Optimal vaccination at high reproductive numbers: sharp transitions and counterintuitive allocations.

Optimization of vaccine allocations among different segments of a heterogeneous population is important for enhancing the effectiveness of vaccination campaigns in reducing the burden of epidemics. Intuitively, it would seem that allocations designed to minimize infections should prioritize those with the highest risk of being infected and infecting others. This prescription is well supported by vaccination theory, e.g. when the vaccination campaign aims to reach herd immunity. In this work, we show, however, that for vaccines providing partial protection (leaky vaccines) and for sufficiently high values of the basic reproduction number, intuition is overturned: the optimal allocation minimizing the number of infections prioritizes the vaccination of those who are least likely to be infected. The work combines numerical investigations, asymptotic analysis for a general model, and complete mathematical analysis in a two-group model. The results point to important considerations in managing vaccination campaigns for infections with high transmissibility.

Population-level implications of the Israeli booster campaign to curtail COVID-19 resurgence.

Israel was one of the first countries to administer mass vaccination against severe acute respiratory syndrome coronavirus 2. Consequently, it was among the first countries to experience substantial breakthrough infections due to the waning of vaccine-induced immunity, which led to a resurgence of the epidemic. In response, Israel launched a booster campaign to mitigate the outbreak and was the first country to do so. Israel's success in curtailing the Delta resurgence while imposing only mild nonpharmaceutical interventions influenced the decision of many countries to initiate a booster campaign. By constructing a detailed mathematical model and calibrating it to the Israeli data, we extend the understanding of the impact of the booster campaign from the individual to the population level. We used the calibrated model to explore counterfactual scenarios in which the booster vaccination campaign is altered by changing the eligibility criteria or the start time of the campaign and to assess the direct and indirect effects in the different scenarios. The results point to the vast benefits of vaccinating younger age groups that are not at a high risk of developing severe disease but play an important role in transmission. We further show that, when the epidemic is exponentially growing, the success of the booster campaign is highly sensitive to the timing of its initiation. Hence, a rapid response is an important factor in reducing disease burden using booster vaccination.

The role of childrens' vaccination for COVID-19-Pareto-optimal allocations of vaccines.

COVID-19 vaccines have been approved for children of age five and older in many countries. However, there is an ongoing debate as to whether children should be vaccinated and at what priority. In this work, we use mathematical modeling and optimization to study how vaccine allocations to different age groups effect epidemic outcomes. In particular, we consider the effect of extending vaccination campaigns to include the vaccination of children. When vaccine availability is limited, we consider Pareto-optimal allocations with respect to competing measures of the number of infections and mortality and systematically study the trade-offs among them. In the scenarios considered, when some weight is given to the number of infections, we find that it is optimal to allocate vaccines to adolescents in the age group 10-19, even when they are assumed to be less susceptible than adults. We further find that age group 0-9 is included in the optimal allocation for sufficiently high values of the basic reproduction number.

Bending and pinching of three-phase stripes: From secondary instabilities to morphological deformations in organic photovoltaics.

Optimizing the properties of the mosaic nanoscale morphology of bulk heterojunction (BHJ) organic photovoltaics (OPV) is not only challenging technologically but also intriguing from the mechanistic point of view. Among the recent breakthroughs is the identification and utilization of a three-phase (donor-mixed-acceptor) BHJ, where the (intermediate) mixed phase can inhibit mesoscale morphological changes, such as phase separation. Using a mean-field approach, we reveal and distinguish between generic mechanisms that alter, through transverse instabilities, the evolution of stripes: the bending (zigzag mode) and the pinching (cross-roll mode) of the donor-acceptor domains. The results are summarized in a parameter plane spanned by the mixing energy and illumination, and show that donor-acceptor mixtures with higher mixing energy are more likely to develop pinching under charge-flux boundary conditions. The latter is notorious as it leads to the formation of disconnected domains and hence to loss of charge flux. We believe that these results provide a qualitative road map for BHJ optimization, using mixed-phase composition and, therefore, an essential step toward long-lasting OPV. More broadly, the results are also of relevance to study the coexistence of multiple-phase domains in material science, such as in ion-intercalated rechargeable batteries.

