{"id":"https://openalex.org/W2954240226","doi":"https://doi.org/10.1137/19m1276030","title":"Global $L^\\infty$-bounds and Long-time Behavior of a Diffusive Epidemic System in A Heterogeneous Environment","display_name":"Global $L^\\infty$-bounds and Long-time Behavior of a Diffusive Epidemic System in A Heterogeneous Environment","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W2954240226","doi":"https://doi.org/10.1137/19m1276030","mag":"2954240226"},"language":"en","primary_location":{"id":"doi:10.1137/19m1276030","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1276030","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1276030","source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1276030","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057259121","display_name":"Rui Peng","orcid":"https://orcid.org/0000-0003-1481-1878"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rui Peng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5019493257","display_name":"Yixiang Wu","orcid":"https://orcid.org/0009-0003-1165-5993"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yixiang Wu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00234175,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"53","issue":"3","first_page":"2776","last_page":"2810"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9943000078201294,"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"}},{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.988099992275238,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.6441785097122192},{"id":"https://openalex.org/keywords/mechanism","display_name":"Mechanism (biology)","score":0.6313190460205078},{"id":"https://openalex.org/keywords/incidence","display_name":"Incidence (geometry)","score":0.5832902789115906},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.5653097629547119},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5524291396141052},{"id":"https://openalex.org/keywords/infection-rate","display_name":"Infection rate","score":0.5409345030784607},{"id":"https://openalex.org/keywords/epidemic-model","display_name":"Epidemic model","score":0.48845210671424866},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.46382179856300354},{"id":"https://openalex.org/keywords/transmission-rate","display_name":"Transmission rate","score":0.45342326164245605},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43160149455070496},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4253448247909546},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.41950303316116333},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40643078088760376},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3746787905693054},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3049014210700989},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.24971213936805725},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23767146468162537},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.17576801776885986},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09655576944351196},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09560731053352356},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.08883902430534363},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.08505064249038696},{"id":"https://openalex.org/keywords/surgery","display_name":"Surgery","score":0.08310997486114502},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07834789156913757}],"concepts":[{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.6441785097122192},{"id":"https://openalex.org/C89611455","wikidata":"https://www.wikidata.org/wiki/Q6804646","display_name":"Mechanism (biology)","level":2,"score":0.6313190460205078},{"id":"https://openalex.org/C61511704","wikidata":"https://www.wikidata.org/wiki/Q1671857","display_name":"Incidence (geometry)","level":2,"score":0.5832902789115906},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.5653097629547119},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5524291396141052},{"id":"https://openalex.org/C2781254715","wikidata":"https://www.wikidata.org/wiki/Q28454687","display_name":"Infection rate","level":2,"score":0.5409345030784607},{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.48845210671424866},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.46382179856300354},{"id":"https://openalex.org/C2989335485","wikidata":"https://www.wikidata.org/wiki/Q17130189","display_name":"Transmission rate","level":3,"score":0.45342326164245605},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43160149455070496},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4253448247909546},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.41950303316116333},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40643078088760376},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3746787905693054},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3049014210700989},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.24971213936805725},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23767146468162537},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.17576801776885986},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09655576944351196},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09560731053352356},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.08883902430534363},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.08505064249038696},{"id":"https://openalex.org/C141071460","wikidata":"https://www.wikidata.org/wiki/Q40821","display_name":"Surgery","level":1,"score":0.08310997486114502},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07834789156913757},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/19m1276030","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1276030","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1276030","source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1906.11699","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1906.11699","pdf_url":"https://arxiv.org/pdf/1906.11699","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2954240226","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1906.11699.