Role of farming awareness in crop pest management - A mathematical model

A mathematical model of invasion and control of coconut rhinoceros beetle Oryctes rhinoceros (L.) in Guam

The coconut rhinoceros beetle (CRB), is one of the most damaging pests to coconut palms causing severe economic harm. Its expansion from Asia to the Pacific in the early 20th century has been stopped by virus control. However, a new haplotype CRB-Guam has recently escaped this control and invaded Guam, other Pacific islands, and has even established itself in the Western Hemisphere. In this paper, we present a compartmental ODE model of CRB population and control. We carefully consider CRB life stages and its interplay with coconut palms as well as "the green waste", the organic matters used by CRB for breeding sites. We calibrate and validate the model based on data count of CRBs trapped in Guam between 2008 and 2014. We derive the basic reproduction number determining the CRB population growth without any control measures. We also identify control levels required to eliminate CRBs. We show that, in the absence of viable virus control, the sanitation, i.e., the removal of the green waste is the most efficient way to control the population. Our model predicts that the sanitation efforts need to roughly double from the current levels to eliminate CRB from Guam. Furthermore, we demonstrate that a rare event like Typhoon Dolphin that hit Guam in 2015 can lead to a quick rise of the CRB population.

A prey–predator model approach to increase the production of crops: Mathematical modeling and qualitative analysis

This paper expresses the concepts, methods, and applications of mathematical models in agriculture. We propose and analyze an ecosystem consisting of two types of preys and their predators; here the prey-I like sugarcane crops that take a long time to grow and prey-II like vegetables, which have a short life, are grown with sugarcane crops and predators that harm both prey-I and prey-II. The various equilibria of the system are obtained, and the stability conditions are analyzed. Furthermore, a comprehensive analysis of the optimal control strategy is also performed. The optimal control model includes the use of three control variables, such as pesticide application rate, biomass application rate, and control of Cassava mosaic virus in the system. Finally, we apply Pontryagin’s maximum principle to find the optimal control. Furthermore, analytical results are verified by numerical simulations.

Modelling the effect of desert locust infestation on crop production with intervention measures

The Desert Locust, Schistocerca gregaria(Forskål), is the most devastating migratory pest in the world. The Desert Locust persists as the principal threat to food security in the infested region and beyond. In the inadequacy of reliable and efficient prevention and control measures, strategies for controlling and mitigating the trouble of the Desert Locust are focused on non-risk-free interventions such as chemical pesticides. We formulated and analyzed a mathematical model to assess the impact of this devastating pest on crop production. The theoretical analysis of the model shows that the trivial and locust free equilibriums are unstable, whereas interior equilibrium is asymptotically stable if crop growth rate r is greater than a maturity rate σ Numerical simulations of the model using the baseline parametric values are consistent with theoretical analysis. The conventional scenario projections for crop production (based on the baseline levels of anti-Desert Locust interventions considered in the study) increase by 70.44%(2663.26)kg per hectare) if the low depletion pesticide measures performed are maintained proportionally with locust population. This study notes that high-level depletion of the chemical pesticide spray measures could lead to devastating crop losses (similar to those projections before the onset of the pesticide spray) and severe human health and environmental risks. At a baseline harvesting coverage could shelter 44.43kg to 1176.82kg per hectare of mature crops. Combining early harvesting and low depletion chemical pesticide with ultra-low volume (ULV) spray devices and formulation could mitigate and eliminate Desert Locust infestation.

Farming awareness based optimum interventions for crop pest control

We develop a mathematical model, based on a system of ordinary differential equations, to the upshot of farming alertness in crop pest administration, bearing in mind plant biomass, pest, and level of control. Main qualitative analysis of the proposed mathematical model, akin to both pest-free and coexistence equilibrium points and stability analysis, is investigated. We show that all solutions of the model are positive and bounded with initial conditions in a certain significant set. The local stability of pest-free and coexistence equilibria is shown using the Routh-Hurwitz criterion. Moreover, we prove that when a threshold value is less than one, then the pest-free equilibrium is locally asymptotically stable. To get optimum interventions for crop pests, that is, to decrease the number of pests in the crop field, we apply optimal control theory and find the corresponding optimal controls. We establish existence of optimal controls and characterize them using Pontryagin's minimum principle. Finally, we make use of numerical simulations to illustrate the theoretical analysis of the proposed model, with and without control measures.

A Review on Prediction Models for Pesticide Use, Transmission, and Its Impacts

The lure of increased productivity and crop yield has caused the imprudent use of pesticides in great quantity that has unfavorably affected environmental health. Pesticides are chemicals intended for avoiding, eliminating, and mitigating any pests that affect the crop. Lack of awareness, improper management, and negligent disposal of pesticide containers have led to the permeation of pesticide residues into the food chain and other environmental pathways, leading to environmental degradation. Sufficient steps must be undertaken at various levels to monitor and ensure judicious use of pesticides. Development of prediction models for optimum use of pesticides, pesticide management, and their impact would be of great help in monitoring and controlling the ill effects of excessive use of pesticides. This paper aims to present an exhaustive review of the prediction models developed and modeling strategies used to optimize the use of pesticides.

A multi-delay model for pest control with awareness induced interventions — Hopf bifurcation and optimal control analysis

Farming awareness is an important measure for pest controlling in agricultural practice. Time delay in controlling pest may affect the system. Time delay occurs in organizing awareness campaigns, also time delay may takes place in becoming aware of the control strategies or implementing suitable controlling methods informed through social media. Thus we have derived a mathematical model incorporating two time delays into the system and Holling type-II functional response. The existence and the stability criteria of the equilibria are obtained in terms of the basic reproduction number and time delays. Stability changes occur through Hopf-bifurcation when time delays cross the critical values. Optimal control theory has been applied for cost-effectiveness of the delayed system. Numerical simulations are carried out to justify the analytical results. This study shows that optimal farming awareness through radio, TV etc. can control the delay induced bifurcation in a cost-effective way.