{"references": ["K. L. Bassil, C. Vakil, M. D. Sanborn, D. C. Cole, J. S. Kaur, K. J. Kerr\n(2007). Cancer health effects of pesticides: a systematic review. Can\nFam Physician2007;53:1704-11.", "B. R. W. Mnif, A. I. H.Hassine, A.Bouaziz, A. Bartegi, O. Thomas\n(2011) Effect of Endocrine Disruptor Pesticides: A Review Int J Environ\nRes Public Health. 8(6): 2265\u20132303. doi: 10.3390/ijerph8062265", "D. W. Kolpin, E. M. Thurman, S. M. Linhart (2000). Finding minimal\nherbicide concentrations in ground water? Try looking for their\ndegradates. Sci. Total Environ. 248:115\u2013122.", "S. I\u00f1igo-Nu\u00f1ez, M. A. Herreros, T. Encinas, A. Gonzalez-Bulnes\n(2010). Estimated daily intake of pesticides and xenoestrogenic exposure\nby fruit consumption in the female population from a Mediterranean\ncountry (Spain) Food Control. 21:471\u2013477", "K. A. Osman, A. I. Al-Humaid, S. M. Al-Rehiayani, K. N. Al-\nRedhaiman (2010). Estimated daily intake of pesticide residues exposure\nby vegetables grown in greenhouses in al-qassim region; Saudi Arabia.\nFood Control. doi: 10.1016/j.foodcont.2010.11.031.", "C. L. Curl, R. A. Fenske, J. C. Kissel, J. H. Shirai, T. F. Moate, W.\nGriffith, G. Coronado, B. Thompson (2002). Evaluation of take-home\norganophosphorus pesticide exposure among agricultural workers and\ntheir children. Environ. Health Perspect. 2002;110:A787\u2013A792.", "T. Berman, D. Hochner-Celnikier, B. D Boyd, L. L. Needham, Y.\nAmitai, U. Wormser, E. Richter (2011). Pesticide exposure among\npregnant women in Jerusalem, Israel: Results of a pilot study. Environ.\nInt. 37:198\u2013203.", "R. M. Whyatt, D. Camann, F. P. Perera, V. A. Rauh, D. Tang, P. L.\nKinney, R. Garfinkel, H. Andrews, L. Hoepner, D. B. Barr (2005).\nBiomarkers in assessing residential insecticide exposures during\npregnancy and effects on fetal growth. Toxicol. Appl. Pharmacol.\n2005;206:246\u2013254.", "D. Payne-Sturges, J. Cohen, R. Castorina, D. A. Axelrad, T. J.Woodruff\n(2009). Evaluating cumulative organophosphorus pesticide body burden\nof children, a national case study. Environ. Sci. Technol. 2009;43:7924\u2013\n7930.\n[10] P. Reynolds, J. B. Von, R. B. Gunier, D. E. Goldberg, A. Hertz, M. E.\nHarnly (2002) . Childhood cancer and agricultural pesticide use, an\necologic study in California. Environ. Health Perspect.;110:319\u2013324\n[11] J.T.Efrid, E.A.Holly, S.Preston-Martin, B. A. Mueller, F. Lubin, G.\nFilippini, R. Peris-Bonet, M. McCredie, S. Cordier, A. Arslan, P. M.\nBracci (2003). Farm \u2013 related exposures and childhood brain tumours in\nseven countries: results from the SEARCH International Brain Tumour\nStudy, Paediatric and perinatal Epidemiology, 17(2): 201-11\n[12] J. M. Pogoda, S.Preston \u2013Martins (1997). Household pesticides and risk\nof pediatric brain tumours, Environmental Health Perspectives, 1997;\n105: 1214-1220\n[13] W. E. Van, P. A. Stewart, A.F. Olshan, D. A. Savitz, G. R. Bunin (2003)\nParental occupational exposure to pesticides and childhood brain cancer.\nAmerican Journal of Epidemiology. 2003; 157(11): 989-97\n[14] J.F. Viel, B. Challier, A. Pitard, D. Pobel (1998). Brain cancer mortality\namong French farmers: the vineyard pesticide hypothesis. Archives of\nEnvironmental Health. 1998; 53: 65-70\n[15] Y.Fujii, K.Haraguchi, K.H.Harada, T.Hitomi, K.Inoue, Y.Itoh, T.\nWatanabe, K. Takenaka, S. Uehara, H. R.Yang (2011). Detection of\ndicofol and related pesticides in human breast milk from China; Korea\nand Japan. Chemosphere. 82:25\u201331.\n[16] M. K.Kettles, S.R.Browning, T.SPrince, S.W.Horstman (1997). Triazine\nherbicides exposure and breast cancer incidence: an ecological study of\nKentucky countries. Environmental Health Perspectives; 1997; 105:\n1222-27\n[17] B. A.Cohn (2011). Developmental and environmental origins of breast\ncancer: DDT as a case study. Reprod. Toxicol. 