Modelling the effects of awareness-based interventions to control the mosaic disease of Jatropha curcas

Plant diseases are responsible for substantial and sometimes devastating economic and societal costs and thus are a major limiting factor for stable and sustainable agricultural production. Diseases of crops are particular crippling in developing countries that are heavily dependent on agriculture for food security and income. Various techniques have been developed to reduce the negative impact of plant diseases and eliminate the associated parasites, but the success of these approaches strongly depends on population awareness and the degree of engagement with disease control and prevention programs. In this paper we derive and analyse a mathematical model of mosaic disease of Jatropha curcas, an important biofuel plant, with particular emphasis on the effects of interventions in the form of nutrients and insecticides, whose use depends on the level of population awareness. Two contributions to disease awareness are considered in the model: global awareness campaigns, and awareness from observing infected plants. All steady states of the model are found, and their stability is analysed in terms of system parameters. We identify parameter regions associated with eradication of disease, stable endemic infection, and periodic oscillations in the level of infection. Analytical results are supported by numerical simulations that illustrate the behaviour of the model in different dynamical regimes. Implications of theoretical results for practical implementation of disease control are discussed

Dynamics of a Double-Impulsive Control Model of Integrated Pest Management Using Perturbation Methods and Floquet Theory

We formulate an integrated pest management model to control natural pests of the crop through the periodic application of biopesticide and chemical pesticides. In a theoretical analysis of the system pest eradication, a periodic solution is found and established. All the system variables are proved to be bounded. Our main goal is then to ensure that pesticides are optimized, in terms of pesticide concentration and pesticide application frequency, and that the optimum combination of pesticides is found to provide the most benefit to the crop. By using Floquet theory and the small amplitude perturbation method, we prove that the pest eradication periodic solution is locally and globally stable. The acquired results establish a threshold time limit for the impulsive release of various controls as well as some valid theoretical conclusions for effective pest management. Furthermore, after a numerical comparison, we conclude that integrated pest management is more effective than single biological or chemical controls. Finally, we illustrate the analytical results through numerical simulations.Comment: This is a preprint of a paper whose final and definite form is published Open Access in 'Axioms' at [https://doi.org/10.3390/axioms12040391

A model analysis to measure the adherence of Etanercept and Fezakinumab therapy for the treatment of psoriasis

This article deals with a immunological model, which includes multiple classes of T cells, namely, the naive T cell, type I, type II and type 17 T helper cells (Th1, Th2, Th17), regulatory T cell (Treg) along with the activated natural killer cells (NK cells) and epidermal keratinocytes. In order to describe the etiology of psoriasis development, we have studied the basic mathematical properties of the model, existence and stability of the interior equilibrium. We have also derived the drug-induced mathematical model using impulse differential equation to determine the effects of combined biologics Etanercept (TNF-α inhibitor) and Fezakinumab (IL-22 monoclonal antibody) therapy considering perfect dosing during the inductive phase. We have determined the required dosing interval of both drugs to maintain the keratinocytes concentration below a threshold level. This study shows that Etanercept alone could theoretically maintain the keratinocytes level, whereas frequent dosing of Fezakinumab alone may not be enough to control the hyper-proliferation of keratinocytes. Furthermore, combination of the drugs with perfect dosing has the noticeable effect on keratinocytes dynamics, which may be suitable therapeutic approaches for treatment of psoriasis

Renewable energy biodiesel: a mathematical approach from ecology to production

Paper presented at the 3rd Strathmore International Mathematics Conference (SIMC 2015), 3 - 7 August 2015, Strathmore University, Nairobi, Kenya.Biodiesel is one of promising renewable energy source and used as an alternative of conventional hydrocarbon fuels. Jatropha curcas plant oil (JCPO) is the most cost effective sources of biodiesel. The plant can be cultivated in wastelands and grows on almost any type of territory, even on sandy and saline soils. Judicious agricultural practices and effective crop management of Jatropha curcas is preliminary requisite to get maximum yield of oil. Production of biodiesel by transesterification of Jatropha oil significantly depends on four reaction parameters viz., reaction time, temperature, oil to alcohol molar ratio and stirrer speed. In this work, we have formulated a mathematical model of Jatropha curcas plant, which is affected by many type of pest with the aim to control the pest through Nuclear Polyhedrosis Virus (NPV). Here we have also concentrated on insecticide spraying as controlling measure to reduce the pest, to get maximum yield of Jatropha seeds, which gives Jatropha oil. We have also shown the effect of different variants on mass transfer in biodiesel production from JC oil and how the control theoretic approach flags the maximum production of biodiesel under the mathematical paradigm. Our analytical results provide an idea of the cost effective faster rate of biodiesel production, which satisfies our numerical conclusions

