{"id":"https://openalex.org/W7204490227","doi":"https://doi.org/10.36719/2707-1146/67/91-103","title":"Modeling Nutrient-Release Dynamics of Organic and Inorganic Fertilizers Using Differential Equations: A Comparative Analysis of Fast and Slow Release Kinetics","display_name":"Modeling Nutrient-Release Dynamics of Organic and Inorganic Fertilizers Using Differential Equations: A Comparative Analysis of Fast and Slow Release Kinetics","publication_year":2026,"publication_date":"2026-08-25","ids":{"openalex":"https://openalex.org/W7204490227","doi":"https://doi.org/10.36719/2707-1146/67/91-103"},"language":"en","primary_location":{"id":"doi:10.36719/2707-1146/67/91-103","doi":"https://doi.org/10.36719/2707-1146/67/91-103","is_oa":true,"landing_page_url":"https://doi.org/10.36719/2707-1146/67/91-103","pdf_url":"https://doi.org/10.36719/2707-1146/67/91-103","source":{"id":"https://openalex.org/S4210194033","display_name":"NATURE AND SCIENCE","issn_l":"2707-1146","issn":["2707-1146","2709-4189"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nature & Science","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://doi.org/10.36719/2707-1146/67/91-103","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038943531","display_name":"Jean de Dieu Niyomugabo","orcid":"https://orcid.org/0000-0003-2979-9787","observed_orcids":["https://orcid.org/0000-0003-2979-9787"]},"institutions":[{"id":"https://openalex.org/I4405262977","display_name":"Rwanda Polytechnic","ror":"https://ror.org/00w5bze11","country_code":"RW","type":"education","lineage":["https://openalex.org/I4405262977"]}],"countries":["RW"],"is_corresponding":false,"raw_author_name":"Jean de Dieu Niyomugabo","raw_affiliation_strings":["\u00b9Rwanda Polytechnic , Karongi College , Master's degree , Karongi District , Rwanda"],"raw_orcid":"https://orcid.org/0000-0003-2979-9787","affiliations":[{"raw_affiliation_string":"\u00b9Rwanda Polytechnic , Karongi College , Master's degree , Karongi District , Rwanda","institution_ids":["https://openalex.org/I4405262977"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148457654","display_name":"Victoire Ayingeneye","orcid":"https://orcid.org/0009-0002-4475-515X","observed_orcids":["https://orcid.org/0009-0002-4475-515X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Victoire Ayingeneye","raw_affiliation_strings":["University of Technology and Arts of Byumba , Bachelor's degree , Byumba District , Rwanda"],"raw_orcid":"https://orcid.org/0009-0002-4475-515X","affiliations":[{"raw_affiliation_string":"University of Technology and Arts of Byumba , Bachelor's degree , Byumba District , Rwanda","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148465601","display_name":"Angelique Nyiramahoro","orcid":"https://orcid.org/0009-0004-3686-7236","observed_orcids":["https://orcid.org/0009-0004-3686-7236"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Angelique Nyiramahoro","raw_affiliation_strings":["University of Technology and Arts of Byumba , Bachelor's degree , Byumba District , Rwanda"],"raw_orcid":"https://orcid.org/0009-0004-3686-7236","affiliations":[{"raw_affiliation_string":"University of Technology and Arts of Byumba , Bachelor's degree , Byumba District , Rwanda","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5148423224","display_name":"Marie Ange Cyuzuzo","orcid":"https://orcid.org/0009-0007-7486-4628","observed_orcids":["https://orcid.org/0009-0007-7486-4628"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marie Ange Cyuzuzo","raw_affiliation_strings":["Groupe Scolaire Rega Catholique , Bachelor's degree , Nyabihu , Rwanda"],"raw_orcid":"https://orcid.org/0009-0007-7486-4628","affiliations":[{"raw_affiliation_string":"Groupe Scolaire Rega Catholique , Bachelor's degree , Nyabihu , Rwanda","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"4","first_page":"91","last_page":"103"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12642","display_name":"Polymer-Based Agricultural Enhancements","score":0.7401999831199646,"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"}},"topics":[{"id":"https://openalex.org/T12642","display_name":"Polymer-Based