{"id":"https://openalex.org/W7224019262","doi":"https://doi.org/10.3390/v18111189","title":"Mathematical Analysis and Optimal Control Investigation of Lumpy Skin Disease Transmission with Heterogeneous Host Susceptibility","display_name":"Mathematical Analysis and Optimal Control Investigation of Lumpy Skin Disease Transmission with Heterogeneous Host Susceptibility","publication_year":2026,"publication_date":"2026-10-26","ids":{"openalex":"https://openalex.org/W7224019262","doi":"https://doi.org/10.3390/v18111189"},"language":"en","primary_location":{"id":"doi:10.3390/v18111189","doi":"https://doi.org/10.3390/v18111189","is_oa":true,"landing_page_url":"https://doi.org/10.3390/v18111189","pdf_url":null,"source":{"id":"https://openalex.org/S55776271","display_name":"Viruses","issn_l":"1999-4915","issn":["1999-4915"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","medline","norway-1","poland-100","russia-white-list-2","vabb-shw"],"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":"Viruses","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/v18111189","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077061689","display_name":"Mudassar Imran","orcid":"https://orcid.org/0000-0002-6506-8730","observed_orcids":["https://orcid.org/0000-0002-6506-8730"]},"institutions":[{"id":"https://openalex.org/I182000528","display_name":"Ajman University","ror":"https://ror.org/01j1rma10","country_code":"AE","type":"education","lineage":["https://openalex.org/I182000528"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Mudassar Imran","raw_affiliation_strings":["College of Humanities and Sciences, Ajman University, Ajman P.O. Box 346, United Arab Emirates"],"raw_orcid":"https://orcid.org/0000-0002-6506-8730","affiliations":[{"raw_affiliation_string":"College of Humanities and Sciences, Ajman University, Ajman P.O. Box 346, United Arab Emirates","institution_ids":["https://openalex.org/I182000528"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039910801","display_name":"Waheed Ahmad","orcid":"https://orcid.org/0000-0003-2541-4421","observed_orcids":["https://orcid.org/0000-0003-2541-4421"]},"institutions":[{"id":"https://openalex.org/I43879129","display_name":"Government College University, Lahore","ror":"https://ror.org/040gec961","country_code":"PK","type":"education","lineage":["https://openalex.org/I43879129"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Waheed Ahmad","raw_affiliation_strings":["Department of Mathematics, Government College University, Lahore 54000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0003-2541-4421","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Lahore 54000, Pakistan","institution_ids":["https://openalex.org/I43879129"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5159783807","display_name":"Abdul Moheman Iqbal","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I43879129","display_name":"Government College University, Lahore","ror":"https://ror.org/040gec961","country_code":"PK","type":"education","lineage":["https://openalex.org/I43879129"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Abdul Moheman Iqbal","raw_affiliation_strings":["Department of Mathematics, Government College University, Lahore 54000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Lahore 54000, Pakistan","institution_ids":["https://openalex.org/I43879129"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005732217","display_name":"Muhammad Rafiq","orcid":"https://orcid.org/0000-0002-2165-3479","observed_orcids":["https://orcid.org/0000-0002-2165-3479"]},"institutions":[{"id":"https://openalex.org/I2802902501","display_name":"Namal University","ror":"https://ror.org/00zcxra43","country_code":"PK","type":"education","lineage":["https://openalex.org/I2802902501"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Rafiq","raw_affiliation_strings":["Department of Mathematics, Namal University, 30KM Talagang Road, Mianwali 42250, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Namal University, 30KM Talagang Road, Mianwali 42250, Pakistan","institution_ids":["https://openalex.org/I2802902501"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039910801"],"corresponding_institution_ids":["https://openalex.org/I43879129"],"apc_list":{"value":2600,"currency":"CHF","value_usd":3137},"apc_paid":{"value":2600,"currency":"CHF","value_usd":3137},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.8878363,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"11","first_page":"1189","last_page":"1189"},"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":0.9326000213623047,"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":0.9326000213623047,"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/T11560","display_name":"Animal Disease Management and