Phase transition in the cuprates from a magnetic-field-free stiffness meter viewpoint.

A method to measure the superconducting (SC) stiffness tensor [Formula: see text], without subjecting the sample to external magnetic field, is applied to La1.875Sr0.125CuO4. The method is based on the London equation [Formula: see text], where J is the current density and A is the vector potential which is applied in the SC state. Using rotor free A and measuring J via the magnetic moment of superconducting rings, [Formula: see text] at T → Tc is extracted. The technique is sensitive to very small stiffnesses (penetration depths on the order of a few millimeters). The method is applied to two different rings: one with the current running only in the CuO2 planes, and another where the current must cross planes. We find different transition temperatures for the two rings, namely, there is a temperature range with two-dimensional stiffness. Additional low energy muon spin rotation measurements on the same sample determine the stiffness anisotropy at T < Tc.

Do Bistable Steric Poisson-Nernst-Planck Models Describe Single-Channel Gating?

Experiments measuring currents through single protein channels show unstable currents, a phenomena called the gating of a single channel. Channels switch between an "open" state with a well-defined single amplitude of current and "closed" states with nearly zero current. The existing mean-field theory of ion channels focuses almost solely on the open state. The physical modeling of the dynamical features of ion channels is still in its infancy and does not describe the transitions between open and closed states nor the distribution of the duration times of open states. One hypothesis is that gating corresponds to noise-induced fast transitions between multiple steady (equilibrium) states of the underlying system. In this work, we aim to test this hypothesis. Particularly, our study focuses on the (high-order) steric Poisson-Nernst-Planck (PNP)-Cahn-Hilliard model since it has been successful in predicting permeability and selectivity of ionic channels in their open state and since it gives rise to multiple steady states. We show that this system gives rise to a gatinglike behavior, but that important features of this switching behavior are different from the defining features of gating in biological systems. Furthermore, we show that noise prohibits switching in the system of study. The above phenomena are expected to occur in other PNP-type models, strongly suggesting that one has to go beyond overdamped (gradient flow) Nernst-Planck type dynamics to explain the spontaneous gating of single channels.

From Solvent-Free to Dilute Electrolytes: Essential Components for a Continuum Theory.

The increasing number of experimental observations on highly concentrated electrolytes and ionic liquids show qualitative features that are distinct from dilute or moderately concentrated electrolytes, such as self-assembly, multiple-time relaxation, and underscreening, which all impact the emergence of fluid/solid interfaces, and the transport in these systems. Because these phenomena are not captured by existing mean-field models of electrolytes, there is a paramount need for a continuum framework for highly concentrated electrolytes and ionic liquid mixtures. In this work, we present a self-consistent spatiotemporal framework for a ternary composition that comprises ions and solvent employing a free energy that consists of short- and long-range interactions, along with an energy dissipation mechanism obtained by Onsager's relations. We show that the model can describe multiple bulk and interfacial morphologies at steady-state. Thus, the dynamic processes in the emergence of distinct morphologies become equally as important as the interactions that are specified by the free energy. The model equations not only provide insights into transport mechanisms beyond the Stokes-Einstein-Smoluchowski relations but also enable qualitative recovery of three distinct regions in the full range of the nonmonotonic electrical screening length that has been recently observed in experiments in which organic solvent is used to dilute ionic liquids.

From bulk self-assembly to electrical diffuse layer in a continuum approach for ionic liquids: The impact of anion and cation size asymmetry.

Ionic liquids are solvent-free electrolytes, some of which possess an intriguing self-assembly at finite length scale due to Coulombic interactions. Using a continuum framework (based on Onsager's relations), it is shown that bulk nanostructures arise via linear (supercritical) and nonlinear (subcritical) bifurcations (morphological phase transitions), which also directly affect the electrical double layer structure. A Ginzburg-Landau amplitude equation is derived and the bifurcation type is related to model parameters, such as temperature, potential, and interactions. Specifically, the nonlinear bifurcation occurs for geometrically dissimilar ions and, surprisingly, is induced by perturbations on the order of thermal fluctuations. Finally, qualitative insights and comparisons to the experimentally decaying charge layers within the electrical double layer are discussed.

