[en] Theoretical description of epidemics of plant diseases is an invaluable resource for their efficient management. Here we propose a mathematical model for describing the dispersal by wind of fungal pathogens in plant populations. The dispersal of pathogen spores was modelled using a non-local diffusion equation which took into account variations in wind velocity components and contained a threshold in the convolution kernel defining the non-local diffusion term. The model was analyzed and the epidemic levels and patterns of the plant disease were derived, based upon defined assumptions of the time and space variables (i.e., represented by continuous parameters), and the host population (i.e., fixed population size). Numerical applications were then performed using reported characteristic values for wheat leaf rust, stripe rust and stem rust.
Disciplines :
Agriculture & agronomy
Author, co-author :
El Jarroudi, Mustapha
Karjoun, Hasan
Kouadiou, Louis
El Jarroudi, Moussa ; Université de Liège - ULiège > DER Sc. et gest. de l'environnement (Arlon Campus Environ.) > Eau, Environnement, Développement
Language :
English
Title :
Mathematical modelling of non-local spore dispersion of wind-borne pathogens causing fungal diseases
Jeger, M.J., Improved understanding of dispersal in crop pest and disease management: current status and future directions. Agric For Meteorol. 97:4 (1999), 331–349, 10.1016/S0168-1923(99)00076-3.
Anderson, R.M., Transmission dynamics and control of infectious disease agents. Anderson, R.M., May, R.M., (eds.) Population Biology of Infectious Diseases, 1982, Springer-Verlag, Berlin, Germany, 149–176, 10.1002/9780470114209.ch22.
Waggoner, P.E., Models of plant disease. BioScience 31:4 (1981), 315–319.
Choisy, M., Guégan, J.-F., Rohani, P., Mathematical modeling of infectious diseases dynamics. Tibayrenc, M., (eds.) Encyclopedia of infectious diseases: Modern Methodologies, 2006, Wiley-Blackwell, Hoboken, NJ, USA, 379–404, 10.1002/9780470114209.ch22.
Hamer, W.H., Epidemic disease in england - the evidence of variability and of persistency of type. The Lancet 167:4307 (1906), 733–739, 10.1016/S0140-6736(01)80340-8.
Ross, R., The Prevention of Malaria. 1911, John Murray, London, UK.
Kermack, W.O., McKendrick, A.G., A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 115:772 (1927), 700–721, 10.1098/rspa.1927.0118.
Van der Plank, J.E., Analysis of Epidemics. Horsfall, J.G., Cowling, E.B., (eds.) Plant Pathology: An Advance Treatise, 3, 1960, Academic Press, New York, USA, 229–289.
Van der Plank, J.E., Plant Diseases: Epidemics and Control. 1963, Academic Press, New York, USA, London, UK.
Van der Plank, J.E., Dynamics of epidemics of plant disease. Science 147:3654 (1965), 120–124.
Cooke, B.M., Gareth, J.D., Kaye, B.e., The Epidemiology of Plant Diseases. 2, 2006, Springer Netherlands, Dordrecht, Netherlands, 10.1007/1-4020-4581-6.
Madden, C.V., Hughes, G., van den Bosch, F., The study of the plant disease epidemics. 2007, The American Phytopathological Society, St. Paul, MN, USA.
Moore, D., Robson, G.D., Trinci, A.P.J., 21st century guidebook to fungi. 2000, Cambridge University Press, Cambridge, 10.1017/CBO9780511977022.
Horst, R.K., Classification of plant pathogens. Westcott's Plant Disease Handbook, 2001, Springer USA, Boston, MA, USA, 33–63, 10.1007/978-1-4757-3376-1_2.
Struck, C., Infection strategies of plant parasitic fungi. Cooke, B.M., Gareth, J.D., Kaye, B., (eds.) The Epidemiology of Plant Diseases, 2006, Springer Netherlands, Dordrecht, Netherlands, 117–137, 10.1007/1-4020-4581-6_4.
Hau, B., de Vallavieille-Pope, C., Wind-dispersed Diseases. Cooke, B.M., Gareth, J.D., Kaye, B., (eds.) The Epidemiology of Plant Diseases, 2006, Springer Netherlands, Dordrecht, Netherlands, 387–416, 10.1007/1-4020-4581-6_15.
Mendgen, K., Struck, C., Voegele, R.T., Hahn, M., Biotrophy and rust haustoria. Physiol. Mol. Plant Pathol. 56:4 (2000), 141–145, 10.1006/pmpp.2000.0264.
Staples, R.C., Nutrients for a rust fungus: the role of haustoria. Trends Plant Sci. 6:11 (2001), 496–498, 10.1016/S1360-1385(01)02126-4.
Mendgen, K., Hahn, M., Plant infection and the establishment of fungal biotrophy. Trends Plant Sci. 7:8 (2002), 352–356, 10.1016/S1360-1385(02)02297-5.
Murray, J.D., Mathematical biology. Biomathematics 19, 1993, Springer-Verlag Berlin Heidelberg, New York, USA, 10.1007/978-3-662-08542-4.
Okubo, A., Levin, S.A., Diffusion and ecological problems: Modern perspectives. Interdisciplinary Applied Mathematics 14, 2001, Springer-Verlag New York, New York, USA, 10.1007/978-1-4757-4978-6.