Epidemiology","score":0.06599999964237213,"subfield":{"id":"https://openalex.org/subfields/1102","display_name":"Agronomy and Crop Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11767","display_name":"Poxvirus research and outbreaks","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/2406","display_name":"Virology"},"field":{"id":"https://openalex.org/fields/24","display_name":"Immunology and Microbiology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lumpy-skin-disease","display_name":"lumpy skin disease","score":0.9900000095367432},{"id":"https://openalex.org/keywords/cattle","display_name":"cattle","score":0.6940000057220459},{"id":"https://openalex.org/keywords/basic-reproduction-number","display_name":"basic reproduction number","score":0.8730000257492065},{"id":"https://openalex.org/keywords/disease-free-equilibrium","display_name":"disease-free equilibrium","score":0.7689999938011169},{"id":"https://openalex.org/keywords/global-stability","display_name":"global stability","score":0.8109999895095825},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.8640000224113464},{"id":"https://openalex.org/keywords/nonstandard-finite-difference-scheme","display_name":"nonstandard finite difference scheme","score":0.9710000157356262},{"id":"https://openalex.org/keywords/vaccination","display_name":"vaccination","score":0.8610000014305115},{"id":"https://openalex.org/keywords/farmer-awareness","display_name":"farmer awareness","score":0.9959999918937683},{"id":"https://openalex.org/keywords/treatment","display_name":"treatment","score":0.8370000123977661},{"id":"https://openalex.org/keywords/sensitivity-analysis","display_name":"sensitivity analysis","score":0.8610000014305115},{"id":"https://openalex.org/keywords/bifurcation-analysis","display_name":"bifurcation analysis","score":0.9229999780654907},{"id":"https://openalex.org/keywords/optimal-control","display_name":"optimal control","score":0.9869999885559082},{"id":"https://openalex.org/keywords/livestock-disease-transmission","display_name":"livestock disease transmission","score":0.7680000066757202}],"concepts":[{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.5324000120162964},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5264000296592712},{"id":"https://openalex.org/C204264503","wikidata":"https://www.wikidata.org/wiki/Q901464","display_name":"Basic reproduction number","level":3,"score":0.5128999948501587},{"id":"https://openalex.org/C2779134260","wikidata":"https://www.wikidata.org/wiki/Q12136","display_name":"Disease","level":2,"score":0.4724999964237213},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4535999894142151},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.4471000134944916},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4447999894618988},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.43380001187324524},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4052000045776367},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.3928000032901764},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3785000145435333},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.37630000710487366},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3758000135421753},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.357699990272522},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.3253999948501587},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.2797999978065491},{"id":"https://openalex.org/C126831891","wikidata":"https://www.wikidata.org/wiki/Q221673","display_name":"Host (biology)","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.26969999074935913},{"id":"https://openalex.org/C112930515","wikidata":"https://www.wikidata.org/wiki/Q4389547","display_name":"Risk analysis (engineering)","level":1,"score":0.2687000036239624},{"id":"https://openalex.org/C2992243407","wikidata":"https://www.wikidata.org/wiki/Q525512","display_name":"Disease transmission","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.26350000500679016},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2628999948501587},{"id":"https://openalex.org/C2991862235","wikidata":"https://www.wikidata.org/wiki/Q170201","display_name":"Animal health","level":2,"score":0.2587999999523163},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.2572999894618988},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.2567000091075897},{"id":"https://openalex.org/C27415008","wikidata":"https://www.wikidata.org/wiki/Q7256382","display_name":"Psychological