Non-smooth plant disease models with economic thresholds

Mathematical Biosciences

Volumn 241, Issue 1, 2013, Pages 34-48

  Zhao, Tingting ^a   Xiao, Yanni ^a   Smith, Robert J ^b  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b UNIVERSITY OF OTTAWA   (Canada)

Author keywords

Economic threshold; Filippov system; Integrated disease management; Lyapunov function; Plant disease

Indexed keywords

CONTROL PLANTS; CULTURAL CONTROL; DISEASE MANAGEMENT; ECONOMIC THRESHOLD; FILIPPOV SYSTEMS; GLOBAL ATTRACTOR; GLOBAL DYNAMIC BEHAVIOR; GLOBAL STRUCTURE; ITERATIVE EQUATION; LOTKA-VOLTERRA; MANAGEMENT STRATEGIES; NON-SMOOTH; PIECEWISE-SMOOTH SYSTEMS; PLANT DISEASE; RIGHT-HAND SIDES; THRESHOLD POLICIES;

DIFFERENTIAL EQUATIONS; DISEASES; ITERATIVE METHODS;

LYAPUNOV FUNCTIONS;

DISEASE CONTROL; INTEGRATED APPROACH; LOTKA-VOLTERRA MODEL; PLANT;

ARTICLE; ECONOMIC ASPECT; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; PLANT DISEASE; PLANT DISEASE CONTROL; PLANTING DENSITY;

MATHEMATICAL CONCEPTS; MODELS, BIOLOGICAL; MODELS, ECONOMIC; PLANT DISEASES;

EID: 84870883879     PISSN: 00255564     EISSN: 18793134     Source Type: Journal    
DOI: 10.1016/j.mbs.2012.09.005     Document Type: Article

References (32)

1. Gibson R.W., Legg J.P., Otim-Nape G.W. Unusually severe symptoms are a characteristic of the current epidemic of mosaic virus disease of cassava in Uganda. Ann. Appl. Biol. 1996, 128:479.
2. T. Iljon, J. Stirling, R.J. Smith, A mathematical model describing an outbreak of Fire Blight, in: S. Mushayabasa, C.P. Bhunu (Eds.), Understanding the Dynamics of Emerging and Re-emerging Infectious Diseases Using Mathematical Models, 2012, pp 91-104.
3. Medina L.M.C., Pacheco I.T., Gonzalez R.G.G., et al. Mathematical modeling tendencies in plant pathology. Afr. J. Biotechnol. 2009, 8:7399.
4. Jones R.A.C. Determining threshold levels for seed-borne virus infection in seed stocks. Virus Res. 2000, 71:171.
5. Jones R.A.C. Using epidemiological information to develop effective integrated virus disease management strategies. Virus Res. 2004, 100:5.
6. Zhao T.T., Tang S.Y. Plant disease control with economic threshold. J. Biomater. 2009, 24:385.
7. Thieme H.R., Heesterbeek J.A.P. How to estimate the efficacy of periodic control of an infectious plant disease. Math. Biosci. 1989, 93:15.
8. van den Bosch F., McRoberts N., van den Berg F., Madden L.V. The basic reproduction number of plant pathogens: matrix approaches to complex dynamics. Phytopathology 2008, 98:239.
9. van den Bosch F., Jeger M.J., Gilligan C.A. Disease control and its selection for damaging plant virus strains in vegetatively propagated staple food crops; a theoretical assessment. Proc. R. Soc. B 2007, 274:11.
10. van den Bosch F., Roos A.M. The dynamics of infectious diseases in orchards with roguing and replanting as control strategy. J. Math. Biol. 1996, 35:129.
11. Chan M.S., Jeger M.J. An analytical model of plant virus disease dynamics with roguing. J. Appl. Ecol. 1994, 31:413.
12. Zadoks J.C., Schein R.D. Epidemiology and Plant Disease Management 1979, Oxford University, New York.
13. Madden L.V., Hughes G., van den Bosch F. The Study of Plant Disease Epidemics 2007, The American Phytopathological Society, St. Paul, Minnesota, USA.
14. Fishman S., Marcus R., Talpaz H., et al. Epidemiological and economic models for the spread and control of citrus tristeza virus disease. Phytoparasitica 1983, 11:39.
15. Capasso V. Mathematical Structures of Epidemic Systems 1993, Springer-Verlag, Berlin.
16. Tang S.Y., Xiao Y.N., Cheke R.A. Multiple attractors of host-parasitoid models with integrated pest management strategies: eradication, persistence and outbreak. Theor. Popul. Biol. 2008, 73:181.
17. Tang S.Y., Cheke R.A. Models for integrated pest control and their biological implications. Math. Biosci. 2008, 215:115.
18. Tang S.Y., Xiao Y.N., Cheke R.A. Dynamical analysis of plant disease models with cultural control strategies and economic thresholds. Math. Comput. Simul. 2010, 80:894.
19. Filippov A.F. Differential Equations with Discontinuous Righthand Sides 1988, Kluwer Academic, Dordrecht.
20. Utkin V.I. Sliding Modes in Control and Optimization 1992, Springer, Berlin.
21. V.I. Utkin, J. Guldner, J.X. Shi, Sliding Mode Control in Electro-mechanical Systems, second ed., Taylor & Francis Group, 2009.
22. Bernardo M.D., Budd C.J., Champneys A.R., et al. Bifurcations in nonsmooth dynamical system. SIAM Rev. 2008, 50:629.
23. Brogliato B. Nonsmooth Mechanics 1999, Springer-Verlag, NY.
24. Costa M.I.S. Harvesting induced fluctuations: insights from a threshold management policy. Math. Biosci. 2007, 205:77.
25. Costa M.I.S., Kaszkurewicz E., Bhaya A., Hsu L. Achieving global convergence to an equilibrium population in predator-prey systems by the use of a discontinuous harvesting policy. Ecol. Model. 2000, 128:88.
26. Dercole F., Gragnani A., Rinaldi S. Bifurcation analysis of piecewise smooth ecological models. Theor. Popul. Biol. 2007, 72:197.
27. di Bernardo M., Kowalczyk P., Nordmark A. Bifurcation of dynamical systems with silding: derivation of normal-form mappings. Physica D 2002, 170:175.
28. Corless R.M., Gonnet G.H., Hare D.E.G., et al. On the Lambert W function. Adv. Comput. Math. 1996, 5:329.
29. Boukal D.S., Krivan V. Lyapunov functions for Lotka-Volterra predator-prey models with optimal forging behavior. J. Math. Biol. 1999, 39:493.
30. Costa M.I.S., Faria L.D.B. Integrated pest management: theoretical insights from a threshold policy. Neotrop. Entomol. 2010, 39:1.
31. Meza M.E.M., Bhaya A., Kaszkurewicz E., Costa M.I.da S. Threshold policies control for predator-prey systems using a control Liapunov function approach. Theor. Popul. Biol. 2005, 67:273-284.
32. Krivan V. Effects of optimal antipredator behavior of prey on predator-prey dynamics: the role of refuges. Theor. Popul. Biol. 1998, 53:131.