Agricultural Enhancements","score":0.7401999831199646,"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/T12294","display_name":"Agricultural Science and Fertilization","score":0.17910000681877136,"subfield":{"id":"https://openalex.org/subfields/1111","display_name":"Soil 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/T10004","display_name":"Soil Carbon and Nitrogen Dynamics","score":0.04039999842643738,"subfield":{"id":"https://openalex.org/subfields/1111","display_name":"Soil 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"}}],"keywords":[{"id":"https://openalex.org/keywords/nutrient-release-kinetics","display_name":"nutrient release kinetics","score":0.8169999718666077},{"id":"https://openalex.org/keywords/fertilizer-dissolution","display_name":"fertilizer dissolution","score":0.45399999618530273},{"id":"https://openalex.org/keywords/slow-release-fertilizer","display_name":"slow-release fertilizer","score":0.8500000238418579},{"id":"https://openalex.org/keywords/organic-fertilizer","display_name":"organic fertilizer","score":0.8759999871253967},{"id":"https://openalex.org/keywords/chemical-fertilizers","display_name":"mineral fertilizers","score":0.9520000219345093},{"id":"https://openalex.org/keywords/two-pool-model","display_name":"two-pool model","score":0.6309999823570251},{"id":"https://openalex.org/keywords/weibull-model","display_name":"Weibull model","score":0.8399999737739563},{"id":"https://openalex.org/keywords/korsmeyer-peppas-model","display_name":"Korsmeyer-Peppas model","score":0.9150000214576721},{"id":"https://openalex.org/keywords/fickian-diffusion","display_name":"Fickian diffusion","score":0.9639999866485596},{"id":"https://openalex.org/keywords/nitrogen-mineralization","display_name":"nitrogen mineralization","score":0.5759999752044678},{"id":"https://openalex.org/keywords/poultry-manure","display_name":"poultry manure","score":0.8809999823570251},{"id":"https://openalex.org/keywords/compost","display_name":"compost","score":0.9940000176429749},{"id":"https://openalex.org/keywords/green-manure","display_name":"green manure","score":0.902999997138977},{"id":"https://openalex.org/keywords/urea","display_name":"urea","score":0.8970000147819519},{"id":"https://openalex.org/keywords/ammonium-nitrate","display_name":"ammonium nitrate","score":0.9990000128746033},{"id":"https://openalex.org/keywords/temperature-response","display_name":"temperature sensitivity","score":0.7250000238418579},{"id":"https://openalex.org/keywords/arrhenius-equation","display_name":"Arrhenius equation","score":0.7680000066757202},{"id":"https://openalex.org/keywords/nutrient-use-efficiency","display_name":"nutrient use efficiency","score":0.6779999732971191},{"id":"https://openalex.org/keywords/polymer-coated-fertilizer","display_name":"polymer-coated fertilizer","score":0.7450000047683716}],"concepts":[{"id":"https://openalex.org/C2780560099","wikidata":"https://www.wikidata.org/wiki/Q83323","display_name":"Fertilizer","level":2,"score":0.6043000221252441},{"id":"https://openalex.org/C126674687","wikidata":"https://www.wikidata.org/wiki/Q1662573","display_name":"Akaike information criterion","level":2,"score":0.4943999946117401},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.46939998865127563},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.4359000027179718},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.40450000762939453},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.391400009393692},{"id":"https://openalex.org/C148898269","wikidata":"https://www.wikidata.org/wiki/Q1108792","display_name":"Kinetics","level":2,"score":0.37389999628067017},{"id":"https://openalex.org/C93391505","wikidata":"https://www.wikidata.org/wiki/Q658700","display_name":"Reaction rate constant","level":3,"score":0.3644999861717224},{"id":"https://openalex.org/C2775878893","wikidata":"https://www.wikidata.org/wiki/Q539815","display_name":"Organic