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.Comment: This is a preprint of a paper whose final and definite form is published Open Access in 'Mathematical Biosciences and Engineering', available in [https://doi.org/10.3934/mbe.2021272]. Please cite this article as: T. Abraha, F. Al Basir, L. L. Obsu and D. F. M. Torres, Farming awareness based optimum interventions for crop pest control, Math. Biosci. Eng. 18 (2021), no. 5, 5364--539

Stability and bifurcation analysis of a multi-delay model for mosaic disease transmission

A mathematical model is developed for analysis of the spread of mosaic disease in plants, which account for incubation period and latency that are represented by time delays. Feasibility and stability of different equilibria are studied analytically and numerically. Conditions that determine the type of behavior exhibited by the system are found in terms of various parameters. We have derived the basic reproduction number and identify the conditions resulting in eradication of the disease, as well as those that lead to the emergence of stable oscillations in the population of infected plants, as a result of Hopf bifurcation of the endemic equilibrium. Numerical simulations are performed to verify the analytical results and also to illustrate different dynamical regimes that can be observed in the system. In this research, the stabilizing role of both the time delay has been established i.e. when delay time is large, disease will persist if the infection rate is higher. The results obtained here are useful for plant disease management

Control of mosaic disease using microbial biostimulants: insights from mathematical modelling

A major challenge to successful crop production comes from viral diseases of plants that cause significant crop losses, threatening global food security and the livelihoods of countries that rely on those crops for their staple foods or source of income. One example of such diseases is a mosaic disease of plants, which is caused by begomoviruses and is spread to plants by whitefly. In order to mitigate negative impact of mosaic disease, several different strategies have been employed over the years, including roguing/replanting of plants, as well as using pesticides, which have recently been shown to be potentially dangerous to the environment and humans. In this paper we derive and analyse a mathematical model for control of mosaic disease using natural microbial biostimulants that, besides improving plant growth, protect plants against infection through a mechanism of RNA interference. By analysing the stability of the system’s steady states, we will show how properties of biostimulants affect disease dynamics, and in particular, how they determine whether the mosaic disease is eradicated or is rather maintained at some steady level. We will also present the results of numerical simulations that illustrate the behaviour of the model in different dynamical regimes, and discuss biological implications of theoretical results for the practical purpose of control of mosaic disease

Biochar optimizes wheat quality, yield, and nitrogen acquisition in low fertile calcareous soil treated with organic and mineral nitrogen fertilizers

Crop quality and nutrient uptake are considerably influenced by fertilizers inputs and their application rate. Biochar (BC) improves nitrogen uptake and crop productivity. However, its interaction with synthetic and organic fertilizers in calcareous soil is not fully recognized. Therefore, we inspected the role of biochar (0, 10, 20, and 30 t ha–1) in improving N uptake and quality of wheat in a calcareous soil under integrated N management (90, 120, and 150 kg N ha–1) applied each from urea, farmyard manure (FYM) and poultry manure (PM) along with control) in 2 years field experiments. Application of 20 t BC along with 150 kg N ha–1 as poultry manure considerably improved wheat grain protein content (14.57%), grain (62.9%), straw (28.7%), and biological (38.4%) yield, grain, straw, and total N concentration by 14.6, 19.2, and 15.6% and their uptake by 84.6, 48.8, and 72.1%, respectively, over absolute control when averaged across the years. However, their impact was more pronounced in the 2nd year (2016–2017) after application compared to the 1st year (2015–2016). Therefore, for immediate crop benefits, it is recommended to use 20 t BC ha–1 once in 50 years for enhancing the nitrogen use efficiency of fertilizers and crop yield