Reliable numerical treatment with Adams and BDF methods for plant virus propagation model by vector with impact of time lag and density

Anwar, Nabeela; Naz, Shazia; Shoaib, Mohammed

doi:10.3389/fams.2022.1001392

Cited by 3 publications

(2 citation statements)

References 67 publications

(38 reference statements)

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“…A two-step process called the ADS numerical solver is used to solve an ODE [63,64]. Initially, the predictive stage provides a rough approximation of the target outcome in order to utilize an explicit technique.…”

Section: Adams Methodsmentioning

confidence: 99%

Numerical treatment for mathematical model of farming awareness in crop pest management

Anwar,

Ahmad,

Kiani

et al. 2023

Front. Appl. Math. Stat.

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The most important factor for increasing crop production is pest and pathogen resistance, which has a major impact on global food security. Pest management also emphasizes the need for farming awareness. A high crop yield is ultimately achieved by protecting crops from pests and raising public awareness of the devastation caused by pests. In this research, we aim to investigate the intricate impacts of nonlinear delayed systems for managing crop pest management (CPM) supervised by Ordinary Differential Equations (ODEs). Our focus will be on highlighting the intricate and often unpredictable relationships that occur over time among crops, pests, strategies for rehabilitation, and environmental factors. The nonlinear delayed CPM model incorporated the four compartments: crop biomass density [B(t)], susceptible pest density [S(t)], infected pest density [I(t)], and population awareness level [A(t)]. The approximate solutions for the four compartments B(t), S(t), I(t), and A(t) are determined by the implementation of sundry scenarios generated with the variation in crop biomass growth rate, rate of pest attacks, pest natural death rate, disease associated death rate and memory loss of aware people, by means of exploiting the strength of the Adams (ADS) and explicit Runge-Kutta (ERK) numerical solvers. Comparative analysis of the designed approach is carried out for the dynamic impacts of the nonlinear delayed CPM model in terms of numerical outcomes and simulations based on sundry scenarios.

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Section: Adams Methodsmentioning

confidence: 99%

Numerical treatment for mathematical model of farming awareness in crop pest management

Anwar,

Ahmad,

Kiani

et al. 2023

Front. Appl. Math. Stat.

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“…Epidemic models with an exposed class are very common (for plant virus propagation, see, for example, [30,52]). The advantages of using models with exposed populations are that they are based on ODEs, so they only require the initial condition at the initial time, and, as with all epidemic models based on ODEs, the local asymptotic stability at the beginning of the epidemic can be determined using the next-generation matrix method [53,54].…”

Section: Plant Virus With Vector Transmission Modelsmentioning

confidence: 99%

On Population Models with Delays and Dependence on Past Values

Chen-Charpentier

2024

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The current values of many populations depend on the past values of the population. In many cases, this dependence is caused by the time certain processes take. This dependence on the past can be introduced into mathematical models by adding delays. For example, the growth rate of a population depends on the population τ time units ago, where τ is the maturation time. For an epidemic, there is a time τ between the contact of an infected individual and a susceptible one, and the time the susceptible individual actually becomes infected. This time τ is also a delay. So, the number of infected individuals depends on the population at the time τ units ago. A second way of introducing this dependence on past values is to use non-local operators in the description of the model. Fractional derivatives have commonly been used to provide non-local effects. In population growth models, it can also be done by introducing a new compartment, the immature population, and in epidemic models, by introducing an additional exposed population. In this paper, we study and compare these methods of adding dependence on past values. For models of processes that involve delays, all three methods include dependence on past values, but fractional-order models do not justify the form of the dependence. Simulations show that for the models studied, the fractional differential equation method produces similar results to those obtained by explicitly incorporating the delay, but only for specific values of the fractional derivative order, which is an extra parameter. But in all three methods, the results are improved compared to using ordinary differential equations.

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A Review on Understanding the Impact of Pesticides Towards Greener Harvests Using Mathematical Modelling

Tripathi,

Kumar,

Dipesh

2024

Advances in Bioinformatics and Biomedical Engineering

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Protecting our environment and ensuring the safety of our food supply stand as paramount concerns in today's world. Pesticides have become a global solution for managing pests and diseases in agriculture. Employing sophisticated mathematical modeling techniques allows for a comprehensive examination of their adverse effects. Pesticides have the ability to kill plants and damage soil, potentially leading to a fall in both plant numbers and soil quality. The use of delay differential equations is important in capturing the long-term effects of pesticides on plants and soil health. These equations model the various impacts of altering pesticide dosages and application rates on plants and soil, exposing crucial elements determining pesticide use's environmental implications. MATLAB also provides a graphical model of this complicated system, providing a visual understanding of the complex interaction between pesticides and ecological processes.

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Reliable numerical treatment with Adams and BDF methods for plant virus propagation model by vector with impact of time lag and density

Cited by 3 publications

References 67 publications

Numerical treatment for mathematical model of farming awareness in crop pest management

Numerical treatment for mathematical model of farming awareness in crop pest management

On Population Models with Delays and Dependence on Past Values

A Review on Understanding the Impact of Pesticides Towards Greener Harvests Using Mathematical Modelling

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