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Impact of farming awareness based roguing, insecticide spraying and optimal control on the dynamics of mosaic disease

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Abstract

Control interventions and farming knowledge are equally important for plant disease control. In this article, a mathematical model has been derived using saturated response functions (nonlinear infection rate) for studying the dynamics of mosaic disease with farming awareness based roguing (removal of infected plants) and insecticide spraying . It is assumed that the use of roguing and spraying depend on the level of awareness about the disease. The model possesses three equilibria namely the trivial, which is always unstable, the disease-free equilibrium which is stable if the basic reproduction number is below unity and the coexisting which may be stable or can exhibit Hopf-bifurcation under certain condition. Finally, we have opted an optimal control problem introducing three control parameters for determining the optimal level of roguing, spraying and cost regarding media awareness for cost-effective control of mosaic disease. Numerical simulations establish the main results suggesting that the awareness campaigns through radio, TV advertisement are important for eradication of the disease. Also, awareness campaign, roguing and spraying should be incorporated with optimal level for cost effective control of mosaic disease.

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References

  1. Seal, S.E., Jeger, M.J., Van den Bosch, F.: Begomovirus evolution and disease management. Adv. Virus Res. 67, 297–316 (2006)

    Article  Google Scholar 

  2. Moses, E.: Development of Appropriate Strategies to Control Cassava Diseases in Ghana, In: The Role of Plant Pathology in Food Safety and Food Security, pp. 11–24. Springer, Berlin (2009)

    Book  Google Scholar 

  3. Schumann, G.L., D’Arcy, C.J.: Plant pathology courses for agricultural awareness. Plant Dis 83(6), 492–501 (1999)

    Article  Google Scholar 

  4. World Health Organization. Food Safety: What you should know. http://www.searo.who.int/entity/world_health_day/2015/whd-what-you-should-know/en/

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

    Article  Google Scholar 

  6. Akhter, M.S., Akanda, A.M., Kobayashi, K., Jain, R.K., Mandal, B.: Plant virus diseases and their management in Bangladesh. Crop Prot. 118, 57–65 (2019)

    Article  Google Scholar 

  7. Yemataw, Z., Mekonen, A., Chala, A., Tesfaye, K., Mekonen, K., Studholme, D.J., Sharma, K.: Farmers’ knowledge and perception of enset Xanthomonas wilt in southern Ethiopia. Agric. Food Secur. 6(1), 62 (2017)

    Article  Google Scholar 

  8. Khan, G.A., Muhammad, S., Khan, M.A.: Information regarding agronomic practices and plant protection measures obtained by the farmers through electronic media. J. Animal Plant Sci. 23(2), 647–650 (2013)

    Google Scholar 

  9. Nakato, G.V., Beed, F., Bouwmeester, H., Ramathani, I., Mpiira, S., Kubiriba, J., Nanavati, S.: Building agricultural networks of farmers and scientists via mobile phones: Case study of banana disease surveillance in Uganda. Canad. J. Plant Pathol 38(3), 307–16 (2016)

    Article  Google Scholar 

  10. Al Basir, F., Banerjee, A., Ray, S.: Role of farming awareness in crop pest management—A mathematical model. J. Theor. Biol. 461, 59–67 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gao, S., Xia, L., Liu, Y., Xie, D.: A plant virus disease model with periodic environment and pulse roguing. Stud. Appl. Math. 136, 357–381 (2015)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  13. Basir, F.A., Blyuss, K.B., Ray, S.: Modelling the effects of awareness-based interventions to control the mosaic disease of Jatropha curcas. Ecol. Complex. 36, 92–100 (2018)

    Article  Google Scholar 

  14. Basir, F.A., Venturino, E., Ray, S., Roy, P.K.: Impact of farming awareness and delay on the dynamics of mosaic disease in Jatropha curcas plantations. Comput. Appl. Math. 37(5), 6108–6131 (2018)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. Basir, F.A., Roy, P.K.: Dynamics of mosaic disease with roguing and delay in Jatropha curcas plantations. J. Appl. Math. Comput. 58(1–2), 1–31 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  17. Holt, J.M., Jeger, 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), 793–806 (1997)

    Article  Google Scholar 

  18. Pontryagin, L.S., Boltyanskii, V.G., Gamkarelidze, R.V., Mishchenko, E.F.: Mathematical Theory of Optimal Process, vol. 4. Gordon and Breach Science Publishers, London (1986)

    Google Scholar 

  19. Basir, F.A., Roy, P.K., Ray, S.: Impact of roguing and insecticides spraying on mosaic disease in Jatropha curcas. Control Cybern. 46(4), 325–344 (2017)

    MathSciNet  MATH  Google Scholar 

  20. Rakshit, N., Basir, F.A., Banerjee, A., Ray, S.: Dynamics of plant mosaic disease propagation and the usefulness of roguing as an alternative biological control. Ecol. Complex. 38, 15–23 (2019)