intervention","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/v18111189","doi":"https://doi.org/10.3390/v18111189","is_oa":true,"landing_page_url":"https://doi.org/10.3390/v18111189","pdf_url":null,"source":{"id":"https://openalex.org/S55776271","display_name":"Viruses","issn_l":"1999-4915","issn":["1999-4915"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","medline","norway-1","poland-100","russia-white-list-2","vabb-shw"],"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":"Viruses","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/v18111189","doi":"https://doi.org/10.3390/v18111189","is_oa":true,"landing_page_url":"https://doi.org/10.3390/v18111189","pdf_url":null,"source":{"id":"https://openalex.org/S55776271","display_name":"Viruses","issn_l":"1999-4915","issn":["1999-4915"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","medline","norway-1","poland-100","russia-white-list-2","vabb-shw"],"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":"Viruses","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W268614176","https://openalex.org/W396155428","https://openalex.org/W1559587608","https://openalex.org/W2011850230","https://openalex.org/W2104395499","https://openalex.org/W2112680994","https://openalex.org/W2127737653","https://openalex.org/W2170930106","https://openalex.org/W2521212497","https://openalex.org/W2766429162","https://openalex.org/W2829746041","https://openalex.org/W2947651356","https://openalex.org/W2950005378","https://openalex.org/W3137506426","https://openalex.org/W4315780657","https://openalex.org/W4316927653","https://openalex.org/W4364375892","https://openalex.org/W4385284650","https://openalex.org/W4389095850","https://openalex.org/W4391625880","https://openalex.org/W4405909571","https://openalex.org/W4408755594","https://openalex.org/W4409167207","https://openalex.org/W4409665473","https://openalex.org/W4409980723","https://openalex.org/W4413396031","https://openalex.org/W4413811671","https://openalex.org/W4414307898","https://openalex.org/W4415659064","https://openalex.org/W7118942990","https://openalex.org/W7162803145"],"related_works":["https://openalex.org/W4409980723","https://openalex.org/W7125472633","https://openalex.org/W7172003732","https://openalex.org/W4364375892","https://openalex.org/W4389095850","https://openalex.org/W4405694478","https://openalex.org/W7214597879","https://openalex.org/W4397030749","https://openalex.org/W7220489912","https://openalex.org/W4407358571"],"abstract_inverted_index":{"Lumpy":[0],"Skin":[1],"Disease":[2],"(LSD)":[3],"remains":[4],"a":[5,30,180,184,194],"major":[6],"challenge":[7],"to":[8,39,54,95,124,159,192,198],"livestock":[9],"production":[10],"and":[11,18,71,78,119,130,140,167,188,202],"cattle":[12,37],"farming,":[13],"causing":[14],"substantial":[15],"economic":[16],"losses":[17],"adverse":[19],"health":[20],"effects":[21,114],"despite":[22],"existing":[23],"disease":[24,126,138,205],"management":[25,206],"strategies.":[26,207],"This":[27],"study":[28,175],"develops":[29],"nonlinear":[31],"mathematical":[32,50,196],"model":[33],"with":[34,145],"two":[35],"susceptible":[36],"groups":[38],"investigate":[40,74,111],"the":[41,56,60,64,69,97,102,106,112,177],"role":[42],"of":[43,59,105,115,173,179],"varying":[44],"susceptibility":[45],"in":[46,148],"LSD":[47,200],"transmission.":[48,127,149],"Rigorous":[49],"analysis":[51,191],"is":[52,93,157,176],"conducted":[53],"establish":[55,79],"fundamental":[57],"properties":[58,104],"proposed":[61],"model,":[62],"derive":[63],"basic":[65],"reproduction":[66],"number,":[67],"determine":[68,160],"LSD-free":[70],"LSD-present":[72],"equilibria,":[73],"their":[75,122],"local":[76],"stability,":[77],"global":[80],"stability":[81],"using":[82],"Lyapunov":[83],"function":[84],"theory.":[85],"A":[86],"structure-preserving":[87,185],"Nonstandard":[88],"Finite":[89],"Difference":[90],"(NSFD)":[91],"scheme":[92],"developed":[94],"validate":[96],"analytical":[98],"results":[99],"while":[100],"preserving":[101],"essential":[103],"continuous":[107],"model.":[108],"Numerical":[109],"simulations":[110],"individual":[113],"vaccination,":[116],"farmer":[117],"awareness,":[118],"treatment,":[120],"demonstrating":[121],"potential":[123],"reduce":[125],"Furthermore,":[128],"sensitivity":[129],"numerical":[131,186],"bifurcation":[132],"analyses":[133],"identify":[134],"key":[135],"parameters":[136],"influencing":[137],"dynamics":[139],"reveal":[141],"critical":[142],"thresholds":[143],"associated":[144],"qualitative":[146],"changes":[147],"An":[150],"optimal":[151,189],"control":[152,190],"problem":[153],"incorporating":[154],"time-dependent":[155],"interventions":[156],"formulated":[158],"cost-effective":[161],"strategies":[162],"for":[163],"reducing":[164],"infection":[165],"prevalence":[166],"intervention":[168],"costs.":[169],"The":[170],"principal":[171],"contribution":[172],"this":[174],"integration":[178],"bi-susceptible":[181],"modelling":[182],"framework,":[183],"scheme,":[187],"provide":[193],"comprehensive":[195],"approach":[197],"understanding":[199],"transmission":[201],"informing":[203],"effective":[204]},"counts_by_year":[],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2026-10-28T00:00:00"}