{"id":"https://openalex.org/W2890638219","doi":"https://doi.org/10.4236/am.2018.99070","title":"Stability Analysis for a Discrete SIR Epidemic Model with Delay and General Nonlinear Incidence Function","display_name":"Stability Analysis for a Discrete SIR Epidemic Model with Delay and General Nonlinear Incidence Function","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2890638219","doi":"https://doi.org/10.4236/am.2018.99070","mag":"2890638219"},"language":"en","primary_location":{"id":"doi:10.4236/am.2018.99070","doi":"https://doi.org/10.4236/am.2018.99070","is_oa":true,"landing_page_url":"https://doi.org/10.4236/am.2018.99070","pdf_url":"http://www.scirp.org/journal/PaperDownload.aspx?paperID=87357","source":{"id":"https://openalex.org/S4210211746","display_name":"Applied Mathematics","issn_l":"2152-7385","issn":["2152-7385","2152-7393"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://www.scirp.org/journal/PaperDownload.aspx?paperID=87357","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035257965","display_name":"Aboudramane Guiro","orcid":"https://orcid.org/0000-0001-9337-632X","observed_orcids":["https://orcid.org/0000-0001-9337-632X"]},"institutions":[{"id":"https://openalex.org/I3131918342","display_name":"Nazi Boni University","ror":"https://ror.org/04cq90n15","country_code":"BF","type":"education","lineage":["https://openalex.org/I3131918342"]}],"countries":["BF"],"is_corresponding":true,"raw_author_name":"Aboudramane Guiro","raw_affiliation_strings":["D\u00e9partement de Math\u00e9matiques, UFR des Sciences et Techniques Universit\u00e9 Nazi Boni de Bobo-Dioulasso & LAboratoire de Math\u00e9matique et d'Informatique (LAMI), Bobo-Dioulasso, Burkina Faso"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques, UFR des Sciences et Techniques Universit\u00e9 Nazi Boni de Bobo-Dioulasso & LAboratoire de Math\u00e9matique et d'Informatique (LAMI), Bobo-Dioulasso, Burkina Faso","institution_ids":["https://openalex.org/I3131918342"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002667317","display_name":"Dramane Ouedraogo","orcid":"https://orcid.org/0000-0002-1218-1289","observed_orcids":["https://orcid.org/0000-0002-1218-1289"]},"institutions":[{"id":"https://openalex.org/I3131918342","display_name":"Nazi Boni University","ror":"https://ror.org/04cq90n15","country_code":"BF","type":"education","lineage":["https://openalex.org/I3131918342"]}],"countries":["BF"],"is_corresponding":false,"raw_author_name":"Dramane Ouedraogo","raw_affiliation_strings":["D\u00e9partement de Math\u00e9matiques, UFR des Sciences et Techniques Universit\u00e9 Nazi Boni de Bobo-Dioulasso & LAboratoire de Math\u00e9matique et d'Informatique (LAMI), Bobo-Dioulasso, Burkina Faso"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques, UFR des Sciences et Techniques Universit\u00e9 Nazi Boni de Bobo-Dioulasso & LAboratoire de Math\u00e9matique et d'Informatique (LAMI), Bobo-Dioulasso, Burkina Faso","institution_ids":["https://openalex.org/I3131918342"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007520771","display_name":"Harouna Ouedraogo","orcid":"https://orcid.org/0009-0000-4680-9321","observed_orcids":["https://orcid.org/0009-0000-4680-9321"]},"institutions":[{"id":"https://openalex.org/I3131918342","display_name":"Nazi Boni University","ror":"https://ror.org/04cq90n15","country_code":"BF","type":"education","lineage":["https://openalex.org/I3131918342"]}],"countries":["BF"],"is_corresponding":false,"raw_author_name":"Harouna Ouedraogo","raw_affiliation_strings":["D\u00e9partement de Math\u00e9matiques, UFR des Sciences et Techniques Universit\u00e9 Nazi Boni de Bobo-Dioulasso & LAboratoire de Math\u00e9matique et d'Informatique (LAMI), Bobo-Dioulasso, Burkina Faso"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques, UFR des Sciences et Techniques Universit\u00e9 Nazi Boni de Bobo-Dioulasso & LAboratoire de Math\u00e9matique et d'Informatique (LAMI), Bobo-Dioulasso, Burkina Faso","institution_ids":["https://openalex.org/I3131918342"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5035257965"],"corresponding_institution_ids":["https://openalex.org/I3131918342"],"apc_list":null,"apc_paid":null,"fwci":0.4601,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.50413073,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":93},"biblio":{"volume":"09","issue":"09","first_page":"1039","last_page":"1054"},"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":1.