Kolmogorov, A.N., Petrovskii, I.G., Piskounov, N.S., Etude de l’équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique. Bulletin Université d'Etat de Moscou (Bjul. Moskowskogo Gos. Univ), Série internationale A1 (1937), 1–26.
Bates, P., Fife, P.C., Ren, V., Wang, X., Travelling waves in convolution model for phase transitions. Arch Rat Mech Anal 138 (1997), 105–136.
Pan, S., Li, W.-T., Lin, G., Travelling wave fronts in nonlocal delayed reaction-diffusion systems and applications. Zeitschrift für angewandte Mathematik und Physik 60:3 (2009), 377–392, 10.1007/s00033-007-7005-y.
Gourley, S.A., Wu, J., Delayed nonlocal diffusion systems in biological invasion and diseases spread. nonlinear dynamics and evolution equations, volume Fields Inst Commun 48. 2010, American Mathematical Society, Providence, RI, USA.
Othmer, H.G., Dunbar, S.R., Alt, W., Models of dispersal in biological systems. J. Math. Biol. 26:3 (1988), 263–298, 10.1007/BF00277392.
van den Bosch, F., Metz, J.A.J., Zadoks, J.C., Pandemics of focal plant disease, a model. Phytopathology 89 (1999), 495–505, 10.1094/PHYTO.1999.89.6.495.
Segarra, J., Jeger, M.J., van den Bosch, F., Epidemic dynamics and patterns of plant diseases. Phytopathology 91 (2001), 1001–1010, 10.1094/PHYTO.2001.91.10.1001.
Diekmann, O., Heesterbeek, J.A.P., Metz, J.A.J., On the definition and the computation of the basic reproduction ratio r0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28:4 (1990), 365–382, 10.1007/BF00178324.
Roelfs, A.P., Singh, R.P., Saari, E.E., Rust diseases of wheat: Concepts and methods of disease management. 1992, CIMMYT, Mexico, D.F, Mexico.
Hovmøer, M.S., Sørensen, C.K., Walter, S., Justesen, A.F., Diversity of puccinia striiformis on cereals and grasses. Annu. Rev. Phytopathol. 49:1 (2011), 197–217, 10.1146/annurev-phyto-072910-095230.
EL Jarroudi, M., Kouadio, L., Beyer, M., Junk, J., Hoffmann, L., Tychon, B., Maraite, H., Bock, C.H., Delfosse, P., Economics of a decision-support system for managing the main fungal diseases of winter wheat in the grand-duchy of luxembourg. Field Crops Res. 172 (2015), 32–41, 10.1016/j.fcr.2014.11.012.
Oerke, E.-C., Dehne, H.-W., Global crop production and the efficacy of crop protection - current situation and future trends. Eur. J. Plant Pathol. 103:3 (1997), 203–215, 10.1023/A:1008602111248.
sache, I., Short-distance dispersal of wheat rust spores by wind and rain. Agronomie 20 (2000), 757–767.
Aylor, D.E., Spread of plant disease on a continental scale: role of aerial dispersal of pathogens. Ecology 84:8 (2003), 1989–1997, 10.1890/01-0619.
Line, R.F., Stripe rust of wheat and barley in north america: a retrospective historical review. Annu. Rev. Phytopathol. 40:1 (2002), 75–118, 10.1146/annurev.phyto.40.020102.111645.
El Jarroudi, M., Kouadio, L., Delfosse, P., Tychon, B., Brown rust disease control in winter wheat: i. exploring an approach for disease progression based on night weather conditions. Environ. Sci. Pollut. Res. 21:7 (2014), 4797–4808, 10.1007/s11356-013-2463-6.
El Jarroudi, M., Kouadio, L., Bock, C.H., El Jarroudi, M., Junk, J., Pasquali, M., Maraite, H., Delfosse, P., A threshold-based weather model for predicting stripe rust infection in winter wheat. Plant Dis. 101 (2017), 693–703, 10.1094/PDIS-12-16-1766-RE.
Mehta, Y., Zadoks, J., Uredospore production and sporulation period of pucciniarecondita f.sp. triticina on primary leaves of wheat. Netherlands J. Plant Pathol. 76 (1970), 267–276.
Eversmeyer, M.G., Kramer, C.L., Hassan, Z.M., Environmental influences on the establishment of puccinia recondita infection structures. Plant Dis. 72 (1988), 409–412, 10.1094/PD-72-0409.
Eversmeyer, M.G., Kramer, C.L., Epidemiology of wheat leaf and stem rust in the central great plains of the usa. Annu. Rev. Phytopathol. 38:1 (2000), 491–513, 10.1146/annurev.phyto.38.1.491.
Stockmarr, A., Andreasen, V., Østergård, H., Dispersal distances for airborne spores based on deposition rates and stochastic modeling. Phytopathology 97 (2007), 1325–1330, 10.1094/PHYTO-97-10-1325.
van den Bosch, F., Frinking, H.D., Metz, J.A.J., Zadoks, J.C., Focus expansion in plant disease. iii: two experimental examples. Phytopathology 78 (1988), 919–925, 10.1094/Phyto-78-919.
Huber, L., Madden, L., Fitt, B., Environmental biophysics applied to the dispersal of fungal spores by rain-splash. Cooke, B.M., Gareth, J.D., Kaye, B., (eds.) The Epidemiology of Plant Diseases, 2006, Springer Netherlands, Dordrecht, Netherlands, 417–444, 10.1007/1-4020-4581-6_16.