Dependence of the dielectric constant of electrolyte solutions on ionic concentration: A microfield approach.

We present a microfield approach for studying the dependence of the orientational polarization of the water in aqueous electrolyte solutions upon the salt concentration and temperature. The model takes into account the orientation of the solvent dipoles due to the electric field created by ions, and the effect of thermal fluctuations. The model predicts a dielectric functional dependence of the form ɛ(c)=ɛ_{w}-ßL(3αc/ß),ß=ɛ_{w}-ɛ_{ms}, where L is the Langevin function, c is the salt concentration, ɛ_{w} is the dielectric of pure water, ɛ_{ms} is the dielectric of the electrolyte solution at the molten salt limit, and α is the total excess polarization of the ions. The functional form gives a remarkably accurate description of the dielectric constant for a variety of salts and a wide range of concentrations.

Theory of Phase Separation and Polarization for Pure Ionic Liquids.

Room temperature ionic liquids are attractive to numerous applications and particularly, to renewable energy devices. As solvent free electrolytes, they demonstrate a paramount connection between the material morphology and Coulombic interactions: the electrode/RTIL interface is believed to be a product of both polarization and spatiotemporal bulk properties. Yet, theoretical studies have dealt almost exclusively with independent models of morphology and electrokinetics. Introduction of a distinct Cahn-Hilliard-Poisson type mean-field framework for pure molten salts (i.e., in the absence of any neutral component), allows a systematic coupling between morphological evolution and the electrokinetic phenomena, such as transient currents. Specifically, linear analysis shows that spatially periodic patterns form via a finite wavenumber instability and numerical simulations demonstrate that while labyrinthine type patterns develop in the bulk, lamellar structures are favored near charged surfaces. The results demonstrate a qualitative phenomenology that is observed empirically and thus, provide a physically consistent methodology to incorporate phase separation properties into an electrochemical framework.

Systematic interpretation of differential capacitance data.

Differential capacitance (DC) data have been widely used to characterize the structure of electrolyte solutions near charged interfaces and as experimental validation of models for electrolyte structure. Fixing a large class of models of electrolyte free energy that incorporate finite-volume effects, a reduction is identified which permits the identification of all free energies within that class that return identical DC data. The result is an interpretation of DC data through the equivalence classes of nonideality terms, and associated boundary layer structures, that cannot be differentiated by DC data. Specifically, for binary salts, DC data, even if measured over a range of ionic concentrations, are unable to distinguish among models which exhibit charge asymmetry, charge reversal, and even ion crowding. The reduction applies to capacitors which are much wider than the associated Debye length and to finite-volume terms that are algebraic in charge density. However, within these restrictions the free energy is shown to be uniquely identified if the DC data are supplemented with measurements of the excess chemical potential of the system in the bulk state.

Pulse splitting in the anomalous group-velocity-dispersion regime.

We investigate experimentally the role that the initial temporal profile of ultrashort laser pulses has on the self-focusing dynamics in the anomalous group-velocity dispersion (GVD) regime. We observe that pulse-splitting occurs for super-Gaussian pulses, but not for Gaussian pulses. The splitting does not occur for either pulse shape when the GVD is near-zero. These observations agree with predictions based on the nonlinear Schrödinger equation, and can be understood intuitively using the method of nonlinear geometrical optics.

Collapse dynamics of super-Gaussian Beams.

We investigate the self-focusing dynamics of super-Gaussian optical beams in a Kerr medium. We find that up to several times the critical power for self-focusing, super-Gaussian beams evolve towards a Townes profile. At higher powers the super-Gaussian beams form rings which break into filaments as a result of noise. Our results are consistent with the observed self-focusing dynamics of femtosecond laser pulses in air [1] in which filaments are formed along a ring about the axis of the initial beam where the initial beam did not form a ring.