Reaction-diffusion spatial modeling of COVID-19: Greece and Andalusia as case examples

We examine the spatial modeling of the outbreak of COVID-19 in two regions: the autonomous community of Andalusia in Spain and the mainland of Greece. We start with a 0D compartmental epidemiological model consisting of Susceptible, Exposed, Asymptomatic, (symptomatically) Infected, Hospitalized, Recovered, and deceased populations. We emphasize the importance of the viral latent period and the key role of an asymptomatic population. We optimize model parameters for both regions by comparing predictions to the cumulative number of infected and total number of deaths via minimizing the $\ell^2$ norm of the difference between predictions and observed data. We consider the sensitivity of model predictions on reasonable variations of model parameters and initial conditions, addressing issues of parameter identifiability. We model both pre-quarantine and post-quarantine evolution of the epidemic by a time-dependent change of the viral transmission rates that arises in response to containment measures. Subsequently, a spatially distributed version of the 0D model in the form of reaction-diffusion equations is developed. We consider that, after an initial localized seeding of the infection, its spread is governed by the diffusion (and 0D model "reactions") of the asymptomatic and symptomatically infected populations, which decrease with the imposed restrictive measures. We inserted the maps of the two regions, and we imported population-density data into COMSOL, which was subsequently used to solve numerically the model PDEs. Upon discussing how to adapt the 0D model to this spatial setting, we show that these models bear significant potential towards capturing both the well-mixed, 0D description and the spatial expansion of the pandemic in the two regions. Veins of potential refinement of the model assumptions towards future work are also explored.Comment: 28 pages, 16 figures and 2 movie

Spatial dynamics of airborne infectious diseases

Disease outbreaks, such as those of Severe Acute Respiratory Syndrome in 2003 and the 2009 pandemic A(H1N1) influenza, have highlighted the potential for airborne transmission in indoor environments. Respirable pathogen-carrying droplets provide a vector for the spatial spread of infection with droplet transport determined by diffusive and convective processes. An epidemiological model describing the spatial dynamics of disease transmission is presented. The effects of an ambient airflow, as an infection control, are incorporated leading to a delay equation, with droplet density dependent on the infectious density at a previous time. It is found that small droplets ($\sim 0.4\ \mu$m) generate a negligible infectious force due to the small viral load and the associated duration they require to transmit infection. In contrast, larger droplets ($\sim 4\ \mu$m) can lead to an infectious wave propagating through a fully susceptible population or a secondary infection outbreak for a localised susceptible population. Droplet diffusion is found to be an inefficient mode of droplet transport leading to minimal spatial spread of infection. A threshold air velocity is derived, above which disease transmission is impaired even when the basic reproduction number $R_{0}$ exceeds unity.Comment: 31 pages, 6 figures, to appear in the Journal of Theoretical Biolog

Dynamical Barrier for the Formation of Solitary Waves in Discrete Lattices

We consider the problem of the existence of a dynamical barrier of ``mass'' that needs to be excited on a lattice site to lead to the formation and subsequent persistence of localized modes for a nonlinear Schrodinger lattice. We contrast the existence of a dynamical barrier with its absence in the static theory of localized modes in one spatial dimension. We suggest an energetic criterion that provides a sufficient, but not necessary, condition on the amplitude of a single-site initial condition required to form a solitary wave. We show that this effect is not one-dimensional by considering its two-dimensional analog. The existence of a sufficient condition for the excitation of localized modes in the non-integrable, discrete, nonlinear Schrodinger equation is compared to the dynamics of excitations in the integrable, both discrete and continuum, version of the nonlinear Schrodinger equation.Comment: 9 pages, 3 figures, Phys. Lett. A (in press

Modelling Electro-mobility: An Integrated Modelling Platform for Assessing European Policies

Recently, the European Union (EU) adopted the Directive on the deployment of alternative fuels infrastructure, which defines minimum requirements on alternative fuels infrastructure build up, including recharging points for electric vehicles. Moreover, the European Commission is currently working towards a Communication on decarbonising the transport sector, including an action plan on second and third generation biofuels and other alternative, sustainable fuels. Various Member States have set up incentives to foster electrified or low-emission vehicle purchases. The Joint Research Centre, as the European Commission's in-house science service, has created a suite of models on electro-mobility, which serves to assess policies towards electrification of road transport and their effects on energy demand, emission reduction and costs. The models are soft-linked and the structure is flexible enough to make sure that the appropriate tools can be used for various studies. The models within this suite include: A Market Agent model that captures the dynamics between automobile manufacturers, infrastructure providers, authorities and users in order to model competition between and transition of current and future powertrain technologies; A Fleet Impact tool, containing up-to-date vehicle stock data and energy and emission factors of all vehicle types in the EU, as well as fuel consumption and (real world & type approval) emission calculation, both for Tank-to-Wheel and Well-to-Wheel; An EV-Charging model that estimates the energy-consumption of electric vehicles and calculates their power demand (load) on the basis of usage statistics (e.g., daily distance travelled, parking duration, number of daily trips); An Energy System Model (JRC-EU-TIMES) that models energy technologies’ uptake and deployment and their interaction with the energy infrastructure from an energy systems perspective; Various others depending on the needs of the assessment to be made. This paper shows key results of studies that were performed with the JRC integrated electro-mobility modelling platform

Vaccination compartmental epidemiological models for the delta and omicron SARS-CoV-2 variants

We explore the inclusion of vaccination in compartmental epidemiological models concerning the delta and omicron variants of the SARS-CoV-2 virus that caused the COVID-19 pandemic. We expand on our earlier compartmental-model work by incorporating vaccinated populations. We present two classes of models that differ depending on the immunological properties of the variant. The first one is for the delta variant, where we do not follow the dynamics of the vaccinated individuals since infections of vaccinated individuals were rare. The second one for the far more contagious omicron variant incorporates the evolution of the infections within the vaccinated cohort. We explore comparisons with available data involving two possible classes of counts, fatalities and hospitalizations. We present our results for two regions, Andalusia and Switzerland (including the Principality of Liechtenstein), where the necessary data are available. In the majority of the considered cases, the models are found to yield good agreement with the data and have a reasonable predictive capability beyond their training window, rendering them potentially useful tools for the interpretation of the COVID-19 and further pandemic waves, and for the design of intervention strategies during these waves

The role of mobility in the dynamics of the COVID-19 epidemic in Andalusia

Metapopulation models have been a popular tool for the study of epidemic spread over a network of highly populated nodes (cities, provinces, countries) and have been extensively used in the context of the ongoing COVID-19 pandemic. In the present work, we revisit such a model, bearing a particular case example in mind, namely that of the region of Andalusia in Spain during the period of the summer-fall of 2020 (i.e., between the first and second pandemic waves). Our aim is to consider the possibility of incorporation of mobility across the province nodes focusing on mobile-phone time dependent data, but also discussing the comparison for our case example with a gravity model, as well as with the dynamics in the absence of mobility. Our main finding is that mobility is key towards a quantitative understanding of the emergence of the second wave of the pandemic and that the most accurate way to capture it involves dynamic (rather than static) inclusion of time-dependent mobility matrices based on cell-phone data. Alternatives bearing no mobility are unable to capture the trends revealed by the data in the context of the metapopulation model considered herein

Langevin agglomeration of nanoparticles interacting via a central potential

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