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The purpose of this paper is to present a discrete compartmental susceptible-asymptomatic-infected-dead (SAID) model to address the expansion of plant pests. The authors examined the case of Xylella fastidiosa in almond trees in the province of Alicante (Spain) to define the best eradication/contention protocol depending on the environmental parameters such as climatic factors, distance between trees, isolation of the plots, etc.

This approach considers the expansion of the disease among the almond trees orchards by means of a grid model. The cells of the grid represent a tree (or even a group of trees) that can be susceptible (healthy), asymptomatic (infected by the bacterium but without symptoms), infected or dead. When time passes, the status of the cells is determined by binary rules that update following both a neighborhood and a delay pattern. The model assumes that the environmental parameters have a crucial impact on the expansion of the disease, so a grid is assigned to each parameter to model the single effect caused by this parameter. The expansion is then the weighted sum of all the grids.

This proposal shows how the grid architecture, along with an update rule and a neighborhood pattern, is a valuable tool to model the pest expansion. This model has already been analyzed in previous works and has been compared with the corresponding continuous models solved by ordinary differential equations, coming to find the homologous parameters between both approaches. Thus, it has been possible to prove that the combination neighborhood-update rule is responsible for the rate of expansion and recovering/death of the illness. The delays (between susceptible and asymptomatic, asymptomatic and infected, infected and recovered/dead) may have a crucial impact on both the peak of infected and the recovery/death rate. This theoretical model has been successfully tested in the case of the dissemination of information through mobile social networks and is also currently under study in the case of expansion of COVID-19.

This work develops a new approach for the analysis of expansion of plant pests. This approach provides both behavioral variability at the cell level (by its capability to modify the neighborhood and/or the update rule and/or the delays) and modularity (by easy scaling the number of grids). This provides a wide range of possibilities to deal with realistic scenarios.

Nowadays, the agri-food industry is called to face several sustainability challenges that require the development of new sustainable models. The adoption of new technological assets from Industry 4.0 supports the companies during the implementation of sustainability practices. Several models design the operation management of the food supply chains (FSCs). Because none extant models resulted complete in technological and sustainability elements, this paper aims to propose an innovative and sustainable agri-food value chain model, contributing to extend understating of how supply chains can become more sustainable through the Industry 4.0 technologies.

Thanks to a well-structured and replicable systematic literature review and sequent content analysis, this work recognized and compared the extant FSC models, focusing on the interaction of five key elements: activities, flows, stakeholders, technologies and sustainability. The output of the comparison leading in the definition of the proposed model is discussed in a focus group of 10 experts and tested in a case study.

Fifteen extant models were recognized in literature and analysed to discover their features and to putt in light peculiarities and differences among them. This analysis provided useful insights to design and propose a new innovative and sustainable agri-food value chain model; an example for the olive oil business case is provided.

The adding value of the work is the proposed model which regards innovative elements such as recirculation flows, external stakeholders and Industry 4.0 technologies usage which allows enhancing the agri-FSCs operational efficiency and sustainability.

The purpose of this article is to provide information about interactions between pink-pigmented facultative methylotroph (PPFM) organisms and plants, their molecular mechanisms of methylotrophic metabolism, application of PPFMs in agriculture, biotechnology and bioremediation and also to explore lacuna in PPFMs research and direction for future research.

Research findings on PPFM organisms as potent plant growth promoting organisms are discussed in the light of reports published by various workers. Unexplored field of PPFM research are detected and their application as a new group of biofertilizer that also help host plants to overcome draught stress in poorly irrigated crop field is suggested.

PPFMs are used as plant growth promoters for improved crop yield, seed germination capacity, resistance against pathogens and tolerance against drought stress. Anti-oxidant and UV resistant properties of PPFM pigments protect the host plants from strong sunshine. PPFMs have excellent draught ameliorating capacity.

To meet the ever increasing world population, more and more barren, less irrigated land has to be utilized for agriculture and horticulture purpose and use of PPFM group of organisms due to their draught ameliorating properties in addition to their plant growth promoting characters will be extremely useful. PPFMs are also promising candidates for the production of various industrially and medicinally important enzymes and other value-added products. Wider application of this ecofriendly group of bacteria will reduce crop production cost thus improving economy of the farmers and will be a greener alternative of hazardous chemical fertilizers and fungicides.

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