{"id":"https://openalex.org/W4306406292","doi":"https://doi.org/10.1137/22m1472127","title":"Sparse Optimal Control of Pattern Formations for an SIR Reaction-Diffusion Epidemic Model","display_name":"Sparse Optimal Control of Pattern Formations for an SIR Reaction-Diffusion Epidemic Model","publication_year":2022,"publication_date":"2022-10-17","ids":{"openalex":"https://openalex.org/W4306406292","doi":"https://doi.org/10.1137/22m1472127"},"language":"en","primary_location":{"id":"doi:10.1137/22m1472127","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1472127","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055338343","display_name":"Lili Chang","orcid":"https://orcid.org/0000-0003-3744-1902"},"institutions":[{"id":"https://openalex.org/I181877577","display_name":"Shanxi University","ror":"https://ror.org/03y3e3s17","country_code":"CN","type":"education","lineage":["https://openalex.org/I181877577"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lili Chang","raw_affiliation_strings":["Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China, and Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis for Disease Control and Prevention, Taiyuan 030006, Shanxi, China (, , )"],"raw_orcid":"https://orcid.org/0000-0003-3744-1902","affiliations":[{"raw_affiliation_string":"Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China, and Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis for Disease Control and Prevention, Taiyuan 030006, Shanxi, China (, , )","institution_ids":["https://openalex.org/I181877577"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113681346","display_name":"Wei Gong","orcid":"https://orcid.org/0000-0003-3251-8771"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Gong","raw_affiliation_strings":["LSEC & NCMIS, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China "],"raw_orcid":"https://orcid.org/0000-0003-3251-8771","affiliations":[{"raw_affiliation_string":"LSEC & NCMIS, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China ","institution_ids":["https://openalex.org/I4210120485"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100779363","display_name":"Zhen Jin","orcid":"https://orcid.org/0000-0002-9763-707X"},"institutions":[{"id":"https://openalex.org/I181877577","display_name":"Shanxi University","ror":"https://ror.org/03y3e3s17","country_code":"CN","type":"education","lineage":["https://openalex.org/I181877577"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhen Jin","raw_affiliation_strings":["Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China, and Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis for Disease Control and Prevention, Taiyuan 030006, Shanxi, China (, , )"],"raw_orcid":"https://orcid.org/0000-0002-9763-707X","affiliations":[{"raw_affiliation_string":"Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China, and Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis for Disease Control and Prevention, Taiyuan 030006, Shanxi, China (, , )","institution_ids":["https://openalex.org/I181877577"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033844050","display_name":"Gui\u2010Quan Sun","orcid":"https://orcid.org/0000-0002-1831-1603"},"institutions":[{"id":"https://openalex.org/I181877577","display_name":"Shanxi University","ror":"https://ror.org/03y3e3s17","country_code":"CN","type":"education","lineage":["https://openalex.org/I181877577"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gui-Quan Sun","raw_affiliation_strings":["Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China, and Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis for Disease Control and Prevention, Taiyuan 030006, Shanxi, China (, , )"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China, and Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis for Disease Control and Prevention, Taiyuan 030006, Shanxi, China (, , )","institution_ids":["https://openalex.org/I181877577"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":13.1525,"has_fulltext":false,"cited_by_count":80,"citation_normalized_percentile":{"value":0.99383402,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"82","issue":"5","first_page":"1764","last_page":"1790"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.9923999905586243,"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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/epidemic-model","display_name":"Epidemic model","score":0.7333157062530518},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.6834002733230591},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5246486663818359},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5018925666809082},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43336641788482666},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.426442414522171},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3818334639072418},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3622046113014221},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32165849208831787},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2605307102203369},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24730491638183594},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.19561871886253357},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.10100024938583374},{"id":"https://openalex.org/keywords/sociology","display_name":"Sociology","score":0.10050925612449646},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.08560335636138916}],"concepts":[{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.7333157062530518},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.6834002733230591},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5246486663818359},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5018925666809082},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43336641788482666},