Stability Analysis of a Plant Pathogen Evolution Model
Narawitch Lertngim1, Usa Humphries2, Frank van den Bosch3
1Narawitch Lertngim, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand.
2Usa Humphries, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand.
3Frank van den Bosch, Department of Environment & Agriculture, Centre for Crop and Disease Management, Curtin University, Bentley, Perth, Australia.
Manuscript received on 18 June 2019 | Revised Manuscript received on 25 June 2019 | Manuscript Published on 19 June 2019 | PP: 251-254 | Volume-8 Issue-8S June 2019 | Retrieval Number: H10410688S19/19©BEIESP
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Stacking of multiple resistance genes in crop cultivars, pyramiding, is an effective way to control plant diseases. However, due to the evolution of the pathogen, resistance cultivar can be overcome. Breeders develop pyramids with more resistance genes to improve the durability of resistance. Since it is difficult to do field experiments on the evolution of the pathogen, mathematical models become an important tool to study the behavior of evolution of plant pathogen through stability analysis. A model for the evolution of pathogen is developed towards virulence against cultivar resistance genes. The aims of this research are to analyze the stability of the steady states of the model. The results from the analysis show that only the equilibrium point (0,0,0,1) was stable while the others were unstable. This stable equilibrium point is characterized by the strain virulent to both resistance genes. The other pathogen strains disappear from the population. Inthe future, the model can be used to determine the breeding strategic for plants which can delay the evolution of pathogen and prolong durability of pyramided plant.
Keywords: Evolution Model, Stability Analysis, Stacking of Multiple, Mathematical Models.
Scope of the Article: Analysis of Algorithms and Computational Complexity