{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T08:52:04Z","timestamp":1765961524229,"version":"3.37.3"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2022,4,28]],"date-time":"2022-04-28T00:00:00Z","timestamp":1651104000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,4,28]],"date-time":"2022-04-28T00:00:00Z","timestamp":1651104000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001501","name":"university grants commission","doi-asserted-by":"publisher","award":["2061530673"],"award-info":[{"award-number":["2061530673"]}],"id":[{"id":"10.13039\/501100001501","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2022,6]]},"DOI":"10.1007\/s40314-022-01864-9","type":"journal-article","created":{"date-parts":[[2022,4,28]],"date-time":"2022-04-28T17:23:45Z","timestamp":1651166625000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Stage-structure model for the dynamics of whitefly transmitted plant viral disease: an optimal control approach"],"prefix":"10.1007","volume":"41","author":[{"given":"Sagar","family":"Adhurya","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fahad Al","family":"Basir","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Santanu","family":"Ray","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,4,28]]},"reference":[{"issue":"4","key":"1864_CR1","first-page":"325","volume":"46","author":"F Al Basir","year":"2017","unstructured":"Al Basir F, Roy PK, Ray S (2017) Impact of roguing and insecticide spraying on mosaic disease in Jatropha curcas. Control Cybern 46(4):325\u2013344","journal-title":"Control Cybern"},{"issue":"8","key":"1864_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11538-021-00921-4","volume":"83","author":"F Al Basir","year":"2021","unstructured":"Al Basir F, Kyrychko YN, Blyuss KB, Ray S (2021) Effects of vector maturation time on the dynamics of cassava mosaic disease. Bull Math Biol 83(8):1\u201321","journal-title":"Bull Math Biol"},{"key":"1864_CR3","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1007\/978-90-481-2460-2_15","volume-title":"Bemisia: bionomics and management of a global pest","author":"J Arn\u00f3","year":"2009","unstructured":"Arn\u00f3 J, Gabarra R, Liu TX, Simmons AM, Gerling D (2009) Natural enemies of Bemisia tabaci: predators and parasitoids. Bemisia: bionomics and management of a global pest. Springer, Dordrecht, pp 385\u2013421"},{"key":"1864_CR4","volume-title":"The mathematical theory of infectious diseases and its applications","author":"NT Bailey","year":"1975","unstructured":"Bailey NT (1975) The mathematical theory of infectious diseases and its applications. Charles Griffin & Company Ltd, Bucks"},{"issue":"3","key":"1864_CR5","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1016\/j.cropro.2009.11.007","volume":"29","author":"FJ Byrne","year":"2010","unstructured":"Byrne FJ, Oetting RD, Bethke JA, Green C, Chamberlin J (2010) Understanding the dynamics of neonicotinoid activity in the management of Bemisia tabaci whiteflies on poinsettias. Crop Prot 29(3):260\u2013266","journal-title":"Crop Prot"},{"key":"1864_CR6","unstructured":"CAB International (2019a) Bemisia tabaci (MEAM1) (silverleaf whitefly). Invasive species compendium detailed coverage of invasive species threatening livelihoods and the environment worldwide. https:\/\/www.cabi.org\/isc\/datasheet\/8927"},{"key":"1864_CR7","unstructured":"CAB International (2019b) Bemisia tabaci (MED) (silverleaf whitefly). Invasive species compendium detailed coverage of invasive species threatening livelihoods and the environment worldwide. https:\/\/www.cabi.org\/isc\/datasheet\/112682"},{"key":"1864_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1146\/annurev-ento-112408-085504","volume":"56","author":"PJ De Barro","year":"2011","unstructured":"De Barro PJ, Liu SS, Boykin LM, Dinsdale AB (2011) Bemisia tabaci: a statement of species status. Annu Rev Entomol 56:1\u201319","journal-title":"Annu Rev Entomol"},{"issue":"9","key":"1864_CR9","doi-asserted-by":"publisher","first-page":"767","DOI":"10.1016\/S0261-2194(01)00110-7","volume":"20","author":"M Faria","year":"2001","unstructured":"Faria M, Wraight SP (2001) Biological control of Bemisia tabaci with fungi. Crop Prot 20(9):767\u2013778","journal-title":"Crop Prot"},{"issue":"3","key":"1864_CR10","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1002\/ps.1877","volume":"66","author":"Y