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Impact of roguing and insecticide spraying on mosaic disease in Jatropha curcas

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Jatropha curcas plant is greatly impaired by mosaic disease, caused by the viruses (Begomovirus), transmitted by whiteflies, which act as the vector. Roguing (i.e. removal of infected plant) and spraying of insecticides are common methods, employed in order to get rid of the disease. In this article, a mathematical model has been developed to study the mosaic disease dynamics while considering preventive measures of roguing and insecticide spraying. Sufficient conditions for the stability of equilibrium points of the system are among the results obtained through qualitative analysis. We obtain the basic reproduction number R0 and show that the disease free system is stable for R0 < 1 and unstable for R0 > 1. The region of stability of equilibrium points in different parameter spaces have also been analysed. Hopf bifurcation at the endemic steady state has been studied subsequently, as well. Finally, by formulating an optimal control problem, optimal application of roguing and spraying techniques has been determined, keeping in mind the cost effective control of the mosaic disease. Pontryagin minimum principle has been utilized to solve the optimal control problem. Numerical simulations illustrate the validity of the analytical outcomes.
Rocznik
Strony
325--344
Opis fizyczny
Bibliogr. 26 poz., rys.
Twórcy
autor
  • Systems Ecology & Ecological Modeling Laboratory, Department of Zoology, Visva-Bharati University Shantiniketan, West Bengal, India
autor
  • Department of Mathematics Jadavpur University, Kolkata, India
autor
  • Systems Ecology & Ecological Modeling Laboratory, Department of Zoology, Visva-Bharati University Shantiniketan, West Bengal, India
Bibliografia
  • [1] AL BASIR F., DATTA S., ROY P. K. (2015) Studies on Biodiesel Production from Jatropha Curcas Oil using Chemical and Biochemical methods - A Mathematical Approach. Fuel, 158, 503-511.
  • [2] AL BASIR F., ROY P.K. (2017) Dynamics of mosaic disease with roguing and delay in Jatropha curcas plantations, J. Appl. Math. Comput., DOI 10.1007/s12190-017-1131-2.
  • [3] AL BASIR F., VENTURINO E., ROY P.K. (2017) Effects of awareness program for controlling mosaic disease in Jatropha curcas plantations. Mathematical Methods in the Applied Sciences, 40(7) 2441–53.
  • [4] ALLEN, R. N. (1978) Epidemiological factors influencing the success of roguing for the control of bunchy top disease of bananas in New South Wales. Crop and Pasture Science, 29(3), 535-44.
  • [5] ANDERSON R. M., and MAY R. M. (1990) Immunisation and herd immunity. Lancet, 335, 641–645. CHAKRABORTY S., NEWTON A.C. (2011) Climate change, plant diseases and food security: an overview. Plant Pathology, 60(1), 2–14.
  • [6] CHAN M.S., JEGER M.J. (1994) An analytical model of plant virus disease dynamics with roguing and replanting. Journal of Applied Ecology, 31 (3), 413–27.
  • [7] DIEKMANN O., HEESTERBEEK J. A. P., (2000) Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. Wiley, New York.
  • [8] DIEKMANN O., HEESTERBEEK J. A. P., METZ J. A. (1990) On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology 28, 365–382.
  • [9] DORDAS C. (2008) Role of nutrients in controlling plant diseases in sustainable agriculture- A review. Agronomy for Sustainable Development, Springer Verlag/EDP Sciences/INRA, 28 (1), 33–46.
  • [10] ERASLAN F., AKBAS B., INAL A. (2007) Effects of foliar sprayed calcium sources on Tomato mosaic virus (ToMV) infection in tomato plants grown in greenhouses. Phytoparasitica 35, 150, 10.1007/BF02981110.
  • [11] FLEMING W. H., RISHEL R. W. (1975) Deterministic and Stochastic Optimal Control. Springer Verlag.
  • [12] HOLT J., CHANCELLOR T.C. (1996) Simulation modelling of the spread of rice tungro virus disease: the potential for management by roguing. Journal of Applied Ecology, 1, 927-936.
  • [13] HOLT J., JEGER M. J., THRESH J. M., OTIM-NAPE G.W. (1997) An epidemiological model incorporating vector population dynamics applied to African cassava mosaic virus disease. Journal of Applied Ecology, 793806.
  • [14] JEGER M.J., HOLT J., VAN DEN BOSCH F., MADDEN L.V. (2004) Epidemiology of insect-transmitted plant viruses: modelling disease dynamics and control interventions. Physiological Entomology, 29(3), 291–304.
  • [15] KASHINA B. D., ALEGBEJO M. D., BANWO O. O., NIELSEN S. L., NICOLAISEN M. (2013) Molecular identification of a new begomovirus associated with mosaic disease of Jatropha curcas L. in Nigeria. Archives of Virology, 158(2), 511-514.
  • [16] MAKKOUK K.M., KUMARI S.G., VAN LEUR J.A., JONES R.A. (2014) Control of plant virus diseases in cool-season grain legume crops. Advances in Virus Research, 90, 207–54.
  • [17] MELGAREJO T.A., KON T., GILBERTSON R.L. (2015) Molecular and biological characterization of distinct strains of Jatropha mosaic virus from the Dominican Republic reveal a potential to infect crop plants. Phytopathology, 105(1), 141–53.
  • [18] MULENGA R.M., LEGG J.P., NDUNGURU J., MIANO D.W., MUTITU E.W., CHIKOTI P.C., ALABI O.J. (2016) Molecular detection, and characterization of geminiviruses associated with cassava mosaic disease in Zambia. Plant Disease, 100(7), 1379–87.
  • [19] PERRING T.M., GRUENHAGEN N.M., FARRAR C.A. (1999) Management of plant viral diseases through chemical control of insect vectors. Annual Review of Entomology, 44(1), 457–81.
  • [20] PONTRYAGIN L. S., BOLTYANSKII V. G., GAMKARELIDZE R. V., MISHCHENKO E. F. (1986) Mathematical Theory of Optimal Processes. Gordon and Breach Science publishers, Vol. 4.
  • [21] PRIYA M.N., SELVAN A.M., NATESAN U. (2006) Natural occurrence of Jatropha mosaic virus disease in India. Current Science, 91(5).
  • [22] RAMKAT R., CALARI A., MAGHULY F., LAIMER M. (2011) Occurrence of African cassava mosaic virus (ACMV) and East African cassava mosaic virus-Uganda (EACMV-UG) in Jatropha curcas. BMC Proceedings, 5(7), p. P93.
  • [23] ROY P.K., LI XUE-ZHI , AL BASIR F., DATTA A., CHOWDHURY J. (2015) Effect of Insecticide Spraying on Jatropha curcas Plant to Control Mosaic Virus: A Mathematical Study. Commun. Math. Biol. Neurosci., 2015, Article ID 36.
  • [24] THRESH J. M., COOTER R. J. (2005) Strategies for controlling cassava mosaic virus disease in Africa. Plant pathology, 54(5), 587–614.
  • [25] VENTURINO E., ROY P. K., AL BASIR F., DATTA A. (2016) A model for the control of the mosaic virus disease in Jatropha curcas plantations. Energ. Ecol. Environ., 1(6), 360–369.
  • [26] WANG, XUEZHONG (2009) Solving optimal control problems with MATLAB - Indirect methods, ISE Dept., NCSU, Raleigh, NC 27695.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-60d3b3ae-de1c-45f4-a744-572c6bb8fad3
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