{"id":"https://openalex.org/W3132152677","doi":"https://doi.org/10.5220/0010252504750482","title":"A Discrete SIR Model with Spatial Distribution on a Torus for COVID-19 Analysis using Local Neighborhood Properties","display_name":"A Discrete SIR Model with Spatial Distribution on a Torus for COVID-19 Analysis using Local Neighborhood Properties","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3132152677","doi":"https://doi.org/10.5220/0010252504750482","mag":"3132152677"},"language":"en","primary_location":{"id":"doi:10.5220/0010252504750482","is_oa":true,"landing_page_url":"https://doi.org/10.5220/0010252504750482","pdf_url":null,"source":null,"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 14th International Joint Conference on Biomedical Engineering Systems and Technologies","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.5220/0010252504750482","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111500072","display_name":"Reinhard Schuster","orcid":null},"institutions":[{"id":"https://openalex.org/I266832205","display_name":"National Association of Statutory Health Insurance Physicians","ror":"https://ror.org/02jwgg565","country_code":"DE","type":"other","lineage":["https://openalex.org/I266832205"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Reinhard Schuster","raw_affiliation_strings":["Chair of Department of Health Economics, Epidemiology and Medical Informatics, Medical Advisory Board of Statutory Health Insurance in Northern Germany (MDK Nord), 23554 L\u00fcbeck, Germany, --- Select a Country ---"],"affiliations":[{"raw_affiliation_string":"Chair of Department of Health Economics, Epidemiology and Medical Informatics, Medical Advisory Board of Statutory Health Insurance in Northern Germany (MDK Nord), 23554 L\u00fcbeck, Germany, --- Select a Country ---","institution_ids":["https://openalex.org/I266832205"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020331818","display_name":"Klaus-Peter Thiele","orcid":null},"institutions":[{"id":"https://openalex.org/I266832205","display_name":"National Association of Statutory Health Insurance Physicians","ror":"https://ror.org/02jwgg565","country_code":"DE","type":"other","lineage":["https://openalex.org/I266832205"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Klaus-Peter Thiele","raw_affiliation_strings":["Medical Director of the Medical Advisory Service Institution of the Statutory Health Insurance in North Rhine (MDK Nordrhein), 40212 D\u00fcsseldorf, Germany, --- Select a Country ---"],"affiliations":[{"raw_affiliation_string":"Medical Director of the Medical Advisory Service Institution of the Statutory Health Insurance in North Rhine (MDK Nordrhein), 40212 D\u00fcsseldorf, Germany, --- Select a Country ---","institution_ids":["https://openalex.org/I266832205"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005083784","display_name":"Thomas Ostermann","orcid":"https://orcid.org/0000-0003-2695-0701"},"institutions":[{"id":"https://openalex.org/I155976169","display_name":"Witten/Herdecke University","ror":"https://ror.org/00yq55g44","country_code":"DE","type":"education","lineage":["https://openalex.org/I155976169"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Ostermann","raw_affiliation_strings":["Chair of Research Methodology and Statistics in Psychology, Witten/Herdecke University, Alfred-Herrhausen-Stra\u00dfe 50, 58448 Witten, Germany, --- Select a Country ---"],"affiliations":[{"raw_affiliation_string":"Chair of Research Methodology and Statistics in Psychology, Witten/Herdecke University, Alfred-Herrhausen-Stra\u00dfe 50, 58448 Witten, Germany, --- Select a Country ---","institution_ids":["https://openalex.org/I155976169"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011858015","display_name":"Mart\u00edn Schuster","orcid":"https://orcid.org/0000-0002-7674-0887"},"institutions":[{"id":"https://openalex.org/I32021983","display_name":"Kiel University","ror":"https://ror.org/04v76ef78","country_code":"DE","type":"education","lineage":["https://openalex.org/I32021983"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Schuster","raw_affiliation_strings":["Faculty of Epidemiology, Christian-Albrechts University Kiel, 24105 Kiel, Germany, --- Select a Country ---"],"affiliations":[{"raw_affiliation_string":"Faculty of Epidemiology, Christian-Albrechts University Kiel, 24105 Kiel, Germany, --- Select