31:302\u2013311.\n[18] M.H. Abdalla, M.L. Gutierrez-Mohamed, I.O. Farah(2003). Association\nof pesticides exposure and risk of breast cancer mortality in Mississippi.\nBiomedical Science Instrumentation. 39: 397-01\n[19] G. Giacomelli, P. Ling, R. Morden (1996). An Automated Plant\nMonitoring System Using Machine Vision. ActaHorticulturae (ISHS)\n440, 377\u2013382.\n[20] R. Pydipati, T. F. Burks, W. S. Lee (2006). Identification of citrus\ndisease using colour texture features and discriminant analysis, Journal\nof Computers and electronics in Agriculture.\n[21] G. K. Dae, T. F. Burks, Q. Jianwei, D. M. Bulanon (2009).\nClassification of grapefruit peel diseases using color texture feature\nanalysis Int J Agric&BiolEng Vol. 2 No.3\n[22] C.Bauch, T.Rath (2005). Prototype of a Vision Based System for\nMeasurements of White Fly Infestation. In: Acta Horticulturae (ISHS)\n691. pp. 773\u2013780\n[23] B.Skaloudova, V. Krivan, R. Zemek (September, 2006). Computerassisted\nEstimation of Leaf Damage caused by Spider Mites. Computers\nand Electronics in Agriculture 53 (2), 81\u201391\n[24] P. Boissard, M. Vincent, & S. Moisan (2010). A Cognitive Vision\nApproach to Early Pest Detection in Greenhouse Crops. Computers and\nElectronics in Agriculture 62(2): 81-93 &inria 00499603, pp.1-24\n[25] L.O. Solis-Sanchez, R. Castaneda-Miranda, C.L. , Castaneda-Miranda, J.\nJ. Alaniz-Lumbreras, I. Torres-Pacheco, R.G. Guevara-Gonzalez, P.D.\nAlaniz-Lumbreras (2001). scale invariant feature approach for insect\nmonitoring. Comput.Electron.Agric. 75,92-99\n[26] J. A. Jiang, C.L. , Tseng, F. M. Lu, E. C.Yang, Z.S. Wu,C.P.Chen,\nS.H.Lin,K.C.Lin, C. S.Liao (2008). A GSM based remote wireless\nautomatic monitoring system for field information: a case study for\necological monitoring of oriental fruit fly, Bactroceradorsalis(Hendel).\nComputer Electronics Agric. 62, 243-259\n[27] H. Ruizhen, H. Yong, F. Liu (2012). Feasibility Study on a Portable\nField Pest Classification system design based on DSP and 3G wireless\ncommunication technology, Sensor 12, 3118-3130\n[28] B.Datt, A. Apan and R. Kelly (2006). Early detection of Exotic Pests\nand Diseases in Asian vegetable by imaging Spectroscopy, Rural\nIndustrial Research and Development corporation (RIRDC) Publication\nNo 05/170\n[29] R.K.Samanta,and G. Indrajit (2012). Tea Insect Pests Classification\nBased on artificial Neural Networks, IJCES 2(6)\n[30] S. R. Pokharkar, and V. R.Thool (2012). Early pest Identification in\ngreen house crops using image processing technigues IJCSN 1(3)\n[31] L.S.Jamal-Aldin, R. C. D. Young, C.R.Chatwin (1997). Application of\nnonlinearity to wavelet-transformed images to improve correlation filter\nperformance. Applied optics 36 (35), 9212-9224\n[32] F. O. Faithpraise, P.M. Birch, R. C. D. Young,J. Obu, B. Faithpriase, C.\nR. Chatwin (2013a). Automatic Plant pest Detection & Recognition\nusing k-means clustering algorithm & correspondence\nfiltersInternational Journal of Advanced Biotechnology and Research\nISSN 0976-2612, Online ISSN 2278\u2013599X,Vol 4, Issue 2, pp. 1052-\n1062 http://www.bipublication.com\n[33] U. S. Environmental Protection Agency (2012). Integrated Pest\nManagement (IMP) Principles http://www.epa.gov/pesticides/\nfactsheets/ipm.htm (Retrieved 2/10/13)\n[34] BioControl Reference CenterAcosta, EW (1995-2006). The History of\nIntegrated Pest Management (IPM)\nhttp://www.biconet.com/reference/IPMhistory.html (Retrieved 2/10/13)\n[35] A. H. Sandler (2010). Integrated Pest Management Cranberry Station\nBest Management Practices 1(1):12-15.\n[36] I. P. M. Guidelines (2009). UMassAmherst: Integrated Pest\nManagement, Agriculture and Landscape Program.