fertilizer","level":3,"score":0.3644999861717224},{"id":"https://openalex.org/C2779870022","wikidata":"https://www.wikidata.org/wiki/Q190901","display_name":"Ammonium","level":2,"score":0.3596999943256378},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.35580000281333923},{"id":"https://openalex.org/C39432304","wikidata":"https://www.wikidata.org/wiki/Q188847","display_name":"Environmental science","level":0,"score":0.35359999537467957},{"id":"https://openalex.org/C86183883","wikidata":"https://www.wikidata.org/wiki/Q507505","display_name":"Arrhenius equation","level":3,"score":0.3499000072479248},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.3483999967575073},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34139999747276306},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3395000100135803},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.3366999924182892},{"id":"https://openalex.org/C159390177","wikidata":"https://www.wikidata.org/wiki/Q9161265","display_name":"Soil science","level":1,"score":0.3359000086784363},{"id":"https://openalex.org/C537208039","wikidata":"https://www.wikidata.org/wiki/Q627","display_name":"Nitrogen","level":2,"score":0.33329999446868896},{"id":"https://openalex.org/C90982505","wikidata":"https://www.wikidata.org/wiki/Q16938886","display_name":"Leaching (pedology)","level":3,"score":0.31360000371932983},{"id":"https://openalex.org/C142796444","wikidata":"https://www.wikidata.org/wiki/Q181394","display_name":"Nutrient","level":2,"score":0.31060001254081726},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.27309998869895935},{"id":"https://openalex.org/C107872376","wikidata":"https://www.wikidata.org/wiki/Q321355","display_name":"Environmental chemistry","level":1,"score":0.27160000801086426},{"id":"https://openalex.org/C202887219","wikidata":"https://www.wikidata.org/wiki/Q3895221","display_name":"Parametrization (atmospheric modeling)","level":3,"score":0.26739999651908875},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.2554999887943268},{"id":"https://openalex.org/C38304854","wikidata":"https://www.wikidata.org/wiki/Q185716","display_name":"Manure","level":2,"score":0.25440001487731934},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.2526000142097473},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.25110000371932983},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.2508000135421753}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.36719/2707-1146/67/91-103","doi":"https://doi.org/10.36719/2707-1146/67/91-103","is_oa":true,"landing_page_url":"https://doi.org/10.36719/2707-1146/67/91-103","pdf_url":"https://doi.org/10.36719/2707-1146/67/91-103","source":{"id":"https://openalex.org/S4210194033","display_name":"NATURE AND SCIENCE","issn_l":"2707-1146","issn":["2707-1146","2709-4189"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nature & Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.36719/2707-1146/67/91-103","doi":"https://doi.org/10.36719/2707-1146/67/91-103","is_oa":true,"landing_page_url":"https://doi.org/10.36719/2707-1146/67/91-103","pdf_url":"https://doi.org/10.36719/2707-1146/67/91-103","source":{"id":"https://openalex.org/S4210194033","display_name":"NATURE AND SCIENCE","issn_l":"2707-1146","issn":["2707-1146","2709-4189"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nature & Science","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/2","score":0.8409000039100647,"display_name":"Zero hunger"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204490227.pdf","grobid_xml":"https://content.openalex.org/works/W7204490227.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1523723739","https://openalex.org/W1992953206","https://openalex.org/W2007560696","https://openalex.org/W2022035229","https://openalex.org/W2058998445","https://openalex.org/W2069222203","https://openalex.org/W2137255447","https://openalex.org/W2511533868","https://openalex.org/W2778037992","https://openalex.org/W3008015375","https://openalex.org/W3087770414","https://openalex.org/W3121429692","https://openalex.org/W3206114012","https://openalex.org/W4285733389","https://openalex.org/W4311151994","https://openalex.org/W4311416894","https://openalex.org/W4386195469","https://openalex.org/W4388071721","https://openalex.org/W4401465731","https://openalex.org/W4404619636