a Country ---","institution_ids":["https://openalex.org/I32021983"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5111500072"],"corresponding_institution_ids":["https://openalex.org/I266832205"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03838195,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"475","last_page":"482"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9854000210762024,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9854000210762024,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.9842000007629395,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13283","display_name":"Mental Health Research Topics","score":0.9057999849319458,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.7220994830131531},{"id":"https://openalex.org/keywords/epidemic-model","display_name":"Epidemic model","score":0.6042351722717285},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5610823631286621},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.47848886251449585},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46741318702697754},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4476564824581146},{"id":"https://openalex.org/keywords/coronavirus-disease-2019","display_name":"Coronavirus disease 2019 (COVID-19)","score":0.439910888671875},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.42779213190078735},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.38903436064720154},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3570018708705902},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3250347673892975},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21293574571609497},{"id":"https://openalex.org/keywords/infectious-disease","display_name":"Infectious disease (medical specialty)","score":0.19844752550125122},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14253219962120056},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.1354578733444214}],"concepts":[{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.7220994830131531},{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.6042351722717285},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5610823631286621},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.47848886251449585},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46741318702697754},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4476564824581146},{"id":"https://openalex.org/C3008058167","wikidata":"https://www.wikidata.org/wiki/Q84263196","display_name":"Coronavirus disease 2019 (COVID-19)","level":4,"score":0.439910888671875},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.42779213190078735},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.38903436064720154},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3570018708705902},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3250347673892975},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21293574571609497},{"id":"https://openalex.org/C524204448","wikidata":"https://www.wikidata.org/wiki/Q788926","display_name":"Infectious disease (medical specialty)","level":3,"score":0.19844752550125122},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14253219962120056},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.1354578733444214},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C2779134260","wikidata":"https://www.wikidata.org/wiki/Q12136","display_name":"Disease","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C142724271","wikidata":"https://www.wikidata.org/wiki/Q7208","display_name":"Pathology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.5220/0010252504750482","is_oa":true,"landing_page_url":"https://doi.org/10.5220/0010252504750482","pdf_url":null,"source":null,"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 14th International Joint Conference on Biomedical Engineering Systems and Technologies","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.5220/0010252504750482","is_oa":true,"landing_page_url":"https://doi.org/10.5220/0010252504750482","pdf_url":null,"source":null,"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 14th International Joint Conference on Biomedical Engineering Systems and Technologies","raw_type":"proceedings-article"},"sustainable_development_goals":[{"display_name":"Good health and