
Mathematical Biosciences and Engineering, 2019, 16(6): 70227056. doi: 10.3934/mbe.2019353.
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Global dynamical analysis of plantdisease models with nonlinear impulsive cultural control strategy
1 School of Mathematics, Northwest University, Xi’an, Shaanxi 710127, P.R. China
2 Department of Mathematics and Faculty of Medicine, The University of Ottawa, 150 LouisPasteur Pvt, Ottawa, ON, K1N 6N5, Canada
Received: , Accepted: , Published:
Special Issues: Nonsmooth biological dynamical systems and applications
Keywords: plant diseases; economic threshold; integrated disease management; fold bifurcation; impulsive differential equations; persistence
Citation: Tingting Zhao, Robert J. Smith?. Global dynamical analysis of plantdisease models with nonlinear impulsive cultural control strategy. Mathematical Biosciences and Engineering, 2019, 16(6): 70227056. doi: 10.3934/mbe.2019353
References:
 1. R. W. Gibson, J. P. Legg and G. W. OtimNape, Unusually severe symptoms are a characteristic of the current epidemic of mosaic virus disease of cassava in Uganda, Ann. Appl. Biol., 128 (1996), 479–490.
 2. T. Iljon, J. Stirling and R. J. Smith?, A mathematical model describing an outbreak of Fire Blight, in Understanding the dynamics of emerging and reemerging infectious diseases using mathematical models (eds. S. Mushayabasa and C.P. Bhunu), Transworld Research network, (2012), 91–104.
 3. R. A. C. Jones, Using epidemiological information to develop effective integrated virus disease management strategies, Virus Res., 100 (2004), 5–30.
 4. C. A. Gilligan, Sustainable agriculture and plant diseases: an epidemiological perspective, Phil. Trans. R. Soc. B, 363 (2008), 741–759.
 5. L. M. C. Medina, I. T. Pacheco, R. G. G. Gonzalez, et al., Mathematical modeling tendencies in plant pathology, Afr. J. Biotechnol., 8 (2009), 7399–7408.
 6. R. A. C. Jones, Determining threshold levels for seedborne virus infection in seed stocks, Virus Res., 71 (2000), 171–183.
 7. T. T. Zhao and S. Y. Tang, Plant disease control with Economic Threshold, J. Bioma., 24 (2009), 385–396.
 8. F. Van den Bosch and A. M. Roos, The dynamics of infectious diseases in orchards with roguing and replanting as control strategy, J. Math. Biol., 35 (1996), 129–157.
 9. M. S. Chan and M. J. Jeger, An analytical model of plant virus disease dynamics with roguing, J. Appl. Ecol., 31 (1994), 413–427.
 10. H. R. Thieme and J. A. P. Heesterbeek, How to estimate the efficacy of periodic control of an infectious plant disease, Math. Biosci. 93 (1989), 15–29.
 11. R. W. Gibson and V. Aritua, The perspective of sweet potato chlorotic stunt virus in sweet potato production in Africa, a review, Afr. Crop Sci. J., 10 (2002), 281–310.
 12. J. M. Thresh and R. J. Cooter, Strategies for controlling cassava mosaic disease in Africa, Plant Pathol., 54 (2005), 587–614.
 13. J. M. Thresh, The origins and epidemiology of some important plant virus diseases, Appl. Biol., 5 (1980), 1–65.
 14. S. Fishman, R. Marcus, H. Talpaz, et al., Epidemiological and economic models for the spread and control of citrus tristeza virus disease, Phytoparasitica, 11 (1983), 39–49.
 15. J. M. Thresh and G. K. Owusu, The control of cocoa swollen shoot disease in Ghana: an evaluation of eradication procedures, Crop Prot., 5 (1986) 41–52.
 16. A. N. Adams, The incidence of plume pox virus in England and its control in orchards, in Plant Disease Epidemiology (ed. P.R. Scott and A. Bainbridge), Blackwell Scientific Publications, (1978), 213–219.