    Article  Google Scholar 

  21. Basir, F.A., Blyuss, K.B., Ray, S.: Modelling the effects of awareness-based interventions to control the mosaic disease of Jatropha curcas. Ecol. Complex. 36, 92–100 (2018)

    Article  Google Scholar 

  22. Liu, W.M., Levin, S.A., Iwasa, Y.: Influence of nonlinear incidence rates upon thebehavior of SIRS epidemiological models. J. Math. Biol. 23, 187–204 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  23. 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. Archi. Virol. 155(4), 607–612 (2010)

    Article  Google Scholar 

  24. Hahn, S.K., Terry, E.R., Leuschner, K.: Breeding cassava for resistance to cassava mosaic disease. Euphytica 29(3), 673–683 (1980)

    Article  Google Scholar 

  25. Sinha, S., Samad, A.: First report of Cucumber mosaic virus associated with yellowing mosaic disease of African basil (Ocimum gratissimum) in India. Plant Dis. 103(1), 167–167 (2019)

    Article  Google Scholar 

  26. Bokil, V.A., Allen, L.J.S., Jeger, M.J., Lenhart, S.: Optimal control of a vectored plant disease model for a crop with continuous replanting. J. Biol. Dyn. 13, 325–353 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  27. Blyuss, K.B., Al Basir, F., Tsygankova, V.A., Biliavska, L.O., Iutynska, G.O., Kyrychko, S.N., et al.: Control of mosaic disease using microbial biostimulants: insights from mathematical modelling. Ricerche di Matematica (2020). https://doi.org/10.1007/s11587-020-00508-6

    Article  Google Scholar 

  28. Segura, H.R., Barrera, J.F., Morales, H., Nazar, A.: Farmers’ perceptions, knowledge, and management of coffee pests and diseases and their natural enemies in Chiapas, Mexico. J. Econ. Entomol. 97(5), 1491–1499 (2004)

    Article  Google Scholar 

  29. Kiros-Meles, A., Abang, M.M.: Farmers’ knowledge of crop diseases and control strategies in the Regional State of Tigrai, northern Ethiopia: implications for farmer-researcher collaboration in disease management. Agric. Human Values 25(3), 433 (2008)

    Article  Google Scholar 

  30. Sharma, P.: Necessity of education and awareness in farmers: the basis of agricultural progress in developing and underdeveloped nations. Agric. Biol. J. North Am. 1(3), 387–390 (2010)

    Article  Google Scholar 

  31. Abbas, M., Muhammad, S., Nabi, I., Kashif, M.: Farmers’ information sources, their awareness and adoption of recommended sugarcane production technologies in the central Punjab. Paki. J. Agric. Sci. 40, 202–206 (2003)

    Google Scholar 

  32. Lenhart, S., Workman, J.T.: An introduction to optimal control applied to immunology. In: Modeling and Simulation of Biological Networks, vol. 64, p. 85 (2007)

  33. Anggriani, N., Nurul Putri, L., Supriatna, A.K.: Stability analysis and optimal control of plant fungal epidemic: An explicit model with curative factor. AIP Conf. Proc. Am. Inst. Phys. 1651(1), 40–47 (2015)

    Article  Google Scholar 

  34. Collins, O.C., Kevin, J.D.: Optimal control of maize foliar diseases using the plants population dynamics. Acta Agric. Scand. Sect. B Soil Plant Sci. 66(1), 20–26 (2016)

    Google Scholar 

  35. Khan, M.A., Ali, K., Bonyah, E., Okosun, K.O., Islam, S., Khan, A.: Mathematical modeling and stability analysis of pine wilt disease with optimal control. Sci. Rep. 7(1), 1–19 (2017)

    Article  Google Scholar 

  36. Thresh, J.M., Otim-Nape, G.W.: Strategies for controlling African cassava mosaic geminivirus. Adv. Dis. Vector Res. 10, 215–236 (1994)

    Article  Google Scholar 

  37. Dubern, J.: Transmission of African cassava mosaic geminivirus by the whitefly (Bemisia tabaci). Trop. Sci. 34, 82–91 (1994)

    Google Scholar 

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

    Article  Google Scholar 

  39. Prudencio, Y.C., Al-Hassan, R.: The food security stabilization roles of cassava in Africa. Food Policy 19(1), 57–64 (1994)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Asansol Girls’ College, Asansol-4, West Bengal, 713304, India

    Fahad Al Basir

  2. Department of Zoology, Systems Ecology and Ecological Modeling Laboratory, Visva-Bharati, Santiniketan, 731235, India

    Santanu Ray

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  1. Fahad Al Basir
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Correspondence to Fahad Al Basir.

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Al Basir, F., Ray, S. Impact of farming awareness based roguing, insecticide spraying and optimal control on the dynamics of mosaic disease. Ricerche mat 69, 393–412 (2020). https://doi.org/10.1007/s11587-020-00522-8

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