This paper presents a discrete compartmental Susceptible–Exposed–Infected–Recovered/Dead (SEIR/D) model to address the expansion of Covid-19. This model is based on a grid. As time passes, the status of the cells updates by means of binary rules following a neighborhood and a delay pattern. This model has already been analyzed in previous works and successfully compared with the corresponding continuous models solved by ordinary differential equations (ODE), with the intention of finding 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 disease. The delays (between Susceptible and Asymptomatic, Asymptomatic and Infected, Infected and Recovered/Dead) may have a crucial impact on both height and timing of 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 in the case of plant pests.

The population decline of small villages is a very serious problem for our society. This situation is not easy to reverse. The challenge is to generate consensus among the inhabitants of small villages to develop projects that have both a link with social and cultural heritage and the aid of the regional and local authorities. This framework can be successful when it also has the capability to provide new lines of development growing from this initial seed that can attract new inhabitants. In this paper, we present research that follows these requirements. Our proposal is based on a traditional agriculture resource, which is the art of building dry stone walls. We study the case of Tàrbena (642 inhabitants in the province of Alicante, Spain). Stone artifacts are recovered: some of them are still useful for agriculture, and others are cataloged and transformed into a product for cultural tourism. This project is expected to develop local, manual, and specialized work through the development of workshops, crafts, and small businesses. This will provide more income for the municipality and the private sector and more opportunities to attract new inhabitants.

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

The purpose of this paper is to present a stochastic approach of the expansion of adverse environmental events which are enhanced by the wind. Our model follows a scheme based on the well‐known Susceptible‐Infected‐Recovered (SIR) model. The expansion takes place in a grid where the cells represent an individual (or even a group) in the population under study. The state of the cells is modeled by a random variable which is a measure of the intensity and direction of the wind. As time passes, the status of the cells is determined according to both an update criterion and a probabilistic neighborhood relationship. In addition, in building the expansion model, we have defined a set of adjustable parameters, which will have an effect on the rate of propagation of the phenomenon.

The chess game provides a very rich experience in neighborhood types. The chess pieces have vertical, horizontal, diagonal, up/down or combined movements on one or many squares of the chess. These movements can associate with neighborhoods. Our work aims to set a behavioral approximation between calculations carried out by means of traditional computation tools such as ordinary differential equations (ODEs) and the evolution of the value of the cells caused by the chess game moves. Our proposal is based on a grid. The cells' value changes as time pass depending on both their neighborhood and an update rule. This framework succeeds in applying real data matching in the cases of the ODEs used in compartmental models of disease expansion, such as the well-known Susceptible-Infected Recovered (SIR) model and its derivatives, as well as in the case of population dynamics in competition for resources, depicted by the Lotke-Volterra model.