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.

Discrete breathers in Klein-Gordon lattices: A deflation-based approach.

Deflation is an efficient numerical technique for identifying new branches of steady state solutions to nonlinear partial differential equations. Here, we demonstrate how to extend deflation to discover new periodic orbits in nonlinear dynamical lattices. We employ our extension to identify discrete breathers, which are generic exponentially localized, time-periodic solutions of such lattices. We compare different approaches to using deflation for periodic orbits, including ones based on Fourier decomposition of the solution, as well as ones based on the solution's energy density profile. We demonstrate the ability of the method to obtain a wide variety of multibreather solutions without prior knowledge about their spatial profile.

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 toward 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.

Backcasting COVID-19: a physics-informed estimate for early case incidence.

It is widely accepted that the number of reported cases during the first stages of the COVID-19 pandemic severely underestimates the number of actual cases. We leverage delay embedding theorems of Whitney and Takens and use Gaussian process regression to estimate the number of cases during the first 2020 wave based on the second wave of the epidemic in several European countries, South Korea and Brazil. We assume that the second wave was more accurately monitored, even though we acknowledge that behavioural changes occurred during the pandemic and region- (or country-) specific monitoring protocols evolved. We then construct a manifold diffeomorphic to that of the implied original dynamical system, using fatalities or hospitalizations only. Finally, we restrict the diffeomorphism to the reported cases coordinate of the dynamical system. Our main finding is that in the European countries studied, the actual cases are under-reported by as much as 50%. On the other hand, in South Korea-which had a proactive mitigation approach-a far smaller discrepancy between the actual and reported cases is predicted, with an approximately 18% predicted underestimation. We believe that our backcasting framework is applicable to other epidemic outbreaks where (due to limited or poor quality data) there is uncertainty around the actual cases.

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 zero-dimensional (0D; ordinary-differential-equation-level) compartmental epidemiological model consisting of Susceptible, Exposed, Asymptomatic, (symptomatically) Infected, Hospitalized, Recovered, and deceased populations (SEAIHR model). We emphasize the importance of the viral latent period (reflected in the exposed population) 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, the reported data we found to be most reliable, via minimizing the ℓ^{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, and we address issues of parameter identifiability. We model both the prequarantine and postquarantine 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 the finite-element software package COMSOL Multiphysics®, which was subsequently used to numerically solve the model partial differential equations. 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, zero-dimensional 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.

Lockdown measures and their impact on single- and two-age-structured epidemic model for the COVID-19 outbreak in Mexico.

The role of lockdown measures in mitigating COVID-19 in Mexico is investigated using a comprehensive nonlinear ODE model. The model includes both asymptomatic and presymptomatic populations with the latter leading to sickness (with recovery, hospitalization and death as possible outcomes). We consider situations involving the application of social-distancing and other intervention measures in the time series of interest. We find optimal parametric fits to the time series of deaths (only), as well as to the time series of deaths and cumulative infections. We discuss the merits and disadvantages of each approach, we interpret the parameters of the model and assess the realistic nature of the parameters resulting from the optimization procedure. Importantly, we explore a model involving two sub-populations (younger and older than a specific age), to more accurately reflect the observed impact as concerns symptoms and behavior in different age groups. For definiteness and to separate people that are (typically) in the active workforce, our partition of population is with respect to members younger vs. older than the age of 65. The basic reproduction number of the model is computed for both the single- and the two-population variant. Finally, we consider what would be the impact of partial lockdown (involving only the older population) and full lockdown (involving the entire population) on the number of deaths and cumulative infections.

Easing COVID-19 lockdown measures while protecting the older restricts the deaths to the level of the full lockdown.

Guided by a rigorous mathematical result, we have earlier introduced a numerical algorithm, which using as input the cumulative number of deaths caused by COVID-19, can estimate the effect of easing of the lockdown conditions. Applying this algorithm to data from Greece, we extend it to the case of two subpopulations, namely, those consisting of individuals below and above 40 years of age. After supplementing the Greek data for deaths with the data for the number of individuals reported to be infected by SARS-CoV-2, we estimated the effect on deaths and infections in the case that the easing of the lockdown measures is different for these two subpopulations. We found that if the lockdown measures are partially eased only for the young subpopulation, then the effect on deaths and infections is small. However, if the easing is substantial for the older population, this effect may be catastrophic.

