Rich Sliding Motion and Dynamics in a Filippov Plant-Disease System

2018 ◽  
Vol 28 (01) ◽  
pp. 1850012 ◽  
Author(s):  
Can Chen ◽  
Xi Chen
Keyword(s):  
Disease Transmission ◽  
Plant Disease ◽  
Sliding Mode ◽  
Control Strategies ◽  
Disease Model ◽  
Threshold Value ◽  
Plant Diseases ◽  
Positive Equilibrium ◽  
Threshold Values ◽  
Periodic Trajectories

In order to reduce the spread of plant diseases and maintain the number of infected trees below an economic threshold, we choose the number of infected trees and the number of susceptible plants as the control indexes on whether to implement control strategies. Then a Filippov plant-disease model incorporating cutting off infected branches and replanting susceptible trees is proposed. Based on the theory of Filippov system, the sliding mode dynamics and conditions for the existence of all the possible equilibria and Lotka–Volterra cycles are presented. We find that model solutions ultimately approach the positive equilibrium that lies in the region above the infected threshold value [Formula: see text], or the periodic trajectories that lie in the region below [Formula: see text], or the pseudo-attractor [Formula: see text], as we vary the susceptible and infected threshold values. It indicates that the plant-disease transmission is tolerable if the trajectories approach [Formula: see text] or the periodic trajectories lie in the region below [Formula: see text]. Hence an acceptable level of the number of infected trees can be achieved when the susceptible and infected threshold values are chosen appropriately.

scholarly journals Dynamical Analysis of Delayed Plant Disease Models with Continuous or Impulsive Cultural Control Strategies

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Tongqian Zhang ◽  
Xinzhu Meng ◽  
Yi Song ◽  
Zhenqing Li
Keyword(s):  
Control Strategy ◽  
Plant Disease ◽  
Control Strategies ◽  
Disease Model ◽  
Infected Plant ◽  
Transcendental Equation ◽  
Cultural Control ◽  
Dynamical Analysis ◽  
Positive Equilibrium ◽  
Disease Free

Delayed plant disease mathematical models including continuous cultural control strategy and impulsive cultural control strategy are presented and investigated. Firstly, we consider continuous cultural control strategy in which continuous replanting of healthy plants is taken. The existence and local stability of disease-free equilibrium and positive equilibrium are studied by analyzing the associated characteristic transcendental equation. And then, plant disease model with impulsive replanting of healthy plants is also considered; the sufficient condition under which the infected plant-free periodic solution is globally attritive is obtained. Moreover, permanence of the system is studied. Some numerical simulations are also given to illustrate our results.

scholarly journals Modelling interference between vectors of non-persistently transmitted plant viruses to identify effective control strategies

2021 ◽  
Vol 17 (12) ◽  
pp. e1009727
Author(s):  
Marta Zaffaroni ◽  
Loup Rimbaud ◽  
Ludovic Mailleret ◽  
Nik J. Cunniffe ◽  
Daniele Bevacqua
Keyword(s):  
Disease Transmission ◽  
Plant Disease ◽  
Control Strategies ◽  
Management Strategies ◽  
Plant Viruses ◽  
Effective Control ◽  
Agronomic Practices ◽  
Ecological Principles ◽  
Single Host ◽  
Primary Vector

Aphids are the primary vector of plant viruses. Transient aphids, which probe several plants per day, are considered to be the principal vectors of non-persistently transmitted (NPT) viruses. However, resident aphids, which can complete their life cycle on a single host and are affected by agronomic practices, can transmit NPT viruses as well. Moreover, they can interfere both directly and indirectly with transient aphids, eventually shaping plant disease dynamics. By mean of an epidemiological model, originally accounting for ecological principles and agronomic practices, we explore the consequences of fertilization and irrigation, pesticide deployment and roguing of infected plants on the spread of viral diseases in crops. Our results indicate that the spread of NPT viruses can be i) both reduced or increased by fertilization and irrigation, depending on whether the interference is direct or indirect; ii) counter-intuitively increased by pesticide application and iii) reduced by roguing infected plants. We show that a better understanding of vectors’ interactions would enhance our understanding of disease transmission, supporting the development of disease management strategies.

