Mathematical model of potato virus Y disease spread with optimal control
Abstract
Potato virus Y (PVY) is an aphid-borne plant virus that causes substantial yield losses in potato production. Control measures of the viral infection are both limited and expensive. A proper use of mixed-cropping strategy can reduce the spread of PVY. In this paper, we formulate and analyze a mathematical model of PVY spread in a mixed-cropping system. Then, we extend the model to an optimal control problem by considering use of mineral oil, insecticide and farmer’s level of field inspection for infected plants. The analytic results show that the basic reproduction number ℜ0, a threshold parameter that decides properties of the dynamics. The disease free equilibrium is stable if ℜ0 < 1 and unstable when ℜ0 > 1. It is found that ℜ0, and hence, the disease dynamics is highly sensitive to the representative parameters of density the non-host plant and its quality in attracting vectors. The model exhibits forward bifurcation at ℜ0 = 1. The study of optimal control problem suggests that mixed-cropping combined with either mineral oil or insecticide is the best to control the disease. Furthermore, simulation results show that mixed-cropping can be used as an alternative strategy and can reduce the need of mineral oil or insecticide.
Keyword : PVY, mixed-cropping, mathematical model, optimal control
How to Cite
Degefa, S. T., Makinde, O. D., & Dufera, T. T. (2022). Mathematical model of potato virus Y disease spread with optimal control. Mathematical Modelling and Analysis, 27(3), 408–428. https://doi.org/10.3846/mma.2022.15077
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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R. Raymundo, S. Asseng, R. Robertson, A. Petsakos, G. Hoogenboom, R. Quiroz, G. Hareau and J. Wolf. Climate change impact on global potato production. European Journal of Agronomy, 100:87–98, 2018. https://doi.org/10.1016/j.eja.2017.11.008
B. Tsedaley. A review paper on potato virus Y (PVY) biology, economic importance and its managements. Journal of Biology, Agriculture and Healthcare, 5(9):110–126, 2015. ISSN 2224-3208.
P. Van den Driessche and J. Watmough. Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180(1):29–48, 2002. https://doi.org/10.1016/S0025-5564(02)00108-6
J.E. Van der Waals, J.M. Steyn, A.C. Franke and A.J. Haverkort. Grower perceptions of biotic and abiotic risks of potato production in South Africa. Crop Protection, 84:44–55, 2016. https://doi.org/10.1016/j.cropro.2016.02.008
E. Venturino, P.K. Roy, F. Al Basir and A. Datta. A model for the control of the mosaic virus disease in Jatropha curcas plantations. Energy, Ecology and Environment, 1(6):360–369, 2016. https://doi.org/10.1007/s40974-016-0033-8
S.P.F. Ximba. Detection, differentiation and genome analysis of potato virus Y isolates infecting potato (Solanum tuberosum L.) in the Msinga area in KwaZuluNatal, Republic of South Africa. PhD thesis, School of Agricultural, Earth and Environmental Science College of Agriculture, Engineering and Science University of KwaZulu-Natal Pietermaritzburg Republic of South Africa, 2016.
F. Zhou and H. Yao. Dynamics and biocontrol: the indirect effects of a predator population on a host-vector disease model. In Abstract and Applied Analysis, volume 2014. Hindawi, 2014. https://doi.org/10.1155/2014/252718
V.K. Arora, J.C. Nath and C.B. Singh. Analyzing potato response to irrigation and nitrogen regimes in a sub-tropical environment using SUBSTOR-Potato model. Agricultural Water Management, 124:69–76, 2013. https://doi.org/10.1016/j.agwat.2013.03.021
L. Bertschinger, L. Bühler, B. Dupuis, B. Duffy, C. Gessler, G.A. Forbes, E.R. Keller, U.C. Scheidegger and P.C. Struik. Incomplete infection of secondarily infected potato plants–an environment dependent underestimated mechanism in plant virology. Frontiers in plant science, 8:74, 2017. https://doi.org/10.3389/fpls.2017.00074
V.A. Bokil, L.J.S. Allen, M.J. Jeger and S. Lenhart. Optimal control of a vectored plant disease model for a crop with continuous replanting. Journal of Biological Dynamics, 13(sup1):325–353, 2019. https://doi.org/10.1080/17513758.2019.1622808
S. Boquel, C. Delayen, A. Couty, P. Giordanengo and A. Ameline. Modulation of aphid vector activity by potato virus y on in vitro potato plants. Plant Disease, 96(1):82–86, 2012. https://doi.org/10.1094/PDIS-06-11-0499
R.H.E. Bradley. Studies of the mechanism of transmission of potato virus Y by the green peach aphid, Myzus persicae (Sulz.)(Homoptera: Aphidae). Canadian Journal of Zoology, 32(2):64–73, 1954. https://doi.org/10.1139/z54-008
R.H.E. Bradley. Loss of virus from the stylets of aphids. Virology, 8(3), 1959. https://doi.org/10.1016/0042-6822(59)90032-7
C. Castillo-Chavez and B. Song. Dynamical models of tuberculosis and their applications. Mathematical Biosciences & Engineering, 1(2):361–404, 2004. https://doi.org/10.3934/mbe.2004.1.361
D.S. Degefa, O.D. Makinde and D.T. Temesgen. Modeling potato virus y disease dynamics in a mixed-cropping system. International Journal of Modelling and Simulation, 42(3):370–387, 2022. https://doi.org/10.1080/02286203.2021.1919818
B. Dupuis, J. Cadby, G. Goy, M. Tallant, J. Derron, R. Schwaerzel and T Steinger. Control of potato virus Y (PVY) in seed potatoes by oil spraying, straw mulching and intercropping. Plant Pathology, 66(6):960–969, 2017. https://doi.org/10.1111/ppa.12698
A.J. Haverkort and P.C. Struik. Yield levels of potato crops: recent achievements and future prospects. Field Crops Research, 182:76–85, 2015. https://doi.org/10.1016/j.fcr.2015.06.002
C.R.R. Hooks and A. Fereres. Protecting crops from non-persistently aphid-transmitted viruses: a review on the use of barrier plants as a management tool. Virus Research, 120(1-2):1–16, 2006. https://doi.org/10.1016/j.virusres.2006.02.006
A. Hussain, M. Arif, A. Abbas, B. Hussain, M. Ali and S. Jaffar. A review on aphid-borne virus (Potato virus Y). Journal of Entomology and Zoology Studies, 4(3):189–192, 2016.