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1906.11699","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1906.11699","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1137/19m1276030","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1276030","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1276030","source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Good health and well-being","score":0.8700000047683716,"id":"https://metadata.un.org/sdg/3"}],"awards":[{"id":"https://openalex.org/G1214771387","display_name":null,"funder_award_id":"PPZY2015A013","funder_id":"https://openalex.org/F4320327518","funder_display_name":"Priority Academic Program Development of Jiangsu Higher Education Institutions"},{"id":"https://openalex.org/G6281681593","display_name":null,"funder_award_id":"11671175","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7762091665","display_name":null,"funder_award_id":"11571200","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320327518","display_name":"Priority Academic Program Development of Jiangsu Higher Education Institutions","ror":null},{"id":"https://openalex.org/F4320327794","display_name":"Qinglan Project of Jiangsu Province of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":68,"referenced_works":["https://openalex.org/W42416990","https://openalex.org/W429124266","https://openalex.org/W573861537","https://openalex.org/W786402039","https://openalex.org/W1502700877","https://openalex.org/W1530753300","https://openalex.org/W1964385385","https://openalex.org/W1965297777","https://openalex.org/W1976180149","https://openalex.org/W1978518692","https://openalex.org/W1982075903","https://openalex.org/W1983289483","https://openalex.org/W1987887637","https://openalex.org/W1991316593","https://openalex.org/W1998454639","https://openalex.org/W2007136636","https://openalex.org/W2008072444","https://openalex.org/W2009974093","https://openalex.org/W2010365240","https://openalex.org/W2026112886","https://openalex.org/W2026613779","https://openalex.org/W2027467474","https://openalex.org/W2030737007","https://openalex.org/W2034567399","https://openalex.org/W2041714615","https://openalex.org/W2043848381","https://openalex.org/W2045441942","https://openalex.org/W2045600974","https://openalex.org/W2046565293","https://openalex.org/W2046573764","https://openalex.org/W2052688383","https://openalex.org/W2053000491","https://openalex.org/W2059655508","https://openalex.org/W2072573489","https://openalex.org/W2075489080","https://openalex.org/W2075732279","https://openalex.org/W2076770469","https://openalex.org/W2078843568","https://openalex.org/W2082344888","https://openalex.org/W2089450265","https://openalex.org/W2090749521","https://openalex.org/W2093076707","https://openalex.org/W2119640236","https://openalex.org/W2120262351","https://openalex.org/W2122128564","https://openalex.org/W2138620270","https://openalex.org/W2140981476","https://openalex.org/W2148301044","https://openalex.org/W2161728228","https://openalex.org/W2324618167","https://openalex.org/W2331010667","https://openalex.org/W2335001735","https://openalex.org/W2417541270","https://openalex.org/W2476416964","https://openalex.org/W2479753101","https://openalex.org/W2494123768","https://openalex.org/W2496244094","https://openalex.org/W2503087438","https://openalex.org/W2513863067","https://openalex.org/W2530986378","https://openalex.org/W2604314459","https://openalex.org/W2734591266","https://openalex.org/W2736745096","https://openalex.org/W2755612150","https://openalex.org/W2771000493","https://openalex.org/W2804930536","https://openalex.org/W2885465254","https://openalex.org/W2963687555"],"related_works":["https://openalex.org/W2923237801","https://openalex.org/W3094393994","https://openalex.org/W2401308580","https://openalex.org/W1494918975","https://openalex.org/W2037917318","https://openalex.org/W3171334301","https://openalex.org/W3100955342","https://openalex.org/W2901554521","https://openalex.org/W3202281170","https://openalex.org/W2187878512","https://openalex.org/W1879209320","https://openalex.org/W1974841834","https://openalex.org/W2224839352","https://openalex.org/W3190961213","https://openalex.org/W2979684187","https://openalex.org/W2788130594","https://openalex.org/W2966912878","https://openalex.org/W3191682343","https://openalex.org/W3191268536","https://openalex.org/W3206547438"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,57],"are":[4,24],"concerned":[5],"with":[6,11],"an":[7],"epidemic":[8],"reaction-diffusion":[9],"system":[10,23],"nonlinear":[12],"incidence":[13,102],"mechanism":[14],"of":[15,21,38,41,44,63,66,75,100],"the":[16,22,36,39,60,64,67,72,76,88],"form":[17],"$S^qI^p\\,(p,\\,q&gt;0)$.":[18],"The":[19],"coefficients":[20],"spatially":[25],"heterogeneous":[26],"and":[27,83],"time":[28,31],"dependent":[29],"(particularly":[30],"periodic).":[32],"We":[33],"first":[34],"establish":[35],"$L^\\infty$-bounds":[37],"solutions":[40,65],"a":[42],"class":[43],"systems,":[45],"which":[46],"improve":[47],"some":[48,97],"previous":[49],"results":[50,70],"in":[51],"[58].":[52],"Based":[53],"on":[54,87],"such":[55],"estimates,":[56],"then":[58],"study":[59],"long-time":[61],"behavior":[62],"system.":[68],"Our":[69,91],"reveal":[71],"delicate":[73],"effect":[74],"infection":[77,89,101],"mechanism,":[78],"transmission":[79],"rate,":[80],"recovery":[81],"rate":[82,86],"disease-induced":[84],"mortality":[85],"dynamics.":[90],"analysis":[92],"can":[93],"be":[94],"adapted":[95],"to":[96],"other":[98],"types":[99],"mechanisms.":[103]},"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