A quantitative framework for exploring exit strategies from the COVID-19 lockdown.

Following the highly restrictive measures adopted by many countries for combating the current pandemic, the number of individuals infected by SARS-CoV-2 and the associated number of deaths steadily decreased. This fact, together with the impossibility of maintaining the lockdown indefinitely, raises the crucial question of whether it is possible to design an exit strategy based on quantitative analysis. Guided by rigorous mathematical results, we show that this is indeed possible: we present a robust numerical algorithm which can compute the cumulative number of deaths that will occur as a result of increasing the number of contacts by a given multiple, using as input only the most reliable of all data available during the lockdown, namely the cumulative number of deaths.

Hydrodynamics and two-dimensional dark lump solitons for polariton superfluids.

We study a two-dimensional incoherently pumped exciton-polariton condensate described by an open-dissipative Gross-Pitaevskii equation for the polariton dynamics coupled to a rate equation for the exciton density. Adopting a hydrodynamic approach, we use multiscale expansion methods to derive several models appearing in the context of shallow water waves with viscosity. In particular, we derive a Boussinesq/Benney-Luke-type equation and its far-field expansion in terms of Kadomtsev-Petviashvili-I (KP-I) equations for right- and left-going waves. From the KP-I model, we predict the existence of vorticity-free, weakly (algebraically) localized two-dimensional dark-lump solitons. We find that, in the presence of dissipation, dark lumps exhibit a lifetime three times larger than that of planar dark solitons. Direct numerical simulations show that dark lumps do exist, and their dissipative dynamics is well captured by our analytical approximation. It is also shown that lumplike and vortexlike structures can spontaneously be formed as a result of the transverse "snaking" instability of dark soliton stripes.

Floquet analysis of Kuznetsov-Ma breathers: A path towards spectral stability of rogue waves.

In the present work, we aim at taking a step towards the spectral stability analysis of Peregrine solitons, i.e., wave structures that are used to emulate extreme wave events. Given the space-time localized nature of Peregrine solitons, this is a priori a nontrivial task. Our main tool in this effort will be the study of the spectral stability of the periodic generalization of the Peregrine soliton in the evolution variable, namely the Kuznetsov-Ma breather. Given the periodic structure of the latter, we compute the corresponding Floquet multipliers, and examine them in the limit where the period of the orbit tends to infinity. This way, we extrapolate towards the stability of the limiting structure, namely the Peregrine soliton. We find that multiple unstable modes of the background are enhanced, yet no additional unstable eigenmodes arise as the Peregrine limit is approached. We explore the instability evolution also in direct numerical simulations.

Impulse-induced generation of stationary and moving discrete breathers in nonlinear oscillator networks.

We study discrete breathers in prototypical nonlinear oscillator networks subjected to nonharmonic zero-mean periodic excitations. We show how the generation of stationary and moving discrete breathers are optimally controlled by solely varying the impulse transmitted by the periodic excitations, while keeping constant the excitation's amplitude and period. Our theoretical and numerical results show that the enhancer effect of increasing values of the excitation's impulse, in the sense of facilitating the generation of stationary and moving breathers, is due to a correlative increase of the breather's action and energy.

From nodeless clouds and vortices to gray ring solitons and symmetry-broken states in two-dimensional polariton condensates.

We consider the existence, stability and dynamics of the nodeless state and fundamental nonlinear excitations, such as vortices, for a quasi-two-dimensional polariton condensate in the presence of pumping and nonlinear damping. We find a series of interesting features that can be directly contrasted to the case of the typically energy-conserving ultracold alkali-atom Bose-Einstein condensates (BECs). For sizeable parameter ranges, in line with earlier findings, the nodeless state becomes unstable towards the formation of stable nonlinear single or multi-vortex excitations. The potential instability of the single vortex is also examined and is found to possess similar characteristics to those of the nodeless cloud. We also report that, contrary to what is known, e.g., for the atomic BEC case, stable stationary gray ring solitons (that can be thought of as radial forms of Nozaki-Bekki holes) can be found for polariton condensates in suitable parametric regimes. In other regimes, however, these may also suffer symmetry-breaking instabilities. The dynamical, pattern-forming implications of the above instabilities are explored through direct numerical simulations and, in turn, give rise to waveforms with triangular or quadrupolar symmetry.