nach oben

Journal of Applied Mathematics and Computing

Erschienen in:

08.09.2017 | Original Research

Dynamics of mosaic disease with roguing and delay in Jatropha curcas plantations

verfasst von: Fahad Al Basir, Priti Kumar Roy

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2018

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

Jatropha curcas plant is seriously affected by the mosaic disease caused by begomovirus which is carried through infected white-flies. It severely affects the Jatropha plants causing leaf damage, yellowing leaves and sap drainage. Traditionally, the diseased is controlled by roguing or removal of infected plant biomass, using insecticides or increasing resistance to host plant. In this article, a mathematical model is formulated to study mosaic disease dynamics in J. curcas plantations with roguing. Also, time delay has been incorporated in roguing and reformulates the mathematical model using delay differential equations. Sufficient conditions for the stability of the equilibrium points of the system are among the results obtained through qualitative analysis. Using the normal form theory and the center manifold theorem, the stability and direction of the bifurcating periodic solutions of the delayed system are determined. The findings are confirmed by means of numerical simulations.

Nächster Artikel Stationary analysis of the infinite-server queue modulated by a multi-phase Markovian environment

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Gao, S., Qu, J., Chua, N.H., Ye, J.: A new strain of Indian cassava mosaic virus causes a mosaic disease in the biodiesel crop Jatropha curcas. Arch. Virol. 155(4), 607–12 (2010)CrossRef

Anitha, K., Varaprasad, K.S.: Jatropha pests and diseases: an overview. In: Carels, N., Sujatha, M., Bahadur, B. (eds.) Jatropha, Challenges for a New Energy Crop, pp. 175–218. Springer, New York (2012)

Snehi, S.K., Prihar, S.S., Gupta, G., Singh, V., Raj, S.K., Prasad, V.: The current status of new emerging begomovirus diseases on Jatropha species from India. J. Plant Pathol. Microbiol. 91(5) (2016)

Fauquet, C., Fargette, D.: African cassava mosaic virus: etiology epidemiology and control. Plant Dis. 74(74), 404–411 (1990)CrossRef

Priya, M.N., Selvan, A.M., Natesan, U.: Natural occurrence of J. atropha mosaic virus disease in India. Curr. Sci. 7(6) (2006)

Jeger, M.J., Laurence, V.M., Van den Bosch, F.: The effect of transmission route on plant virus epidemic development and disease control. J. Theor. Biol. 258(2), 198–207 (2009)MathSciNetCrossRef

Zhang, T., Meng, X., Song, Y., Li, Z.: Dynamical analysis of delayed plant disease models with continuous or impulsive cultural control strategies. Abstr. Appl. Anal. 2012(2012) (2012)

Thresh, J.M., Cooter, R.J.: Strategies for controlling cassava mosaic virus disease in Africa. Plant Pathol. 54(5), 587–614 (2005)CrossRef

Holt, J., Jeger, M.J., Thresh, J.M., Otim-Nape G.W.: An epidemiological model incorporating vector population dynamics applied to African cassava mosaic virus disease. J. Appl. Ecol. 34(3) (1997)

10.

Venturino, E., Roy, P.K., Basir, F.A., Datta, A.: A model for the control of the mosaic virus disease in Jatropha curcas plantations. Energ. Ecol. Environ. 1(6), 360–369 (2016)CrossRef

11.

Basir, F.A., Venturino, E., Roy, P.K.: Effect of awareness program for controlling mosaic disease in Jatropha curcas plantations. Math. Methods Appl. Sci. 40(7), 2441–2453 (2017)MathSciNetCrossRefMATH

12.

Roy, P.K., Li, X.Z., Basir, F.A., Datta, A., Chowdhury, J.: Effect of insecticide spraying on Jatropha curcas plant to control mosaic virus: a mathematical study. Commun. Math. Biol. Neurosci. 2015, article Id 36 (2015)

13.

Yi, X., Song, L., Sun, G.Q., Zhen, J., Zhang, J.: Assessing reappearance factors of H7N9 avian influenza in China. Appl. Math. Comput. 309, 192–204 (2017)

14.

Li, M.T., Zhen, J., Sun, G.Q., Zhang, J.: Modeling direct and indirect disease transmission using multi-group model. J. Math. Anal. Appl. 446(2), 1292–1309 (2017)MathSciNetCrossRefMATH

15.