Global Dynamics and Rich Sliding Motion in an Avian-Only Filippov System in Combating Avian Influenza

2020 ◽  
Vol 30 (01) ◽  
pp. 2050008
Author(s):  
Youping Yang ◽  
Lingjun Wang
Keyword(s):  
Avian Influenza ◽  
Sliding Mode ◽  
Dynamical Behavior ◽  
Threshold Level ◽  
Type Model ◽  
Positive Equilibrium ◽  
Global Dynamics ◽  
Threshold Values ◽  
Threshold Policy ◽  
Existence And Stability

Culling birds has always been an effective method to control the spread of avian influenza. Here, we introduce a Filippov avian-only model with culling of both susceptible and infected birds. The Filippov-type model is formulated by considering that no control strategy is taken if the number of infected birds is less than an infected threshold level [Formula: see text]; further, we cull infected birds once the number of infected birds exceeds [Formula: see text]; meanwhile, we cull susceptible birds if the number of susceptible birds exceeds a susceptible threshold level [Formula: see text]. The global dynamical behavior of the Filippov system, including the existence and stability of various types of equilibria, the existence of the sliding mode and its dynamics, together with bifurcation analyses with regard to local sliding bifurcations, is investigated. It is shown that model solutions ultimately converge to the positive equilibrium that lies in the region above [Formula: see text], or below [Formula: see text], or on [Formula: see text], as we vary the susceptible and infected threshold values [Formula: see text] and [Formula: see text]. Our results indicate that proper combinations of the susceptible and infected threshold values based on the threshold policy can maintain the number of infected birds either below a certain threshold level or at a previously given level.

scholarly journals Stability and Sensitivity Analysis of a Plant Disease Model with Continuous Cultural Control Strategy

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Zhang Zhonghua ◽  
Suo Yaohong
Keyword(s):  
Sensitivity Analysis ◽  
Time Delay ◽  
Control Strategy ◽  
Plant Disease ◽  
Disease Model ◽  
Cultural Control ◽  
Positive Equilibrium ◽  
Normal Form Theory ◽  
Center Manifold Reduction ◽  
Disease Free

In this paper, a plant disease model with continuous cultural control strategy and time delay is formulated. Then, how the time delay affects the overall disease progression and, mathematically, how the delay affects the dynamics of the model are investigated. By analyzing the transendental characteristic equation, stability conditions related to the time delay are derived for the disease-free equilibrium. Specially, whenR0=1, the Jacobi matrix of the model at the disease-free equilibrium always has a simple zero eigenvalue for allτ≥0. The center manifold reduction and the normal form theory are used to discuss the stability and the steady-state bifurcations of the model near the nonhyperbolic disease-free equilibrium. Then, the sensitivity analysis of the threshold parameterR0and the positive equilibriumE*is carried out in order to determine the relative importance of different factors responsible for disease transmission. Finally, numerical simulations are employed to support the qualitative results.

scholarly journals Global asymptotic stability of a delayed plant disease model

2020 ◽  
Vol 1 (1) ◽  
pp. 27-38
Author(s):  
Yuming Chen ◽  
Chongwu Zheng
Keyword(s):  
Plant Disease ◽  
Disease Model ◽  
Plant Diseases ◽  
Threshold Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Sigma 1 ◽  
T Tau ◽  
Theoretical Results ◽  
Disease Free

In this paper, we consider the following system of delayed differentialequations,\[\left\{\begin {array}{rcl}\frac {dS(t)}{dt} & = & \sigma \phi-\beta S(t)I(t-\tau)-\eta S(t),\\\frac {dI(t)}{dt} & = & \sigma(1-\phi)+\betaS(t)I(t-\tau)-(\eta+\omega)I(t),\end {array}\right.\]which can be used to model plant diseases. Here $\phi\in (0,1]$,$\tau\ge 0$, and all other parameters are positive. The case where $\phi=1$ is well studiedand there is a threshold dynamics. Thesystem always has a disease-free equilibrium, which is globallyasymptotically stable if the basic reproduction number $R_0\triangleq\frac{\beta\sigma}{\eta(\eta+\omega)}\le 1$ and is unstable if$R_0>1$; when $R_0>1$, the system also has a unique endemic equilibrium,which is globally asymptotically stable. In this paper, we study thecase where $\phi\in (0,1)$. It turns out that the system only has anendemic equilibrium, which is globally asymptotically stable. Thelocal stability is established by the linearizationmethod while the global attractivity is obtained by the Lyapunovfunctional approach. The theoretical results are illustrated withnumerical simulations.

scholarly journals Dynamics of a delayed plant disease model with Beddington-DeAngelis disease transmission

2021 ◽  
Vol 18 (1) ◽  
pp. 583-599
Author(s):  
Fahad Al Basir ◽  
◽  
Yasuhiro Takeuchi ◽  
Santanu Ray ◽  
◽  
...  
Keyword(s):  
Disease Transmission ◽  
Plant Disease ◽  
Disease Model

Dynamics of a prey predator disease model with Holling type functional response and stochastic perturbation

