×

zbMATH — the first resource for mathematics

Optimization in microbial pest control: An integrated approach. (English) Zbl 1186.93048
Summary: The paper deals with optimal management of agricultural pest population under integrated control arising out of viral infection and spraying of pesticide. The costs of the control measures and the profits or projected profits of the biomass of species give rise to a control theoretic optimization problem. We take a four dimensional mathematical model of pest control under viral infection and pesticide, and apply Pontryagin’s maximum principle (PMP) to find out the necessary conditions on economic as well as on ecological parameters to make the control process maximum profitable.

MSC:
93C95 Application models in control theory
49N90 Applications of optimal control and differential games
92D40 Ecology
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Jones, K.A.; Zelazny, B.; Ketunuti, U.; Cherry, A.; Grazywacz, D., A survey of virus control of insect-pests in south-east Asia and western Pacific, (), 244-248
[2] Narayanan, K., Insect defence: its impact on microbial control oh insect pests, Curr. sci., 86, 800-814, (2004)
[3] L.G. Coping, Baculoviruses in Crop Protection, Agro-Business Report DS 85, Richmond, UK, 1993, pp. 1-3.
[4] O’Reilly, D.R.; Miller, L.K., Improvement of baculovirus pesticide by deletion of EGT gene, Biotechnology, 9, 1086-1089, (1991)
[5] Grazywacz, D.; Mckinley, D.J.; Moawad, G.; Cherry, A., The in vivo production of (spodoptera littoralis) nuclear polyhedrosis virus, J. virol. method, 71, 115-122, (1998)
[6] Bell, M.R., In vivo production of nuclear polyhedrosis virus utilizing tobacco budwarm and a multicellular larval rearing container, J. enomol. sci., 26, 69-75, (1991)
[7] Cherry, A.J.; Rabindra, R.J.; Parnell, M.A.; Geetha, N.; Kennedy, J.S.; Grazywacz, D., Field evaluation of (helicoverpa armigera) nucleopolyhedrovirus formulation for chickpea pod borer, (H. armigera) (hubn.) on chickpea (cicer arietinum var) shoba in southern India, Crop prot., 19, 51-60, (2000)
[8] Kalia, V.; Chaudhari, S.; Gujar, G.T., Optimization of production of nuclepolyhedrovirus of (helicoverpa armigera) throughout larval stages, Phytoparasitica, 29, 1-6, (2001)
[9] Kumar, C.M.; Sathiah, N.; Rabindra, R.J., Optimizing the time of harvest of nucleopolyhedrovirus infected (spodoptera litura) (fabricius) larvae under (in vivo) production system, Curr. sci., 88, 1682-1684, (2005)
[10] Shapiro, M.; Owens, C.D.; Bell, R.A.; Wood, H.A., Simplified efficient sytem for (in vivo) mass production of gypsy moth nucleopolyhedrosis virus, J. econ. entomol., 74, 110-111, (1981)
[11] Subramanian, S.; Santharam, G.; Sathiah, N.; Kennedy, J.S.; Rabindra, R.J., Influence of incubation temperature on productivity and quality of (spodoptera litura) nucleopolyhedro virus, Biol. control., 37, 367-374, (2006)
[12] Cherry, A.J.; Parnell, M.A.; Grzywacz, D.; Jones, K.A., The optimization of in vivo nuclear polyhedrosis virus production in spodoptera exempta (Walker) and spodoptera exigua (hubner), J. invertbr. pathol., 70, 50-58, (1997)
[13] Shieh, T.R., Industrial production of viral pesticides, Adv. virus res., 36, 315-343, (1989)
[14] Sun, X.; Sun, X.; Bai, B.; Werf, W.V.D.; Vlak, J.M.; Hu, Z., Production of polyhedral inclusion bodies from (helicoverpa armigera) larvae infected with wild type and recombinant hasnpv, Biocontrol. sci. technol., 15, 353-366, (2005)
[15] Shapiro, M.; Robertson, J.L.; Bell, R.A., Quantitative and qualitative differences in gypsy moth (lepidoptera: lymantriidae) nucleopolyhedrosis virus produced in different-aged larvae, J. econ. entomol., 79, 1174-1177, (1986)
[16] Sathiah, N.; Palaniswamy, S., Project report on establishment of biopesticides production unit for (helicoverpa armigera) nuclear polyhedrosis virus, (2004), Tamil Nadu Agricultural University Press, pp. 1-17
[17] Bhattacharya, D.K.; Karan, S., On bionomic model of integrated pest management of a single pest population, J. differ. equat. dyn. syst., 12, 3/4, 301-330, (2004) · Zbl 1128.34314
[18] Vincent, T.L., Pest management programs via optimal control theory, Biometrics, 31, 1, 1-10, (1975) · Zbl 0307.92016
[19] Bhattacharyya, S.; Bhattacharya, D.K., An improved integrated pest management model under 2-control parameters (sterile male and pesticide), Math. biosci., 209, 256-281, (2007) · Zbl 1120.92042
[20] Bhattacharyya, S.; Bhattacharya, D.K., A more realistic approach to pest-management problem, Bull. math. biol., 69, 1277-1310, (2007) · Zbl 1298.92109
[21] Bhattacharyya, S.; Bhattacharya, D.K., Pest control through viral diseases: mathematical modeling and analysis, J. theor. biol., 238, 177-197, (2006)
[22] Jacques, R.P.; Morris, O.N., Compatibility of pathogens with other methods of pest control and crop protection, ()
[23] Ghosh, S.; Bhattacharyya, S.; Bhattacharya, D.K., The role of viral infection in pest control: a mathematical study, Bull. math. biol., 69, 2649-2691, (2007) · Zbl 1245.92054
[24] Goh, B.S., Management and analysis of biological populations, (1980), Elsevier Scientific Publishing Company Amsterdam, Oxford, NY · Zbl 0453.92015
[25] Goh, B.S.; Leitman, J.; Vincent, T.L., Optimal control of preypredator systems, Math. biosci., 19, 263-286, (1974)
[26] Bell, D.J.; Jacobson, D.E., Singular control problems, (1975), Academic Press NY
[27] Kelley, H.J.; Kopp, R.E.; Moyer, H.G., Singular extremals, (), 63-101
[28] Becker, N.G., Control of a pest population, Biometrics, 26, 365-375, (1970)
[29] Clark, C.W., Economically optimal policies for the utilization of biologically renewable resources, Math. biosci., 12, 245-260, (1971) · Zbl 0226.92003
[30] Clark, C.W., Mathematical bioeconomics, (1990), Wiley New York · Zbl 0712.90018
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.