Sun, G.Q., Xie, J.H., Huang, S.H., Zhen, J., Li, M.T., Liu, L.: Transmission dynamics of cholera: mathematical modeling and control strategies. Commun. Nonlinear Sci. Numer. Simul. 45, 235–244 (2017)MathSciNetCrossRef

16.

Cao, X., Song, Y., Zhang, T.: Hopf bifurcation and delay-induced turing instability in a diffusive lac operon model. Int. J. Bifurc. Chaos 26(10), 1650167 (2016)MathSciNetCrossRefMATH

17.

Li, L.: Monthly periodic outbreak of hemorrhagic fever with renal syndrome In China. J. Biol. Syst. 24(04), 519–33 (2016)MathSciNetCrossRefMATH

18.

Li, L.: Bifurcation and chaos in a discrete physiological control system. App. Math. Comput. 252, 397–404 (2015)MathSciNetCrossRefMATH

19.

Jeger, M.J., Holt, J., Van Den Bosch, F., Madden, L.V.: Epidemiology of insect transmitted plant viruses: modelling disease dynamics and control interventions. Physiol. Entomol. 29(3), 291–304 (2004)CrossRef

20.

Jeger, M.J., Holt, J., van den Bosch, F., Madden, L.V.: Epidemiology of insecttransmitted plant viruses: modelling disease dynamics and control interventions. Physiol. Entomol. 29, 291304 (2004)CrossRef

21.

Fishman, S., Marcus, R., Talpaz, H., Bar-Joseph, M., Oren, Y., Salomon, R., Zohar, M.: Epidemiological and economic models for spread and control of citrus tristeza virus disease. Phytoparasitica 11, 3949 (1983)CrossRef

22.

Holt, J., Chancellor, T.C.: Simulation modelling of the spread of rice tungro virus disease: the potential for management by roguing. J. Appl. Ecol. 33(5), 927–936 (1996)CrossRef

23.

Allen, R.N.: Epidemiological factors influencing the success of roguing for the control of bunchy top disease of bananas in New South Wales. Crop Pasture Sci. 29(3), 535–44 (1978)CrossRef

24.

Chan, M.S., Jeger, M.J.: An analytical model of plant virus disease dynamics with roguing and replanting. J. Appl. Ecol. 31(3), 413–427 (1994)CrossRef

25.

Neofytou, G., Kyrychko, Y.N., Blyuss, K.B.: Time-delayed model of immune response in plants. J. Theor. Biol. 389, 28–39 (2016)MathSciNetCrossRefMATH

26.

Yu, H., Zhong, S., Ye, M., Chen, W.: Mathematical and dynamic analysis of an ecological model with an impulsive control strategy and distributed time delay. Math. Comput. Model. 50(11), 1622–35 (2009)MathSciNetCrossRefMATH

27.

Xu, R., Du, Y.: A delayed SIR epidemic model with saturation incidence and a constant infectious period. J. Appl. Math. Comput. 35, 229–250 (2011)MathSciNetCrossRefMATH

28.

Cooke, K.L.: Stability analysis for a vector disease model. Rocky Mt. J. Math. 9(1), 3142 (1979)MathSciNetCrossRef

29.

Hale, J.: Theory of Functional Differential Equations. Springer, Heidelberg (1977)CrossRefMATH

30.

Bodnar, M.: The nonnegativity of solutions of delay differential equations. Appl. Math. Lett. 13(6), 91–5 (2000)MathSciNetCrossRefMATH

31.

Yang, X., Chen, L., Chen, J.: Permanence and positive periodic solution for the single species nonautonomus delay diffusive model. Comput. Math. Appl. 32, 109–116 (1996)MathSciNetCrossRefMATH

32.

Hassard, B.D., Kazarinoff, N.D., Wan, Y.H.: Theory and Applications of Hopf Bifurcation. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (1981)MATH

Titel: Dynamics of mosaic disease with roguing and delay in Jatropha curcas plantations
verfasst von: Fahad Al Basir
Priti Kumar Roy
Publikationsdatum: 08.09.2017
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2018
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-017-1131-2

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 1-2/2018

Herd behavior in a predator–prey model with spatial diffusion: bifurcation analysis and Turing instability

A new family of conjugate gradient methods for unconstrained optimization

Primitive idempotents of cyclic codes of length p and 2p

On the error estimation of spline method for second order boundary value problem

Graphs having extremal monotonic topological indices with bounded vertex k-partiteness

A saddle point characterization of efficient solutions for interval optimization problems