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.426442414522171},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3818334639072418},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3622046113014221},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32165849208831787},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2605307102203369},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24730491638183594},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.19561871886253357},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.10100024938583374},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.10050925612449646},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.08560335636138916}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1472127","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1472127","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/3","score":0.8600000143051147,"display_name":"Good health and well-being"}],"awards":[{"id":"https://openalex.org/G1905182098","display_name":null,"funder_award_id":"12022113","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3456523697","display_name":"\u504f\u5fae\u5206\u65b9\u7a0bDirichlet\u8fb9\u754c\u6700\u4f18\u63a7\u5236\u95ee\u9898\u7684\u7406\u8bba\u4e0e\u7b97\u6cd5","funder_award_id":"12071468","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6778380423","display_name":null,"funder_award_id":"2020XM18","funder_id":"https://openalex.org/F4320317788","funder_display_name":"Health Commission of Shanxi Province"},{"id":"https://openalex.org/G7680086882","display_name":null,"funder_award_id":"61873154","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320317788","display_name":"Health Commission of Shanxi Province","ror":null},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W161997657","https://openalex.org/W594510519","https://openalex.org/W596189563","https://openalex.org/W1516984117","https://openalex.org/W1527296550","https://openalex.org/W1820125862","https://openalex.org/W1980274228","https://openalex.org/W1980661496","https://openalex.org/W1982075903","https://openalex.org/W1984935193","https://openalex.org/W1987309612","https://openalex.org/W1998360322","https://openalex.org/W2015074865","https://openalex.org/W2019177912","https://openalex.org/W2030036911","https://openalex.org/W2033593383","https://openalex.org/W2039114462","https://openalex.org/W2045970981","https://openalex.org/W2046841254","https://openalex.org/W2046904024","https://openalex.org/W2046922593","https://openalex.org/W2047506587","https://openalex.org/W2048402528","https://openalex.org/W2075489080","https://openalex.org/W2090430607","https://openalex.org/W2105531341","https://openalex.org/W2120030832","https://openalex.org/W2131506636","https://openalex.org/W2139473935","https://openalex.org/W2145068255","https://openalex.org/W2167829186","https://openalex.org/W2335001735","https://openalex.org/W2337525307","https://openalex.org/W2515040453","https://openalex.org/W2550946907","https://openalex.org/W2750944176","https://openalex.org/W2959652141","https://openalex.org/W2999960596","https://openalex.org/W3082144192","https://openalex.org/W3114706885","https://openalex.org/W3164189468","https://openalex.org/W3186534655","https://openalex.org/W4221070309","https://openalex.org/W4234903469","https://openalex.org/W4239670818","https://openalex.org/W4281634209","https://openalex.org/W4292156591"],"related_works":["https://openalex.org/W1892002403","https://openalex.org/W4309005041","https://openalex.org/W2147581087","https://openalex.org/W2962746246","https://openalex.org/W1989531755","https://openalex.org/W1967384683","https://openalex.org/W2291447000","https://openalex.org/W2892237068","https://openalex.org/W2032624981","https://openalex.org/W1901119619"],"abstract_inverted_index":{".Pattern":[0],"formation":[1],"arising":[2],"from":[3],"the":[4,13,27,48,60,73,116,122,128,135,139,145,151],"reaction-diffusion":[5,34],"epidemic":[6,35,62,118],"model":[7],"is":[8],"a":[9,51,66,69,77,86,93,104,109],"space-time":[10,97],"depiction":[11],"of":[12,17,50,59,72,124,138,155],"distribution":[14],"and":[15,142,153],"transmission":[16,45],"infectious":[18],"diseases.":[19],"Disease":[20],"control":[21,56,70,79,105,112,140,146],"can":[22],"be":[23],"achieved":[24],"by":[25,115],"controlling":[26],"associated":[28],"pattern":[29,41,57,88],"formations.":[30],"For":[31,76],"an":[32],"SIR":[33,61,117],"model,":[36,63],"we":[37,64,107],"review":[38],"its":[39],"Turing":[40],"formations":[42,58],"with":[43],"different":[44],"rates":[46],"under":[47],"case":[49],"constant":[52],"recovery":[53,74],"rate.":[54,75],"To":[55],"introduce":[65],"regulator":[67],"as":[68],"function":[71],"perfect":[78],"strategy,":[80,106],"it":[81],"not":[82],"only":[83],"leads":[84],"to":[85,101],"desired":[87],"formation,":[89],"but":[90],"also":[91],"has":[92],"small":[94],"support":[95],"in":[96],"domains.":[98],"In":[99],"order":[100,130],"obtain":[102,134],"such":[103],"propose":[108],"sparse":[110],"optimal":[111,125],"problem":[113],"governed":[114],"model.":[119],"We":[120],"study":[121],"existence":[123],"solutions,":[126],"derive":[127],"first":[129],"necessary":[131],"optimality":[132],"system,":[133],"sparsity":[136],"structure":[137],"function,":[141],"numerically":[143],"solve":[144],"problem.":[147],"Numerical":[148],"results":[149],"demonstrate":[150],"feasibility":[152],"effectivity":[154],"our":[156],"method.Keywordsreaction-diffusionepidemic":[157],"modelTuring":[158],"patternoptimal":[159],"controlsparse":[160],"controlMSC":[161],"codes35K5749J2049K2092D30":[162]},"counts_by_year":[{"year":2026,"cited_by_count":12},{"year":2025,"cited_by_count":25},{"year":2024,"cited_by_count":25},{"year":2023,"cited_by_count":18}],"updated_date":"2026-07-16T13:24:37.021932","created_date":"2025-10-10T00:00:00"}