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10410","display_name":"COVID-19 epidemiological studies","score":0.0,"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/sir-model","display_name":"SIR model","score":0.9869999885559082},{"id":"https://openalex.org/keywords/discrete-time-epidemic-model","display_name":"discrete-time epidemic model","score":0.7639999985694885},{"id":"https://openalex.org/keywords/time-delay","display_name":"time delay","score":0.7269999980926514},{"id":"https://openalex.org/keywords/backward-difference-scheme","display_name":"backward difference scheme","score":0.9340000152587891},{"id":"https://openalex.org/keywords/global-stability","display_name":"global stability","score":0.8939999938011169},{"id":"https://openalex.org/keywords/endemic-equilibrium","display_name":"endemic equilibrium","score":0.8859999775886536},{"id":"https://openalex.org/keywords/disease-free-equilibrium","display_name":"disease-free equilibrium","score":1.0},{"id":"https://openalex.org/keywords/basic-reproduction-number","display_name":"basic reproduction number","score":0.9860000014305115},{"id":"https://openalex.org/keywords/positivity-and-boundedness-of-solutions","display_name":"positivity and boundedness of solutions","score":0.878000020980835},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.9900000095367432}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7693566679954529},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7532531023025513},{"id":"https://openalex.org/C204264503","wikidata":"https://www.wikidata.org/wiki/Q901464","display_name":"Basic reproduction number","level":3,"score":0.6651841402053833},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6632901430130005},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6423772573471069},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5942268371582031},{"id":"https://openalex.org/C61511704","wikidata":"https://www.wikidata.org/wiki/Q1671857","display_name":"Incidence (geometry)","level":2,"score":0.563287615776062},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.49921488761901855},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.49525871872901917},{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.48471689224243164},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4638500213623047},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.45100322365760803},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22481858730316162},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1479472815990448},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1154046356678009},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.057610273361206055},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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":1,"locations":[{"id":"doi:10.4236/am.2018.99070","doi":"https://doi.org/10.4236/am.2018.99070","is_oa":true,"landing_page_url":"https://doi.org/10.4236/am.2018.99070","pdf_url":"http://www.scirp.org/journal/PaperDownload.aspx?paperID=87357","source":{"id":"https://openalex.org/S4210211746","display_name":"Applied Mathematics","issn_l":"2152-7385","issn":["2152-7385","2152-7393"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4236/am.2018.99070","doi":"https://doi.org/10.4236/am.2018.99070","is_oa":true,"landing_page_url":"https://doi.org/10.4236/am.2018.99070","pdf_url":"http://www.scirp.org/journal/PaperDownload.aspx?paperID=87357","source":{"id":"https://openalex.org/S4210211746","display_name":"Applied Mathematics","issn_l":"2152-7385","issn":["2152-7385","2152-7393"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2890638219.pdf","grobid_xml":"https://content.openalex.org/works/W2890638219.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1522228969","https://openalex.org/W1607633954","https://openalex.org/W1964713842","https://openalex.org/W1991038590","https://openalex.org/W1991566561","https://openalex.org/W2002160569","https://openalex.org/W2017558991","https://openalex.org/W2024193274","https://openalex.org/W2035688920","https://openalex.org/W2040926044","https://openalex.org/W2042391826","https://openalex.org/W2049640908","https://openalex.org/W2060563023","https://openalex.org/W2084954629","https://openalex.org/W2091419790","https://openalex.org/W2112680994","https://openalex.org/W2161728228","https://openalex.org/W4210417410"],"related_works":["https://openalex.org/W3131479719","https://openalex.org/W2369025946","https://openalex.org/W2166388114","https://openalex.org/W2187878512","https://openalex.org/W3163325703","https://openalex.org/W2606772502","https://openalex.org/W7100486240","https://openalex.org/W2035688920","https://openalex.org/W1991566561","https://openalex.org/W2391947453"],"abstract_inverted_index":{"In":[0,80],"this":[1],"paper,":[2],"we":[3,57,82],"construct":[4],"a":[5,10],"backward":[6],"difference":[7],"scheme":[8],"for":[9],"class":[11,95],"of":[12,39,62,71,86,92,100],"SIR":[13],"epidemic":[14],"model":[15,91],"with":[16],"general":[17,47],"incidence":[18,48],"f":[19,50],".":[20],"The":[21,30,68],"step":[22],"size\u03c4":[23],"used":[24],"in":[25],"our":[26],"discretization":[27],"is":[28,74],"one.":[29],"dynamical":[31],"properties":[32],"are":[33],"investigated":[34],"(positivity":[35],"and":[36,89],"the":[37,43,46,59,87,93,98],"boundedness":[38],"solution).":[40],"By":[41],"constructing":[42],"Lyapunov":[44],"function,":[45],"function":[49],"must":[51],"satisfy":[52],"certain":[53],"assumptions,":[54],"under":[55],"which,":[56],"establish":[58],"global":[60,69],"stability":[61,70],"endemic":[63],"equilibrium":[64,73],"when":[65,77],"R0":[66,78],">1.":[67],"diseases-free":[72],"also":[75],"established":[76],"\u22641.":[79],"addition":[81],"present":[83],"numerical":[84],"results":[85],"continuous":[88],"discrete":[90],"different":[94],"according":[96],"to":[97],"value":[99],"basic":[101],"reproduction":[102],"number":[103],"R0.":[104]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2018-09-27T00:00:00"}