{"id":"https://openalex.org/W4389045180","doi":"https://doi.org/10.3390/axioms12121085","title":"Spatiotemporal Dynamics of a Diffusive Immunosuppressive Infection Model with Nonlocal Competition and Crowley\u2013Martin Functional Response","display_name":"Spatiotemporal Dynamics of a Diffusive Immunosuppressive Infection Model with Nonlocal Competition and Crowley\u2013Martin Functional Response","publication_year":2023,"publication_date":"2023-11-27","ids":{"openalex":"https://openalex.org/W4389045180","doi":"https://doi.org/10.3390/axioms12121085"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12121085","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms12121085","pdf_url":"https://www.mdpi.com/2075-1680/12/12/1085/pdf?version=1701229767","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/12/1085/pdf?version=1701229767","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100399510","display_name":"Yuan Xue","orcid":"https://orcid.org/0000-0002-2250-3659"},"institutions":[{"id":"https://openalex.org/I47689461","display_name":"Northeast Forestry University","ror":"https://ror.org/02yxnh564","country_code":"CN","type":"education","lineage":["https://openalex.org/I47689461"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuan Xue","raw_affiliation_strings":["Department of Mathematics, Northeast Forestry University, Harbin 150040, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Northeast Forestry University, Harbin 150040, China","institution_ids":["https://openalex.org/I47689461"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112284213","display_name":"Jinli Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I47689461","display_name":"Northeast Forestry University","ror":"https://ror.org/02yxnh564","country_code":"CN","type":"education","lineage":["https://openalex.org/I47689461"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinli Xu","raw_affiliation_strings":["Department of Mathematics, Northeast Forestry University, Harbin 150040, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Northeast Forestry University, Harbin 150040, China","institution_ids":["https://openalex.org/I47689461"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022372271","display_name":"Yuting Ding","orcid":"https://orcid.org/0000-0002-1372-2585"},"institutions":[{"id":"https://openalex.org/I47689461","display_name":"Northeast Forestry University","ror":"https://ror.org/02yxnh564","country_code":"CN","type":"education","lineage":["https://openalex.org/I47689461"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuting Ding","raw_affiliation_strings":["Department of Mathematics, Northeast Forestry University, Harbin 150040, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Northeast Forestry University, Harbin 150040, China","institution_ids":["https://openalex.org/I47689461"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5022372271"],"corresponding_institution_ids":["https://openalex.org/I47689461"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.28608753,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"12","first_page":"1085","last_page":"1085"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9934999942779541,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9672999978065491,"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/competition","display_name":"Competition (biology)","score":0.7020646333694458},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.676699161529541},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5755696296691895},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5221569538116455},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.5014810562133789},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.45318007469177246},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45099660754203796},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4434109628200531},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.4334176778793335},{"id":"https://openalex.org/keywords/competition-model","display_name":"Competition model","score":0.4235765337944031},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3713790774345398},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.34007135033607483},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33962953090667725},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23837438225746155},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.17922323942184448},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.1591757833957672},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.14254680275917053},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.11191612482070923},{"id":"https://openalex.org/keywords/neoclassical-economics","display_name":"Neoclassical economics","score":0.09579271078109741},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.07675445079803467},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06873142719268799}],"concepts":[{"id":"https://openalex.org/C91306197","wikidata":"https://www.wikidata.org/wiki/Q45767","display_name":"Competition (biology)","level":2,"score":0.7020646333694458},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.676699161529541},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5755696296691895},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5221569538116455},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.5014810562133789},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.45318007469177246},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45099660754203796},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4434109628200531},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.4334176778793335},{"id":"https://openalex.org/C2777963317","wikidata":"https://www.wikidata.org/wiki/Q5156331","display_name":"Competition