\/nphys2160","volume":"8","author":"A Vespignani","year":"2012","unstructured":"Vespignani A (2012) Modelling dynamical processes in complex socio-technical systems. Nat Phys 8(1):32","journal-title":"Nat Phys"},{"key":"814_CR46","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/j.epidem.2016.01.002","volume":"15","author":"C Viboud","year":"2016","unstructured":"Viboud C, Simonsen L, Chowell G (2016) A generalized-growth model to characterize the early ascending phase of infectious disease outbreaks. Epidemics 15:27\u201337","journal-title":"Epidemics"},{"issue":"4","key":"814_CR47","doi-asserted-by":"publisher","first-page":"043157","DOI":"10.1103\/PhysRevResearch.2.043157","volume":"2","author":"I Voitalov","year":"2020","unstructured":"Voitalov I, van der Hoorn P, Kitsak M, Papadopoulos F, Krioukov D (2020) Weighted hypersoft configuration model. Phys Rev Res 2(4):043157","journal-title":"Phys Rev Res"},{"issue":"3","key":"814_CR48","doi-asserted-by":"publisher","first-page":"927","DOI":"10.1007\/s11071-011-0313-y","volume":"69","author":"C Xia","year":"2012","unstructured":"Xia C, Wang L, Sun S, Wang J (2012) An sir model with infection delay and propagation vector in complex networks. Nonlinear Dyn 69(3):927\u2013934","journal-title":"Nonlinear Dyn"},{"key":"814_CR49","doi-asserted-by":"crossref","unstructured":"Zhang JZ, Wang JJ, Su TX, Jin Z (2010) Analysis of a delayed sir epidemic model. In: 2010 international conference on computational aspects of social networks (CASoN), pp 192\u2013195. IEEE","DOI":"10.1109\/CASoN.2010.50"}],"container-title":["Social Network Analysis and Mining"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13278-021-00814-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13278-021-00814-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13278-021-00814-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,20]],"date-time":"2021-11-20T14:37:40Z","timestamp":1637419060000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13278-021-00814-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,22]]},"references-count":49,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["814"],"URL":"https:\/\/doi.org\/10.1007\/s13278-021-00814-3","relation":{},"ISSN":["1869-5450","1869-5469"],"issn-type":[{"value":"1869-5450","type":"print"},{"value":"1869-5469","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,22]]},"assertion":[{"value":"12 April 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 July 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 August 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 October 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declaration"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable. As this work proposes a mathematical model with derivation.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Code availability"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}],"article-number":"105"}}