Feng","year":"2010","unstructured":"Feng Y, Wu Q, Wang S, Chang X, Xie W, Xu B, Zhang Y (2010) Cross-resistance study and biochemical mechanisms of thiamethoxam resistance in B-biotype Bemisia tabaci (Hemiptera: Aleyrodidae). Pest Manage Sci 66(3):313\u2013318","journal-title":"Pest Manage Sci"},{"key":"1864_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6380-7","volume-title":"Deterministic and stochastic optimal control","author":"W Fleming","year":"1975","unstructured":"Fleming W, Rishel R (1975) Deterministic and stochastic optimal control, vol 1. Springer Verlag, New York"},{"issue":"2","key":"1864_CR12","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1002\/ps.2780420210","volume":"42","author":"JJ Fransen","year":"1994","unstructured":"Fransen JJ (1994) Bemisia tabaci in the Netherlands; here to stay? Pest Sci 42(2):129\u2013134","journal-title":"Pest Sci"},{"issue":"1\u20132","key":"1864_CR13","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1016\/0167-8809(86)90022-8","volume":"17","author":"D Gerling","year":"1986","unstructured":"Gerling D, Horowitz AR, Baumgaertner J (1986) Autecology of Bemisia tabaci. Agric Ecosyst Environ 17(1\u20132):5\u201319","journal-title":"Agric Ecosyst Environ"},{"issue":"9","key":"1864_CR14","doi-asserted-by":"publisher","first-page":"779","DOI":"10.1016\/S0261-2194(01)00111-9","volume":"20","author":"D Gerling","year":"2001","unstructured":"Gerling D, Alomar \u00d2, Arn\u00f2 J (2001) Biological control of Bemisia tabaci using predators and parasitoids. Crop Prot 20(9):779\u2013799","journal-title":"Crop Prot"},{"key":"1864_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4342-7","volume-title":"Introduction to functional differential equations","author":"JK Hale","year":"1993","unstructured":"Hale JK, Lunel SV (1993) Introduction to functional differential equations. Springer-Verlag, New York"},{"key":"1864_CR16","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1098\/rsif.2005.0042","volume":"2","author":"JM Heffernan","year":"2005","unstructured":"Heffernan JM, Smith RJ, Wahl LM (2005) Perspectives on the basic reproductive ratio. J R Soc Interface 2:281\u2013293","journal-title":"J R Soc Interface"},{"key":"1864_CR17","doi-asserted-by":"publisher","first-page":"793","DOI":"10.2307\/2404924","volume":"34","author":"J Holt","year":"1997","unstructured":"Holt J, Jeger MJ, Thresh JM, Otim-Nape GW (1997) An epidemilogical model incorporating vector population dynamics applied to African cassava mosaic virus disease. J Appl Ecol 34:793\u2013806","journal-title":"J Appl Ecol"},{"key":"1864_CR18","doi-asserted-by":"publisher","first-page":"893","DOI":"10.1007\/s10340-020-01210-0","volume":"93","author":"AR Horowitz","year":"2020","unstructured":"Horowitz AR, Ghanim M, Roditakis E, Nauen R, Ishaaya I (2020) Insecticide resistance and its management in Bemisia tabaci species. J Pest Sci 93:893\u2013910","journal-title":"J Pest Sci"},{"key":"1864_CR19","doi-asserted-by":"publisher","first-page":"855","DOI":"10.1016\/j.cam.2017.01.005","volume":"330","author":"M Jackson","year":"2018","unstructured":"Jackson M, Chen-Charpentier BM (2018) A model of biological control of plant virus propagation with delays. J Comput Appl Math 330:855\u2013865","journal-title":"J Comput Appl Math"},{"issue":"3","key":"1864_CR20","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1111\/j.0307-6962.2004.00394.x","volume":"29","author":"MJ Jeger","year":"2004","unstructured":"Jeger MJ, Holt J, Van Den Bosch F, Madden LV (2004) Epidemiology of insect-transmitted plant viruses: modelling disease dynamics and control interventions. Physiol Entomol 29(3):291\u2013304","journal-title":"Physiol Entomol"},{"issue":"2","key":"1864_CR21","first-page":"135","volume":"38","author":"SC Kedar","year":"2014","unstructured":"Kedar SC, Saini RK, Kumaranag KM (2014) Biology of cotton whitefly, Bemisia tabaci (Hemiptera: Aleyrodidae) on cotton. J Entomol Res 38(2):135\u2013139","journal-title":"J Entomol Res"},{"key":"1864_CR22","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/978-1-4020-6740-2_3","volume-title":"Classical biological control of Bemisia tabaci in the United States-a review of interagency research and implementation","author":"LA Lacey","year":"2008","unstructured":"Lacey LA, Wraight SP, Kirk AA (2008) Entomopathogenic fungi for control of Bemisia tabaci biotype B: foreign exploration, research and implementation. Classical biological control of Bemisia tabaci in the United States-a review of interagency research and implementation. Springer, Dordrecht, pp 33\u201369"},{"issue":"1","key":"1864_CR23","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1007\/BF02463488","volume":"37","author":"HD Landahl","year":"1975","unstructured":"Landahl HD, Hansen BD (1975) A three stage population model with cannibalism. Bull Math Biol 37(1):11\u201317","journal-title":"Bull Math Biol"},{"key":"1864_CR24","doi-asserted-by":"crossref","unstructured":"Ledder, (2017) Scaling for dynamical systems in biology. Bull Math Biol 79:2747\u20132772","DOI":"10.1007\/s11538-017-0339-5"},{"key":"1864_CR25","doi-asserted-by":"crossref","unstructured":"Lefkovitch LP (1965) The study of population growth in organisms grouped by stages. Biometrics 1-18","DOI":"10.2307\/2528348"},{"issue":"1","key":"1864_CR26","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1111\/j.1744-7917.2010.01395.x","volume":"18","author":"S-J Li","year":"2011","unstructured":"Li S-J, Xue X, Ahmed MZ, Ren S-X, Du Y-Z, Wu J-H, Cuthbertson AGS, Qiu B-L (2011) Host plants and natural enemies of Bemisia tabaci (Hemiptera: Aleyrodidae) in China. Insect Sci 18(1):101\u2013120","journal-title":"Insect Sci"},{"issue":"11\u201313","key":"1864_CR27","doi-asserted-by":"publisher","first-page":"1319","DOI":"10.1016\/S0895-7177(02)00279-0","volume":"36","author":"S Liu","year":"2002","unstructured":"Liu S, Chen L, Agarwal R (2002) Recent progress on stage-structured population dynamics. Math Comput Model 36(11\u201313):1319\u20131360","journal-title":"Math Comput Model"},{"issue":"4","key":"1864_CR28","first-page":"295","volume":"48","author":"G MacDonald","year":"1955","unstructured":"MacDonald G (1955) The measurement of malaria transmission. Proc R Soc Med 48(4):295\u2013302","journal-title":"Proc R Soc Med"},{"key":"1864_CR29","volume-title":"Encyclopedia of virology","author":"BWJ Mahy","year":"2008","unstructured":"Mahy BWJ, Van Regenmortel MHV (2008) Encyclopedia of virology, 3rd edn. Academic Press, Cambridge","edition":"3"},{"key":"1864_CR30","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1017\/S0013091500034428","volume":"44","author":"AG M\u2019Kendrick","year":"1925","unstructured":"M\u2019Kendrick AG (1925) Applications of mathematics to medical problems. Proc Edinb Math Soc 44:98\u2013130","journal-title":"Proc Edinb Math Soc"},{"issue":"1","key":"1864_CR31","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/s10340-013-0522-x","volume":"87","author":"R Moreno-Ripoll","year":"2014","unstructured":"Moreno-Ripoll R, Gabarra R, Symondson WOC, King RA, Agust\u00ed N (2014) Do the interactions among natural enemies compromise the biological control of the whitefly Bemisia tabaci? J Pest Sci 87(1):133\u2013141","journal-title":"J Pest Sci"},{"key":"1864_CR32","unstructured":"Mota-Sanchez D, Wise JC (2020) The arthropod pesticide resistance database. Michigan State University. http:\/\/www.pesticideresistance.org"},{"key":"1864_CR33","doi-asserted-by":"publisher","DOI":"10.1007\/b98868","volume-title":"Mathematical biology. I. An introduction","author":"JD Murray","year":"2002","unstructured":"Murray JD (2002) Mathematical biology. I. An introduction. Springer, New York"},{"issue":"2","key":"1864_CR34","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1111\/j.1570-7458.2005.00297.x","volume":"116","author":"SE Naranjo","year":"2005","unstructured":"Naranjo SE, Ellsworth PC (2005) Mortality dynamics and population regulation in Bemisia tabaci. Entomol Exp Appl 116(2):93\u2013108","journal-title":"Entomol Exp Appl"},{"issue":"3","key":"1864_CR35","doi-asserted-by":"publisher","first-page":"458","DOI":"10.1016\/j.biocontrol.2009.08.006","volume":"51","author":"SE Naranjo","year":"2009","unstructured":"Naranjo SE, Ellsworth PC (2009) The contribution of conservation biological control to integrated control of Bemisia tabaci in cotton. Biol Control 51(3):458\u2013470","journal-title":"Biol Control"},{"key":"1864_CR36","doi-asserted-by":"crossref","unstructured":"Naranjo SE, Castle SJ, De Barro PJ, Liu SS (2009) Population dynamics, demography, dispersal and spread of Bemisia tabaci. In: Stansly P, Naranjo S (eds) Bemisia: