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Analysis of a nonautonomous plant disease model with latent period. (English) Zbl 1329.92080
Summary: In this paper, we consider a plant disease model with latent period and nonautonomous phenomenon. We investigate the long-time behavior of the epidemic model. By constructing auxiliary functions, the weaker integral form conditions for permanence and extinction of the model are obtained. Numerical simulations which support our theoretical analysis are also given.

MSC:
92C80 Plant biology
92D30 Epidemiology
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[1] Fereres, A.; Thresh, J. M.; Irwin, M. E., Plant virus epidemiology: challenges for the twenty-first century, Virus Res., 71, 1-267, (2000)
[2] Thresh, J. M., Progress curves of plant virus disease, Appl. Biol., 8, 1-85, (1983)
[3] Pscheidt, J. W., Plant disease, (Chalker-Scott, L., Sustainable Landscapes and Gardens: Good Science-Practical Application, (2009), Good Fruit Grower Publishing)
[4] V.A. Johnson, P.J. Mattern, Report of Research Findings: Improvement of the nutritional quality of wheat through increased protein content & improved amino acid balance, Agency for International Development Department of State, Washington, 1975.
[5] Ullstrup, A. J., The impacts of the southern corn leaf blight epidemics of 1970-1971, Annu. Rev. Phytopathol., 10, 37-50, (1972)
[6] Ollennu, L. A.A.; Owusu, G. K.; Thresh, J. M., The control of cocoa swollen shoot disease in ghana, Cocoa Growers’ Bull., 42, 25-35, (1989)
[7] 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)
[8] Fishman, S.; Marcus, R.; Talpaz, H., Epidemiological and economic models for spread and control of citrus tristeza virus disease, Phytoparasitica, 11, 39-49, (1983)
[9] De la Sen, M.; Alonso-Quesada, S., Vaccination strategies based on feedback control techniques for a general SEIR-epidemic model, Appl. Math. Comput., 218, 3888-3904, (2011) · Zbl 1238.92030
[10] De la Sen, M.; Ibeas, A.; Alonso-Quesada, S., On a generalized time-varying SEIR epidemic model with mixed point and distributed time-varying delays and combined regular and impulsive vaccination controls, Adv. Differ. Equ., (2010) · Zbl 1219.34104
[11] Gao, S.; Teng, Z.; Xie, D., The effects of pulse vaccination on SEIR model with two time delays, Appl. Math. Comput., 201, 282-292, (2008) · Zbl 1143.92024
[12] 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 - Biol. Sci., 274, 11-18, (2007)
[13] Van den Bosch, F.; Fraaije, B. A.; Van den Berg, F.; Shaw, M. W., Evolutionary bi-stability in pathogen transmission mode, Proc. R. Soc. B - Biol. Sci., 277, 1735-1742, (2010)
[14] Holt, J.; Chancellor, T. C.B., A model of plant virus disease epidemics in asynchronously-planted cropping systems, Plant Pathol., 46, 490-501, (1997)
[15] Grilli, M. P.; Holt, J., Vector feeding period variability in epidemiological models of persistent plant viruses, Ecol. Model., 126, 49-57, (2000)
[16] Zhang, X. S.; Holt, J.; Colvin, J., A general model of plant-virus disease infection incorporating vector aggregation, Plant Pathol., 49, 435-444, (2000)
[17] Wang, J.; Liu, S.; Takeuchi, Y., Threshold dynamics in a periodic SVEIR epidemic model, Int. J. Biomath., 4, 493-509, (2011) · Zbl 1297.92085
[18] Vandermeer, J.; Power, A., An epidemiological model of the corn stunt system in central America, Ecol. Model., 52, 235-248, (1990)
[19] Holt, J.; Colvin, J.; Muniyappa, V., Identifying control strategies for tomato leaf curl virus disease using an epidemiological model, J. Appl. Ecol., 36, 625-633, (1999)
[20] Van Maanen, A.; Xu, X. M., Modelling plant disease epidemics, Eur. J. Plant Pathol., 109, 669-682, (2003)
[21] Gumpert, F. M.; Geiger, H. H.; Staehle, U., A mathematical model of the epidemics in homogeneous and heterogenous host stands, Z. Pflanzenk. Pflanzen., 94, 206-215, (1987)
[22] Nakasuji, F.; Miyai, S.; Kawamoto, H.; Kiritani, K., Mathematical epidemiology of Rice dwarf virus transmitted by Green Rice leafhoppers: adifferential equation model, J. Appl. Ecol., 22, 839-847, (1985)
[23] Zhang, T.; Teng, Z., On a nonautonomous SEIRS model in epidemiology, Bull. Math. Biol., 69, 2537-2559, (2007) · Zbl 1245.34040
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