well-being","id":"https://metadata.un.org/sdg/3","score":0.800000011920929}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2167530280","https://openalex.org/W3124916295","https://openalex.org/W2022411416","https://openalex.org/W2146447767","https://openalex.org/W1487790116","https://openalex.org/W3197597876","https://openalex.org/W4248544590","https://openalex.org/W1529020016","https://openalex.org/W4381247976","https://openalex.org/W2038335296"],"abstract_inverted_index":{"The":[0,91,126,185,248,307,328],"ongoing":[1],"COVID-19":[2],"pandemic":[3],"threatens":[4],"the":[5,16,19,31,38,59,71,100,132,162,168,180,210,213,225,232,236,293,319,332,336,340,343,351],"health":[6],"of":[7,18,30,33,40,158,172,207,212,289,310,331,339,342],"humans,":[8],"causes":[9],"great":[10],"economic":[11],"losses":[12],"and":[13,35,58,82,99,156,202,231,238,241,295,371],"may":[14],"disturb":[15],"stability":[17],"societies":[20],"Mathematical":[22],"models":[23,333,362],"can":[24,94,195,222,262,314,347],"be":[25,95,135,147,177,189,263,298,315],"used":[26,324],"to":[27,36,131,146,176,219,276,292],"understand":[28],"aspects":[29],"dynamics":[32],"epidemics":[34],"increase":[37],"chances":[39],"control":[41,312],"strategies":[42,313],"We":[44],"propose":[45],"a":[46,87,107,114,138,199,203,266],"SIR":[47,88],"graph":[48,268,303],"network":[49],"model,":[50],"in":[51,104,144,148,161,179,282,300,325],"which":[52,119,346],"each":[53],"node":[54],"represents":[55],"an":[56,170,301],"individual":[57],"edges":[60,290],"represent":[61],"contacts":[62],"between":[63],"individuals":[64,124],"For":[66],"this":[67],"purpose,":[68],"we":[69],"use":[70],"healthy":[72],"S":[73,130],"(susceptible)":[74],"population":[75],"without":[76],"immune":[77],"behavior,":[78],"two":[79,83,163,181],"I-compartments":[80],"(infectious)":[81],"R-compartments":[84],"(recovered)":[85],"as":[86,97,355],"model":[89,305],"time":[92,154],"steps":[93],"interpreted":[96],"days":[98],"spatial":[101],"spread":[102],"(limited":[103],"distance":[105],"for":[106,256],"singe":[108],"step)":[109],"shell":[110],"take":[111],"place":[112],"on":[113,137,235],"200":[115,117],"by":[116,140,317,367],"torus,":[118],"should":[120,134,188,296],"simulate":[121],"40":[122],"thousand":[123],"disease":[127],"propagation":[128,159],"form":[129],"I-compartment":[133],"possible":[136],"k":[139,141],"square":[142],"(k=5":[143],"order":[145],"small":[149],"world":[150],"network)":[151],"with":[152,250,265,321],"different":[153,173,287],"periods":[155],"strength":[157],"probability":[160],"I":[164],"compartments":[165,183,252],"After":[167],"infection,":[169],"immunity":[171],"lengths":[174],"is":[175,253,356],"modeled":[178],"R":[182],"incoming":[186],"constants":[187,323],"chosen":[190],"so":[191],"that":[192],"realistic":[193],"scenarios":[194],"arise":[196,223,281],"With":[198],"random":[200],"distribution":[201],"low":[204],"case":[205],"number":[206],"diseases":[208],"at":[209],"beginning":[211],"simulation,":[214],"almost":[215],"periodic":[216],"patterns":[217],"similar":[218],"diffusion":[220],"processes":[221],"over":[224],"years":[226],"Mean":[228],"value":[229],"operators":[230],"Laplace":[233],"operator":[234],"torus":[237,249],"its":[239],"eigenfunctions":[240],"eigenvalues":[242],"are":[243,273,286],"relevant":[244],"reference":[245],"points":[246],"five":[251],"well":[254],"suited":[255],"visualization":[257],"Realistic":[259],"neighborhood":[260],"relationships":[261],"viewed":[264],"inhomogeneous":[267,283,302],"theoretic":[269],"approach,":[270],"but":[271],"they":[272],"more":[274],"difficult":[275],"visualize":[277],"Superspreaders":[279],"naturally":[280],"graphs:":[284],"there":[285],"numbers":[288],"adjacent":[291],"nodes":[294],"therefore":[297],"examined":[299],"theoretical":[304],"expected":[308,353],"effect":[309],"corona":[311],"evaluated":[316],"comparing":[318],"results":[320,334],"various":[322],"simulations":[326],"decisive":[329],"benefit":[330],"from":[335,350,359],"long-term":[337],"observation":[338],"consequences":[341],"assumptions":[344],"made,":[345],"differ":[348],"significantly":[349],"primarily":[352],"effects,":[354],"already":[357],"known":[358],"classic":[360],"predator-prey":[361],"Copyright":[364],"\u00a9":[365],"2021":[366],"SCITEPRESS":[368],"\u2013":[369],"Science":[370],"Technology":[372],"Publications,":[373],"Lda":[374],"All":[376],"rights":[377],"reserved":[378]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}