Bionomics and management of a global pest. Springer, Dordrecht, pp 185\u2013226","DOI":"10.1007\/978-90-481-2460-2_6"},{"issue":"9","key":"1864_CR37","doi-asserted-by":"publisher","first-page":"739","DOI":"10.1016\/S0261-2194(01)00117-X","volume":"20","author":"JC Palumbo","year":"2001","unstructured":"Palumbo JC, Horowitz AR, Prabhaker N (2001) Insecticidal control and resistance management for Bemisia tabaci. Crop Prot 20(9):739\u2013765","journal-title":"Crop Prot"},{"issue":"6","key":"1864_CR38","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1002\/ps.1029","volume":"61","author":"E Roditakis","year":"2005","unstructured":"Roditakis E, Roditakis NE, Tsagkarakou A (2005) Insecticide resistance in Bemisia tabaci (Homoptera: Aleyrodidae) populations from Crete. Pest Manage Sci 61(6):577\u2013582","journal-title":"Pest Manage Sci"},{"issue":"9","key":"1864_CR39","doi-asserted-by":"publisher","first-page":"619","DOI":"10.3390\/insects11090619","volume":"11","author":"I Sani","year":"2020","unstructured":"Sani I, Ismail SI, Abdullah S, Jalinas J, Jamian S, Saad N (2020) A review of the biology and control of whitefly, Bemisia tabaci (Hemiptera: Aleyrodidae), with special reference to biological control using entomopathogenic fungi. Insects 11(9):619","journal-title":"Insects"},{"issue":"124","key":"1864_CR40","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1080\/14786440408637050","volume":"21","author":"FR Sharpe","year":"1911","unstructured":"Sharpe FR, Lotka AJ (1911) LA problem in age-distribution. Lond Edinb Dublin Philos Mag J Sci 21(124):435\u2013438","journal-title":"Lond Edinb Dublin Philos Mag J Sci"},{"key":"1864_CR41","volume-title":"A textbook of plant virus diseases","author":"KM Smith","year":"1972","unstructured":"Smith KM (1972) A textbook of plant virus diseases, 3rd edn. Elsevier, New York","edition":"3"},{"issue":"8","key":"1864_CR42","doi-asserted-by":"publisher","first-page":"701","DOI":"10.1016\/j.cropro.2003.11.016","volume":"23","author":"PA Stansly","year":"2004","unstructured":"Stansly PA, Sanchez PA, Rodr\u0131guez JM, Canizares F, Nieto A, Leyva ML, Fajardo M, Suarez V, Urbaneja A (2004) Prospects for biological control of Bemisia tabaci (Homoptera, Aleyrodidae) in greenhouse tomatoes of southern Spain. Crop Prot 23(8):701\u2013712","journal-title":"Crop Prot"},{"key":"1864_CR43","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1016\/B978-0-12-395678-1.50013-8","volume-title":"Plant pathology: an advance treatise","author":"JE Van der Plank","year":"1960","unstructured":"Van der Plank JE (1960) Analysis of epidemics. In: Horsfall JG, Cowling EB (eds) Plant pathology: an advance treatise. Academic Press, New York, pp 229\u2013289"},{"key":"1864_CR44","volume-title":"Plant diseases: epidemics and control","author":"JE Van der Plank","year":"1963","unstructured":"Van der Plank JE (1963) Plant diseases: epidemics and control. Academic Press, London"},{"issue":"6","key":"1864_CR45","doi-asserted-by":"publisher","first-page":"360","DOI":"10.1007\/s40974-016-0033-8","volume":"1","author":"E Venturino","year":"2016","unstructured":"Venturino E, Roy PK, Al Basir F, Datta A (2016) A model for the control of the mosaic virus disease in Jatropha curcas plantations. Energy Ecol Environ 1(6):360\u2013369","journal-title":"Energy Ecol Environ"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-022-01864-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-022-01864-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-022-01864-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,9]],"date-time":"2022-06-09T21:22:36Z","timestamp":1654809756000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-022-01864-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,28]]},"references-count":45,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["1864"],"URL":"https:\/\/doi.org\/10.1007\/s40314-022-01864-9","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2022,4,28]]},"assertion":[{"value":"28 July 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 March 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 March 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 April 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that no conflict of interest that could have influenced the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"154"}}