model","level":3,"score":0.4235765337944031},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3713790774345398},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.34007135033607483},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33962953090667725},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23837438225746155},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.17922323942184448},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.1591757833957672},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.14254680275917053},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.11191612482070923},{"id":"https://openalex.org/C133425853","wikidata":"https://www.wikidata.org/wiki/Q60571","display_name":"Neoclassical economics","level":1,"score":0.09579271078109741},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07675445079803467},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06873142719268799},{"id":"https://openalex.org/C181622380","wikidata":"https://www.wikidata.org/wiki/Q26911","display_name":"Profit (economics)","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12121085","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms12121085","pdf_url":"https://www.mdpi.com/2075-1680/12/12/1085/pdf?version=1701229767","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:86d256296c814984bf01d7401d85c078","is_oa":true,"landing_page_url":"https://doaj.org/article/86d256296c814984bf01d7401d85c078","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 12, p 1085 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/12/1085/","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12121085","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12121085","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms12121085","pdf_url":"https://www.mdpi.com/2075-1680/12/12/1085/pdf?version=1701229767","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2376276132","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G2558946211","display_name":null,"funder_award_id":"2572022DJ07","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G8951484681","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4389045180.pdf","grobid_xml":"https://content.openalex.org/works/W4389045180.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W617294916","https://openalex.org/W1968416705","https://openalex.org/W1971972446","https://openalex.org/W1981292246","https://openalex.org/W2012659064","https://openalex.org/W2014110552","https://openalex.org/W2037127778","https://openalex.org/W2042160189","https://openalex.org/W2061758202","https://openalex.org/W2061879675","https://openalex.org/W2076027168","https://openalex.org/W2093156174","https://openalex.org/W2099752536","https://openalex.org/W2107014805","https://openalex.org/W2138088412","https://openalex.org/W2143148297","https://openalex.org/W2160961295","https://openalex.org/W2182433753","https://openalex.org/W2323873405","https://openalex.org/W2572520066","https://openalex.org/W2574302933","https://openalex.org/W2610162979","https://openalex.org/W2991710166","https://openalex.org/W2995284206","https://openalex.org/W3021221538","https://openalex.org/W3022492353","https://openalex.org/W3086012612","https://openalex.org/W3104661078","https://openalex.org/W3183473574","https://openalex.org/W3196549322","https://openalex.org/W3206984108","https://openalex.org/W4221015504","https://openalex.org/W4225287054","https://openalex.org/W4290144769","https://openalex.org/W4380091446","https://openalex.org/W4386617092","https://openalex.org/W6619205837","https://openalex.org/W6680701482"],"related_works":["https://openalex.org/W1987790493","https://openalex.org/W2153388945","https://openalex.org/W2038701038","https://openalex.org/W1975783007","https://openalex.org/W2382752082","https://openalex.org/W1988489950","https://openalex.org/W4312255936","https://openalex.org/W4313700716","https://openalex.org/W1986426368","https://openalex.org/W2363522146"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,19,42,79,104],"introduce":[4],"the":[5,21,26,32,44,47,56,64,67,73,81,88,92,97,112,117,125,142],"Crowley\u2013Martin":[6],"functional":[7],"response":[8],"and":[9,23,37,52,122],"nonlocal":[10,35,59,120,126],"competition":[11,36],"into":[12],"a":[13],"reaction\u2013diffusion":[14],"immunosuppressive":[15],"infection":[16],"model.":[17],"First,":[18],"analyze":[20],"existence":[22],"stability":[24],"of":[25,31,49,55,69,72,91,119],"positive":[27],"constant":[28],"steady":[29],"states":[30],"systems":[33,110],"with":[34,58,75],"local":[38,76],"competition,":[39,60,121],"respectively.":[40],"Second,":[41],"deduce":[43],"conditions":[45,65],"for":[46,66,100,108,141],"occurrence":[48,68],"Turing,":[50],"Hopf,":[51],"Turing\u2013Hopf":[53],"bifurcations":[54,71,94],"system":[57,74],"as":[61,63],"well":[62],"Hopf":[70,93],"competition.":[77],"Furthermore,":[78],"employ":[80],"multiple":[82],"time":[83],"scales":[84],"method":[85],"to":[86],"derive":[87],"normal":[89],"forms":[90],"reduced":[95],"on":[96],"center":[98],"manifold":[99],"both":[101,109],"systems.":[102],"Finally,":[103],"conduct":[105],"numerical":[106],"simulations":[107],"under":[111],"same":[113],"parameter":[114],"settings,":[115],"compare":[116],"impact":[118],"find":[123],"that":[124],"term":[127],"can":[128],"induce":[129],"spatially":[130],"inhomogeneous":[131],"stable":[132],"periodic":[133],"solutions.":[134],"We":[135],"also":[136],"provide":[137],"corresponding":[138],"biological":[139],"explanations":[140],"simulation":[143],"results.":[144]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}