2020 ◽  
pp. 471-488
Author(s):  
M. N. Srinivas ◽  
G. Basava Kumar ◽  
V. Madhusudanan
Keyword(s):  
Equilibrium Point ◽  
Disease Model ◽  
Stochastic Perturbation ◽  
Positive Equilibrium ◽  
Type Ii ◽  
Asymptotically Stable ◽  
Unique Positive Solution ◽  
Stochastic Nature ◽  
Research Article ◽  
Positive Equilibrium Point

The present research article constitutes Holling type II and IV diseased prey predator ecosystem and classified into two categories namely susceptible and infected predators.We show that the system has a unique positive solution. The deterministic and stochastic nature of the dynamics of the system is investigated. We check the existence of all possible steady states with local stability. By using Routh-Hurwitz criterion we showed that the positive equilibrium point $E_{7}$ is locally asymptotically stable if $x^{*} > \sqrt{m_{1}}$ .Moreover condition of the global stability of positive equilibrium point $E_{7}$ are also entrenched with help of Lyupunov theorem. Some Numerical simulations are carried out to illustrate our analytical findings.

scholarly journals Estimating asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan: a mathematical modeling study

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Xi Huo ◽  
Jing Chen ◽  
Shigui Ruan
Keyword(s):  
Disease Transmission ◽  
Large Scale ◽  
Transmission Rate ◽  
Control Strategies ◽  
Herd Immunity ◽  
Antibody Prevalence ◽  
Screening Process ◽  
Vaccination Programs ◽  
Prevalence Level ◽  
The Impact

Abstract Background The COVID-19 outbreak in Wuhan started in December 2019 and was under control by the end of March 2020 with a total of 50,006 confirmed cases by the implementation of a series of nonpharmaceutical interventions (NPIs) including unprecedented lockdown of the city. This study analyzes the complete outbreak data from Wuhan, assesses the impact of these public health interventions, and estimates the asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan. Methods By taking different stages of the outbreak into account, we developed a time-dependent compartmental model to describe the dynamics of disease transmission and case detection and reporting. Model coefficients were parameterized by using the reported cases and following key events and escalated control strategies. Then the model was used to calibrate the complete outbreak data by using the Monte Carlo Markov Chain (MCMC) method. Finally we used the model to estimate asymptomatic and undetected cases and approximate the overall antibody prevalence level. Results We found that the transmission rate between Jan 24 and Feb 1, 2020, was twice as large as that before the lockdown on Jan 23 and 67.6% (95% CI [0.584,0.759]) of detectable infections occurred during this period. Based on the reported estimates that around 20% of infections were asymptomatic and their transmission ability was about 70% of symptomatic ones, we estimated that there were about 14,448 asymptomatic and undetected cases (95% CI [12,364,23,254]), which yields an estimate of a total of 64,454 infected cases (95% CI [62,370,73,260]), and the overall antibody prevalence level in the population of Wuhan was 0.745% (95% CI [0.693%,0.814%]) by March 31, 2020. Conclusions We conclude that the control of the COVID-19 outbreak in Wuhan was achieved via the enforcement of a combination of multiple NPIs: the lockdown on Jan 23, the stay-at-home order on Feb 2, the massive isolation of all symptomatic individuals via newly constructed special shelter hospitals on Feb 6, and the large scale screening process on Feb 18. Our results indicate that the population in Wuhan is far away from establishing herd immunity and provide insights for other affected countries and regions in designing control strategies and planing vaccination programs.

scholarly journals Microbial antagonists against plant pathogens in Iran: A review

2020 ◽  
Vol 5 (1) ◽  
pp. 404-440 ◽  
Author(s):  
Mehrdad Alizadeh ◽  
Yalda Vasebi ◽  
Naser Safaie
Keyword(s):  
Biological Control ◽  
Chemical Control ◽  
Plant Disease ◽  
Plant Pathogens ◽  
Plant Diseases ◽  
Agricultural Products ◽  
Control Measures ◽  
Wide Range ◽  
Plant Disease Management ◽  
Published Research

AbstractThe purpose of this article was to give a comprehensive review of the published research works on biological control of different fungal, bacterial, and nematode plant diseases in Iran from 1992 to 2018. Plant pathogens cause economical loss in many agricultural products in Iran. In an attempt to prevent these serious losses, chemical control measures have usually been applied to reduce diseases in farms, gardens, and greenhouses. In recent decades, using the biological control against plant diseases has been considered as a beneficial and alternative method to chemical control due to its potential in integrated plant disease management as well as the increasing yield in an eco-friendly manner. Based on the reported studies, various species of Trichoderma, Pseudomonas, and Bacillus were the most common biocontrol agents with the ability to control the wide range of plant pathogens in Iran from lab to the greenhouse and field conditions.

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