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 ◽  
◽  
...  
2018 ◽  
Vol 28 (01) ◽  
pp. 1850012 ◽  
Author(s):  
Can Chen ◽  
Xi Chen

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.


2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Tongqian Zhang ◽  
Xinzhu Meng ◽  
Yi Song ◽  
Zhenqing Li

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.


Author(s):  
Wencai Zhao ◽  
Juan Li ◽  
Tongqian Zhang ◽  
Xinzhu Meng ◽  
Tonghua Zhang
Keyword(s):  

The development of vector-transmitted disease models and their application to field studies is reviewed. The key concepts of the basic rate of reproduction and disease transmission threshold are explained, and their application to disease control briefly illustrated. The complications involved in producing appropriate models are discussed for the case of the trypanosomatid parasites Leishmania and Trypanosoma that frequently have more than one vertebrate host and are often fatal in the human host. A two-species, vector-borne disease model allows a quantification of the role of animal reservoirs in maintaining human diseases. Human prevalence may be determined more by the parasitological characteristics of wild reservoir species, about which little is generally known, than by any other single feature of the complex interaction between parasites, vectors and hosts. Domestic animals are often ideal reservoirs, maintaining large numbers of vectors and considerably enlarging the parasite pool. When vector-transmitted diseases are fatal to the human host, human and vector dynamics interact in ways which may cause epidemic cycles, low-level endemic equilibria or disease extinction. For both leishmaniasis and trypanosomiasis it is suggested that a very small number of chronic human cases can maintain the disease in the human population over long periods of time between epidemic outbreaks. They may also be important in the maintenance of geographically distinct foci, characteristic of human trypanosomiasis in Africa. Finally there is a plea to establish a tradition of field observation leading to, and being directed by, mathematical models which in turn are modified as the observations accumulate. All too often, one-way traffic between the two results in slow, or misguided, progress.


2018 ◽  
Author(s):  
Joseph R. Mihaljevic ◽  
Carlos M. Polivka ◽  
Constance J. Mehmel ◽  
Chentong Li ◽  
Vanja Dukic ◽  
...  

AbstractA key assumption of models of infectious disease is that population-scale spread is driven by transmission between host individuals at small scales. This assumption, however, is rarely tested, likely because observing disease transmission between host individuals is non-trivial in many infectious diseases. Quantifying the transmission of insect baculoviruses at a small scale is in contrast straightforward. We fit a disease model to data from baculovirus epizootics (= epidemics in animals) at the scale of whole forests, while using prior parameter distributions constructed from branch-scale experiments. Our experimentally-constrained model fits the large-scale data very well, supporting the role of small-scale transmission mechanisms in baculovirus epizootics. We further compared our experimentally-based model to an unconstrained model that ignores our experimental data, serving as a proxy for models that include large-scale mechanisms. This analysis supports our hypothesis that small-scale mechanisms are important, especially individual variability in host susceptibility to the virus. Comparison of transmission rates in the two models, however, suggests that large-scale mechanisms increase transmission compared to our experimental estimates. Our study shows that small-scale and large-scale mechanisms drive forest-wide epizootics of baculoviruses, and that synthesizing mathematical models with data collected across scales is key to understanding the spread of infectious disease.


2020 ◽  
Vol 62 (3) ◽  
pp. 65-83
Author(s):  
Kamaleldin Abodayeh ◽  
Ali Raza ◽  
Muhammad Shoaib Arif ◽  
Muhammad Rafiq ◽  
Mairaj Bibi ◽  
...  

2017 ◽  
Vol 10 (06) ◽  
pp. 1750088
Author(s):  
Shujing Gao ◽  
Lijun Xia ◽  
Jialin Wang ◽  
Zujin Zhang

Cross-protection in plants has been widely used to control losses caused by virus diseases in the world. Here, a non-autonomous plant-virus disease model was developed including cross-protection. Global dynamics of the model was discussed. Under the quite weak assumptions, integral form conditions were resolved for permanence of the system and extinction of diseases. Furthermore, we looked into the sufficient conditions that plants could be protected against the detrimental effects of infection by an infection with the mild virus isolates. Last, we performed numerical simulations. Our investigations suggested that cross-protection played an important role in controlling the spread of the challenging virus in plants.


2019 ◽  
Vol 13 (sup1) ◽  
pp. 325-353 ◽  
Author(s):  
V. A. Bokil ◽  
L. J. S. Allen ◽  
M. J. Jeger ◽  
S. Lenhart

2021 ◽  
Vol 17 (12) ◽  
pp. e1009727
Author(s):  
Marta Zaffaroni ◽  
Loup Rimbaud ◽  
Ludovic Mailleret ◽  
Nik J. Cunniffe ◽  
Daniele Bevacqua

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.


Sign in / Sign up

Export Citation Format

Share Document