 17. G. Hughes, N. McRoberts, L. V. Madden, et al., Validating mathematical models of plantdisease progress in space and time, Math. Med. Biol., 14 (1997), 85–112.
 18. J. Holt and T. C. B. Chancellor, A model of plant virus disease epidemics in asynchronouslyplanted cropping systems, Plant Pathol., 46 (1997), 490–501.
 19. F. van den Bosch, N. McRoberts, F. van den Berg, et al., The basic reproduction number of plant pathogens: matrix approaches to complex dynamics, Phytopathology, 98 (2008), 239–249.
 20. C. Chen, Y. Kang and R. J. Smith?, Sliding motion and global dynamics of a Filippov fireblight model with economic thresholds, Nonlinear Anal.Real, 39 (2018), 492–519.
 21. A. Wang, Y. Xiao and R. J. Smith?, Using nonsmooth models to determine thresholds for microbial pest management, J. Math. Biol., 78 (2019), 1389–1424.
 22. L. V. Madden, G. Hughes and F. van den Bosch, The study of plant disease epidemics, The American Phytopathological Society, St. Paul, 2007.
 23. F. Van den Bosch, M. J. Jeger and C. A. Gilligan, Disease control and its selection for damaging plant virus strains in vegetatively propagated staple food crops; a theoretical assessment, Proc. R. Soc. B, 274 (2007), 11–18.
 24. S. Fishman and R. Marcus, A model for spread of plant disease with periodic removals, J. Math. Biol., 21 (1984), 149–158.
 25. Y. N. Xiao, D. Z. Cheng and H. S. Qin, Optimal impulsive control in periodic ecosystem, Syst. Contr. Lett., 55 (2006), 558–565.
 26. X. Y. Zhang, Z. S. Shuai and K. Wang, Optimal impulsive harvesting policy for single population, Nonlinear Anal.Real, 4 (2003), 639–651.
 27. S. Y. Tang, Y. N. Xiao and R. A. Cheke, Dynamical analysis of plant disease models with cultural control strategies and economic thresholds, Math. Comput. Simul., 80 (2010), 894–921.
 28. M. C. Smith, J. Holt, L. Kenyon, et al., Quantitative epidemiology of banana bunchy top virus disease and its control, Plant Pathol., 47 (1998), 177–187.
 29. S. Y. Tang, Y. N. Xiao and R. A. Cheke, Multiple attractors of hostparasitoid models with integrated pest management strategies: eradication, persistence and outbreak, Theor. Popul. Biol., 73 (2008), 181–197.
 30. T. T. Zhao, Y. N. Xiao and R. J. Smith?, Nonsmooth plant disease models with economic thresholds, Math. Biosci., 241 (2013), 34–48.
 31. S. Y. Tang, R. A. Cheke and Y. N. Xiao, Optimal impulsive harvesting on nonautonomous Beverton–Holt difference equations, Nonlinear Anal.Theor., 65 (2006), 2311–2341.
 32. D. Bainov and P. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, Longman Scientific and Technical, New York, 1993.
 33. J. M. Heffernan, R. J. Smith and L. M. Wahl, Perspectives on the basic reproductive ratio, J. R. Soc. Interface, 2 (2005), 281–293.
 34. J. Li, D. Blakeley and R. J. Smith?, The Failure of R_{0}, Comp. Math. Meth. Med., 2011 (2011), Article ID 527610.
 35. A. Lakmech and O. Arino, Bifurcation of nontrival periodic solutions of impulsive differential equations arising chemotherapeutic treatment, Dyn. Cont. Discr. Impul. Syst., 7 (2000), 265–287.
 36. M. D. McKay, W. J. Conover and R. J. Beckman, A comparison of three models for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21 (1979), 239–245 .
 37. R. M. Corless, G. H. Gonnet, D. E. G. Hare, et al., On the Lambert W Function, Adv. Comput. Math., 5 (1996), 329–359.
 38. S. Y. Tang and Y. N. Xiao, Dynamics System of Single Species, Science Press, Beijing, 2008.
 39. Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, SpringerVerlag, New York, 2004.
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