Stability and bifurcation in plant-pathogens interactions

被引：11

作者：

Buonomo, Bruno ^{[1
]}

Cerasuolo, Marianna ^{[2
]}

机构：

[1] Univ Naples Federico II, Dept Math & Applicat, I-80126 Naples, Italy

[2] Rothamsted Res, Sustainable Soils & Grassland Syst, Harpenden ALS 2JQ, Herts, England

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 232卷

关键词：

Plant pathogen interaction; Mathematical model; Bifurcation; Global stability; GLOBAL-STABILITY; BACKWARD BIFURCATION; POPULATION-DYNAMICS; THRESHOLD CRITERIA; EPIDEMIC MODELS; VACCINATION; INFECTION; TUBERCULOSIS; STAGE;

D O I：

10.1016/j.amc.2014.01.127

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a plant-pathogen interaction model and perform a bifurcation analysis at the threshold where the pathogen-free equilibrium loses its hyperbolicity. We show that a stimulatory-inhibitory host response to infection load may be responsible for the occurrence of multiple steady states via backward bifurcations. We also find sufficient conditions for the global stability of the pathogen-present equilibrium in case of null or linear inhibitory host response. The results are discussed in the framework of the recent literature on the subject. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：858 / 871

页数：14

共 43 条

[1]

ANDERSON R M, 1991

[2] Backward Bifurcation and Optimal Control in Transmission Dynamics of West Nile Virus [J].

Blayneh, Kbenesh W. ;

Gumel, Abba B. ;

Lenhart, Suzanne ;

Clayton, Tim .

BULLETIN OF MATHEMATICAL BIOLOGY, 2010, 72 (04) :1006-1028

[3]

BRASSETT PR, 1988, Z PFLANZENK PFLANZEN, V95, P352

[4] Backward bifurcations in simple vaccination models [J].

Brauer, F .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 298 (02) :418-431

[5] On the backward bifurcation of a vaccination model with nonlinear incidence [J].

Buonomo, B. ;

Lacitignola, D. .

NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2011, 16 (01) :30-46

[6]

Buonomo B, 2013, Modeling the interplay between human behavior and the spread of infectious diseases, P289

[7] Global stability of an SIR epidemic model with information dependent vaccination [J].

Buonomo, Bruno ;

d'Onofrio, Alberto ;

Lacitignola, Deborah .

MATHEMATICAL BIOSCIENCES, 2008, 216 (01) :9-16

[8] Global stability for an HIV-1 infection model including an eclipse stage of infected cells [J].

Buonomo, Bruno ;

Vargas-De-Leon, Cruz .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 385 (02) :709-720

[9]

Buonomo Bruno, 2010, Journal of Biological Dynamics, V4, P571, DOI 10.1080/17513750903518441

[10] On the dynamics of an SEIR epidemic model with a convex incidence rate [J].

Buonomo B. ;

Lacitignola D. .

Ricerche di Matematica, 2008, 57 (2) :261-281

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