M. Jackson and B.M. Chen-Charpentier. Modeling plant virus propagation with seasonality. Journal of Computational and Applied Mathematics, 345:310–319, 2019. https://doi.org/10.1016/j.cam.2018.06.022
M.J. Jeger, F. van den Bosch, L.V. Madden and J. Holt. A model for analysing plant-virus transmission characteristics and epidemic development. Mathematical Medicine and Biology: A Journal of the IMA, 15(1):1–18, 1998. ISSN 14778599. https://doi.org/10.1093/imammb15.1.1
S. Kirchner et al. Epidemiology and enhanced control of potato virus y in high grade seed potato production. Biology, 2014.
A. Kumar, P.K. Srivastava and Y. Takeuchi. Modeling the role of information and limited optimal treatment on disease prevalence. Journal of Theoretical Biology, 414:103–119, 2017. https://doi.org/10.1016/j.jtbi.2016.11.016
L. Lemecha Obsu and S. Feyissa Balcha. Optimal control strategies for the transmission risk of COVID-19. Journal of Biological Dynamics, 14(1):590–607, 2020. https://doi.org/10.1080/17513758.2020.1788182
T.D.B. MacKenzie, J. Lavoie, X. Nie and M. Singh. Effectiveness of combined use of mineral oil and insecticide spray in reducing Potato virus Y (PVY) spread under field conditions in New Brunswick, Canada. American Journal of Potato Research, 94(1):70–80, 2017. https://doi.org/10.1007/s12230-016-9550-4
M. Martcheva. An introduction to mathematical epidemiology, volume 61. Springer, 2015. https://doi.org/10.1007/978-1-4899-7612-3
T. Nemecek. The role of aphid behaviour in the epidemiology of potato virus Y: a simulation study. PhD thesis, ETH Zurich, Zurich, 1993.
R. Raymundo, S. Asseng, R. Robertson, A. Petsakos, G. Hoogenboom, R. Quiroz, G. Hareau and J. Wolf. Climate change impact on global potato production. European Journal of Agronomy, 100:87–98, 2018. https://doi.org/10.1016/j.eja.2017.11.008
B. Tsedaley. A review paper on potato virus Y (PVY) biology, economic importance and its managements. Journal of Biology, Agriculture and Healthcare, 5(9):110–126, 2015. ISSN 2224-3208.
P. Van den Driessche and J. Watmough. Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180(1):29–48, 2002. https://doi.org/10.1016/S0025-5564(02)00108-6
J.E. Van der Waals, J.M. Steyn, A.C. Franke and A.J. Haverkort. Grower perceptions of biotic and abiotic risks of potato production in South Africa. Crop Protection, 84:44–55, 2016. https://doi.org/10.1016/j.cropro.2016.02.008
E. Venturino, P.K. Roy, F. Al Basir and A. Datta. A model for the control of the mosaic virus disease in Jatropha curcas plantations. Energy, Ecology and Environment, 1(6):360–369, 2016. https://doi.org/10.1007/s40974-016-0033-8
S.P.F. Ximba. Detection, differentiation and genome analysis of potato virus Y isolates infecting potato (Solanum tuberosum L.) in the Msinga area in KwaZuluNatal, Republic of South Africa. PhD thesis, School of Agricultural, Earth and Environmental Science College of Agriculture, Engineering and Science University of KwaZulu-Natal Pietermaritzburg Republic of South Africa, 2016.
F. Zhou and H. Yao. Dynamics and biocontrol: the indirect effects of a predator population on a host-vector disease model. In Abstract and Applied Analysis, volume 2014. Hindawi, 2014. https://doi.org/10.1155/2014/252718