\nhttp://www.umass.edu/umext/ipm/publications.( Retrieved 3/03/ 2012).\n[37] H.J.Barclay, I.S.Otvos, and A.J.Thomson, (1970). Models of periodic\ninundation of parasitoids for pest control, Canad.Entomol. 117, pp. 705\u2013\n716.\n[38] R.M. May, M.P. Hassell (1988). Population dynamics and biological\ncontrol, Phil. Trans. R. Soc. Lond. B. 318, 129-169\n[39] W.W.Murdoch (1990). The relevance of pest-enemy models to\nbiological control. In M. Mackauer, L.E. Ehler and J. Roland (Editors),\nCritical Issues in Biological Control. Intercept, Andover, pp. 1-24\n[40] N. J. Mills, W.M. Getz (1996). Modelling the biological control of insect\npests: a review of host-parasitoid models. Ecological Modelling, 92,\npp.121-143.\n[41] Z. Varga, (2008). Applications of mathematical systems theory in\npopulation biology, Period. Math. Hungar. 56 (1) pp. 157\u2013168\n[42] M.G\u00e1mez, I. L\u00f3pez, and A. Shamandy(2010). Open-and closed-loop\nequilibrium control of trophic chains, Ecol. Modell.221, pp. 1839\u20131846\n[43] M. Rafikov, J.M. Balthazar, and H.F. B. Von, (2008). Mathematical\nmodeling and control of population systems: application in biological\npest control, Appl. Math. Comput. 200 pp. 557\u2013573\n[44] M.P.Hassell (2002). The Spatial and Temporal Dynamics of Host\u2013\nparasitoid Interactions, Oxford University Press, Oxford\n[45] K. Stankova, A. Abate, M.W K. Sabells (2013). Irreversible prey\ndiapause as an optimal strategy of a physiologically extended Lokta-\nVolterra model, J. Math. Biol. 66:767\u2013794, DOI 10.1007/s00285-012-\n0599-5\n[46] K. Etebari, R. W. Palfreyman, D. Schlipalius, L. K. Nielsen, R. V. Glatz,\nS. Asgari (2011) . Deep sequencing-based transcriptome analysis of\nPlutellaxylostella larvae parasitized by Diadegmasemiclausum. BMC\nGenomics 12: 446\n[47] J.L.Capinera, (2012). Diamondback moth, Featured creatures \u2013\nEntomology & Nematology, University of Florida, EENY-119,\nRetrieved 23/07/13\n[48] D. G.Harcourt (1957). Biology of the diamondback moth,\nPlutellamaculipennis (Curt.) (Lepidoptera: Plutellidae), in Eastern\nOntario. II. Life-history, behaviour, and host relationships. Canadian\nEntomologist 89: 554-564.\n[49] A. Knutson (2005). The Trichogramma Manual: A guide to the use of\nTrichogramma for Biological Control with Special Reference to\nAugmentative Releases for Control of bollworm and Budworm in\nCotton. (Texas Agricultural Extension Service). 1-42\n[50] A. Knutson (1998). The Trichogrammamanual: a guide to the use of\nTrichogrammafor biological control with species reference to\naugmentative releases for control of bollworm and budworm in cotton.\nPubl. No. B\u20136071. Texas Agric. Ext. Serv., Texas A&M Univ.Res. and\nExt. Center, Dallas, TX. A. Knutson (1998). The Trichogramma\nmanual: a guide to the use of Trichogrammafor biological control with\nspecies reference to augmentative releases for control of bollworm and\nbudworm in cotton. Publ. No. B\u20136071. Texas Agric. Ext. Serv., Texas\nA&M Univ.Res. and Ext. Center, Dallas, TX.\n[51] D. Khatri, Q. Wang, & X.Z. He (2008). Developnment and reproduction\nof Diadegmasemiclausum (Hymenotera: Ichneumonidae) on\nDiamondback moth (Plutellidae). New Zealand Plant protection. 61;\n322-327 and Reproduction of Diadegmasemiclausum, thesis 2011,\nMassey University, Palmerston North, New Zealand.\n[52] S. Liu, X. Wang, Z. Shi, Z. H. Gebremeskel (2001). The biology of\nDiadromus collaris (Hymenoptera: Ichneumonidae), a pupal parasitoid\nof Plutella xylostella (Lepidoptera: Plutellidae), and its interactions with\nOomyzus sokolowskii (Hymenoptera: Eulophidae). Bulletin of\nEntomological Research. 