In this paper we first prove a rather general theorem about existence of solutions for an abstract differential equation in a Banach space by assuming that the nonlinear term is in some sense weakly continuous.   We then apply this result to a lattice dynamical system with delay, proving also the existence of a global compact attractor for such system.

In this paper we study the asymptotic behaviour of solutions of a lattice dynamical system of a logistic type. Namely, we study a system of infinite ordinary differential equations which can be obtained after the spatial discretization of a logistic equation with diffusion. We prove that a global attractor exists in suitable weighted spaces of sequences.

In Spain, the COVID-19 pandemic has impacted the various regions of the country differently. The availability of reliable and up-to-date information has proved to be fundamental for the management of this health crisis. However, especially during the first wave of the pandemic (February–August 2020), the disparity in the recording criteria and in the timing of providing these figures to the central government created controversy and confusion regarding the real dimension of the pandemic. It is therefore necessary to have objective and homogeneous criteria at the national level to guide health managers in the correct recording and evaluation of the magnitude of the pandemic. Within this context, we propose using Benford’s Law as an auditing tool to monitor the reliability of the number of daily COVID-related deaths to identify possible deviations from the expected trend.

Seasonality is a widely recognised and accredited phenomenon known to cause an imbalance in tourism activity throughout the year, prompting tourist destinations, both public and private, to consider how best to plan the use of their resources. One way of mitigating the economic imbalances that seasonality can cause is to find strategies for seasonal adjustment, such as travel programmes aimed at the elderly. This paper analyses the seasonality of tourism activity in some EU countries, and in particular in Spain. Different indicators are used to compare the results and carry out a sensitivity analysis. The study then focuses on tourism programmes for the elderly in Spain to see whether this type of programme helps to alleviate the seasonality of tourism activity. To corroborate this, an econometric model is specified and estimated, which enables the scope of these programmes to be compared.

In this paper, we apply resampling techniques to a modified compartmental SEIR model which takes into account the existence of undetected infected people in an epidemic. In particular, we implement numerical simulations for the evolution of the first wave of the COVID-19 pandemic in Spain in 2020. We show, by using suitable measures of goodness, that the point estimates obtained by the bootstrap samples improve the ones of the original data. For example, the relative error of detected currently infected people is equal to 0.061 for the initial estimates, while it is reduced to 0.0538 for the mean over all bootstrap estimated series.