Browsing by Author "Navnit Jha"

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Analyzing crop production: Unraveling the impact of pests and pesticides through a fractional model
(Vilnius University Press, 2024) Navnit Jha; Akash Yadav; Ritesh Pandey; A.K. Misra
The continuous growth of the human population raises concerns about food, fiber, and agricultural insecurity. Meeting the escalating demand for agricultural products due to this population surge makes protecting crops from pests becomes imperative. While farmers use chemical pesticides as crop protectors, the extensive use of these chemicals adversely affects both human health and the environment. In this research work, we formulate a nonlinear mathematical model using the Caputo fractional (CF) operator to investigate the effects of pesticides on crop yield dynamics. We assume that pesticides are sprayed proportional to the density of pest density and pests not entirely reliant on crops. The feasibility of every possible nonnegative equilibrium and its stability characteristics are explored utilizing the stability theory of fractional differential equations. Our model analysis reveals that in a continuous spray approach, the roles of pesticide abatement rate and pesticide uptake rate can be interchanged. Furthermore, we have identified the optimal time profile for pesticide spraying rate. This profile proves effective in minimizing both the pest population and the associated costs. To provide a practical illustration of our analytical findings and to showcase the impact of key parameters on the system’s dynamics, we conducted numerical simulations. These simulations are conducted employing the generalized Adams– Bashforth–Moulton method, which allowed us to vividly demonstrate the real-world implications of our research. © 2024 The Author(s).
Modeling the effects of insecticides and external efforts on crop production
(Vilnius University Press, 2021) A.K. Misra; Rahul Patel; Navnit Jha
In this paper a nonlinear mathematical model is proposed and analyzed to understand the effects of insects, insecticides and external efforts on the agricultural crop productions. In the modeling process, we have assumed that crops grow logistically and decrease due to insects, which are wholly dependent on crops. Insecticides and external efforts are applied to control the insect population and enhance the crop production, respectively. The external efforts affect the intrinsic growth rate and carrying capacity of crop production. The feasibility of equilibria and their stability properties are discussed. We have identified the key parameters for the formulation of effective control strategies necessary to combat the insect population and increase the crop production using the approach of global sensitivity analysis. Numerical simulation is performed, which supports the analytical findings. It is shown that periodic oscillations arise through Hopf bifurcation as spraying rate of insecticides decreases. Our findings suggest that to gain the desired crop production, the rate of spraying and the quality of insecticides with proper use of external efforts are much important. © 2021 Authors. Published by Vilnius University Press.
Modeling the effects of insects and insecticides on agricultural crops with NSFD method
(Springer, 2020) A.K. Misra; Navnit Jha; Rahul Patel
Worldwide, agricultural crops are vulnerable to insects. During the crop season, insects target plants especially leaves for food and thus harm the agricultural crops. This reduces agricultural production and therefore effects the economy of farmers. To overcome this problem, nowadays farmers spray insecticides on crops to reduce the density of insects. In this paper, a nonlinear mathematical model is formulated to assess the impacts of insecticides on insects and crop production. In the modeling process, it is presumed that the agricultural crops grow logistically and the growth rate of the insect population wholly depends on the agricultural crops. As the excess use of insecticides on crops is harmful to agricultural farms and human health, therefore we have made an assumption that the spray rate of insecticides to kill insects is proportional to the density of insects. The feasibility of all the possible equilibria is shown and their stability properties are discussed. Keeping in mind the nonlinearity of the formulated model and different time scales of the participating variables, we have constructed a non-standard finite difference scheme by discretizing the system. It is shown that the proposed numerical scheme is convergent with second-order accuracy. Numerical simulation by using our computational scheme has been also presented to support the analytical findings. Using the approach of global sensitivity analysis, we have identified the key parameters for the formulation of effective control strategies necessary to combat the insect population and increase the crop production. Our findings suggest that to gain the desired crop production, the rate of spraying and the quality of insecticides are much important. © 2020, Korean Society for Informatics and Computational Applied Mathematics.
Modeling the Effects of Insects and Insecticides with External Efforts on Agricultural Crops
(Springer, 2024) A.K. Misra; Navnit Jha; Rahul Patel
In this paper, we propose a continuous dynamical model along with its discretized system to increase the agricultural crop production using some external efforts in presence of insects and insecticides. It is assumed that agricultural crops grow logistically and its growth deplete due to insect population, which is wholly dependent on crops. Farmers use insecticides to kill insects to protect the crop and its excessive use is hazardous to human health and therefore it is assumed that insecticides are used proportional to the density of insects. To increase field’s growth potential, we presumed that some efforts (e.g. seed selection, use of fertilizers, proper water drainage, etc.) are applied proportional to the difference between carrying capacity and actual production. The quantitative features of the nonlinear crop production model is examined by a coherent non-standard finite difference scheme (NSFDS) in the absence of theoretical solution values. This scheme is formulated by discretizing the model system and renormalizing the denominator of derivatives of continuous system. Convergence analysis of the new NSFD scheme is described in detail. A graphical layout by computer-assisted numerical results is introduced to observe the effects of external efforts on production of agricultural crops. © 2020, Foundation for Scientific Research and Technological Innovation.
MODELING THE EFFECTS OF PESTS AND PESTICIDE ON CROP YIELDS IN A MULTIPLE CROPPING SYSTEM
(World Scientific, 2024) Akash Yadav; Ritesh Pandey; Navnit Jha; Arvind Kumar Misra
Pest infestation poses a significant threat to agricultural crop yields, and to control it, farmers spray chemical pesticides. The persistent use of these chemical agents not only leads to pesticide residues within crops but also exerts collateral damage on the beneficial pest population. In this research work, we formulate a nonlinear mathematical model to assess the impacts of pesticide on crop yields within a multiple cropping system. Model analysis illustrates that crop consumption rates destabilize, and the spraying rate of pesticide stabilizes the system. Furthermore, we determine conditions for the global stability of the coexisting equilibrium and conduct a global sensitivity analysis to identify model parameters that significantly influence pest population density. Our findings emphasize that, for effective pest population control and enhanced crop yields, farmers should choose either pesticides with a high pest abatement rate or those with a higher pesticide uptake rate. Considering the spraying rate of pesticide as time-dependent, we also suggest an optimal control strategy to minimize the pest population and associated costs. We provide analytical results backed by numerical simulations implemented through the non-standard finite difference scheme to support our findings. © 2024 World Scientific Publishing Company.