","https://openalex.org/W4411676195"],"related_works":["https://openalex.org/W4388071721","https://openalex.org/W7152648785","https://openalex.org/W7167277283","https://openalex.org/W2004409645","https://openalex.org/W2393450525","https://openalex.org/W4411410437","https://openalex.org/W2088934229","https://openalex.org/W2106859044","https://openalex.org/W2778037992","https://openalex.org/W2053476781"],"abstract_inverted_index":{"Optimizing":[0],"nutrient-use":[1],"efficiency":[2,112],"(NUE)":[3],"in":[4],"agricultural":[5],"systems":[6],"requires":[7],"a":[8,27,221],"precise":[9],"mechanistic":[10],"understanding":[11],"of":[12,246],"how":[13],"different":[14],"fertilizer":[15,40,98],"types":[16],"release":[17],"their":[18],"nutrients":[19],"over":[20],"time.":[21],"Differential":[22],"equation-based":[23],"kinetic":[24,68,234],"models":[25,138,155],"provide":[26],"rigorous":[28],"mathematical":[29],"framework":[30],"for":[31,95,215,231],"describing,":[32],"comparing,":[33],"and":[34,51,58,64,84,92,118,161,201,208,229,243],"predicting":[35],"nutrient-release":[36],"dynamics":[37],"across":[38],"diverse":[39],"formulations":[41],"from":[42],"rapidly":[43],"solubilizing":[44],"inorganic":[45,125],"salts":[46],"to":[47,156,236],"microbially-mediated":[48],"organic":[49,144],"amendments":[50,145],"polymer-incapsulated":[52],"controlled-release":[53],"fertilizers":[54,126],"(CRFs).":[55],"This":[56],"review":[57],"analytical":[59],"study":[60,219],"systematically":[61],"compile,":[62],"parameterizes,":[63],"comparatively":[65],"evaluates":[66],"eight":[67],"model":[69,87,223],"classes":[70],"\u2014":[71],"zero-order,":[72],"single":[73],"first-order,":[74],"double":[75,152],"first-order":[76,137],"(two-pool),":[77],"logistic/sigmoidal,":[78],"Weibull,":[79],"Korsmeyer\u2013":[80],"Peppas,":[81],"Fickian":[82],"diffusion,":[83],"the":[85,105,158,244],"Stanford\u2013Smith":[86],"against":[88],"published":[89],"laboratory":[90],"incubation":[91],"release-experiment":[93],"datasets":[94],"nine":[96],"representative":[97],"types.":[99],"Model":[100],"performance":[101],"was":[102],"assessed":[103],"using":[104],"root":[106],"mean":[107],"squared":[108],"error":[109],"(RMSE),":[110],"Nash\u2013Sutcliffe":[111],"(NSE),":[113],"Akaike":[114],"Information":[115],"Criterion":[116],"(AIC),":[117],"Percent":[119],"Bias":[120],"(PBias).":[121],"Results":[122],"demonstrate":[123],"that":[124],"(urea,":[127],"ammonium":[128],"nitrate)":[129],"are":[130],"best":[131,183],"described":[132],"by":[133,185],"zero-order":[134],"or":[135,187],"fast":[136],"(k\u2081":[139,165],"\u2248":[140,191],"0.82\u20130.94":[141],"d\u207b\u00b9),":[142],"whereas":[143],"(poultry":[146],"manure,":[147],"compost,":[148],"green":[149],"manure)":[150],"require":[151],"firstorder":[153],"two-pool":[154],"capture":[157],"heterogeneous":[159],"labile":[160],"recalcitrant":[162],"nitrogen":[163],"fractions":[164],"=":[166,170],"0.09\u20130.41":[167],"d\u207b\u00b9;":[168],"k\u2082":[169],"0.003\u20130.012":[171],"d\u207b\u00b9).":[172,193],"Polymer-coated":[173],"CRFs":[174],"exhibit":[175],"three-stage":[176],"kinetics":[177],"with":[178],"an":[179],"initial":[180],"lag":[181],"phase":[182],"modeled":[184],"logistic":[186],"diffusion":[188],"equations":[189],"(k":[190],"0.03\u20130.05":[192],"Temperature":[194],"sensitivity,":[195],"expressed":[196],"through":[197],"modified":[198],"Arrhenius":[199],"relationships":[200],"Q\u2081\u2080":[202],"factors,":[203],"significantly":[204],"modulates":[205],"rate":[206,227],"constants":[207],"must":[209],"be":[210],"incorporated":[211],"into":[212],"predictive":[213],"frameworks":[214,235],"field-scale":[216],"application.":[217],"The":[218],"provides":[220],"unified":[222],"comparison":[224],"matrix,":[225],"parameterized":[226],"constants,":[228],"guidelines":[230],"selecting":[232],"appropriate":[233],"support":[237],"fertilization":[238],"scheduling,":[239],"environmental":[240],"nutrientloss":[241],"modeling,":[242],"design":[245],"next-generation":[247],"CRF":[248],"formulations.":[249]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-08-28T00:00:00"}