91(6):461-69. http://www.ncbi.nlm.nih.gov/\npubmed/11818041retrieved 15/07/13\n[53] H. E. Z. Tonnang, L.V.Nedorezov, J.O. Owino, H.Ochanda, B. Lo\n(2010). Host\u2013parasitoid population density prediction using artificial\nneural networks: diamondback moth and its natural enemies,\nAgricultural and Forest Entomology. 12, 233-242.\n[54] A.M. Sheltonand J. T. Andaloro (1982). Effect of lepidopterous larval\npopulations on processed cabbage grades. J. Econ. Entomol. 75: 141-\n143.\n[55] D. Khatri (2011) . Reproduction of Diadegmasemiclausum, MSc thesis\n2011, Massey University, Palmerston North, New Zealand\n[56] D. C.Lloyd (1940). Host Selection by Hymenopterous Parasites of the\nMoth Plutellamaculipennis Curtis. Proc. Roy. Soc. Lond., Ser. B, no.\n853, vol. cxxviii, pp. 451\u2013484.\n[57] C. Chatfield, statistics for technology: a course in applied statistics, third\nedition (Revised) (1992) Chapman & Hall, London, ISBN 0-412-25340-\n2: pp. 327-330\n[58] B. Ostle, K. V. Turner, Jr., C.R. Hicks, & G. W. McElrath, Engineering\nStatiatics, the Industrial Experience, Duxbury Press, United State of\nAmerica, (1996). ISBN 0-534-26538-3: pg. 161-165.\n[59] W. A. Hoffmann, H. Poorter (2002). Avoiding Bias in Calculations of\nRelative Growth Rate. Annals of Botany 90 (1): 37.\nDOI:10.1093/aob/mcf140\n[60] E. K. Fehlberg, (1969). Runge-Kutta-Formeln f\u00fcnfter and siebenter\nOrdnung mit Schrittweiten-Kontrolle, Computing (Arch. Elektron.\nRechnen) 4 1969 93-106.\n[61] J. R. Dormand, and P. J. Prince, (1981). High order embedded Runge-\nKutta formulae, J. Comput. Appl. Math. 7 (1981), no.1, 67-75.\n[62] J. Butcher (2007). Runge-Kutta methods. Scholarpedia, 2(9):3147.\n[63] R. Schreiber (2007). MATLAB. Scholarpedia, 2(7):2929.\n[64] F. O. Faithpraise, J. Idung, C. R. Chatwin, R. C. D. Young, P.M. Birch\n(2014b).\"Biological Control of Taro Scarab Beetle (Papuanauninodis,\nColeoptera: Scarabaeidae) Instars via scoliid and Voria tachinidae\".\nInternational Journal of Applied Biology and Pharmaceutical\nTechnology, Volume 5, Issue 3, in press, 27th April 2014. July \u2013Sept\n2014, ISSN: 0976-4550.\n[65] F. O. Faithpraise, C. R. Chatwin, J. Obu, B. OlawaleR. C. D. Young,\nP.M. Birch (2014b). Sustainable Control of Anopheles Mosquito\nPopulation. Environment, Ecology & Management, Vol 3(1). 1-19\n[66] F. O. Faithpraise, C. R. Chatwin, R. C. D. Young, P.M. Birch (2013b).\nTimely Control of Aphis craccivora Using an Automatic Robotic Drone\nmanagement system (ARDMS) Technical Report, TR/SU/FF/130617,\n17 June 2013, Page 1-19"]}

A continuous time model of the interaction between crop insect pests and naturally beneficial pest enemies is created using a set of simultaneous, non-linear, ordinary differential equations incorporating natural death rates based on the Weibull distribution. The crop pest is present in all its life-cycle stages of: egg, larva, pupa and adult. The beneficial insects, parasitoid wasps, may be present in either or all parasitized: eggs, larva and pupa. Population modelling is used to estimate the quantity of the natural pest enemies that should be introduced into the pest infested environment to suppress the pest population density to an economically acceptable level within a prescribed number of days. The results obtained illustrate the effect of different combinations of parasitoid wasps, using the Pascal distribution to estimate their success in parasitizing different pest developmental stages, to deliver pest control to a sustainable level. Effective control, within a prescribed number of days, is established by the deployment of two or all three species of wasps, which partially destroy pest: egg, larvae and pupae stages. The selected scenarios demonstrate effective sustainable control of the pest in less than thirty days.