Efficacy of the adjuvanted subunit protein COVID-19 vaccine, SCB-2019: a phase 2 and 3 multicentre, double-blind, randomised, placebo-controlled trial.

BACKGROUND: A range of safe and effective vaccines against SARS CoV 2 are needed to address the COVID 19 pandemic. We aimed to assess the safety and efficacy of the COVID-19 vaccine SCB-2019. METHODS: This ongoing phase 2 and 3 double-blind, placebo-controlled trial was done in adults aged 18 years and older who were in good health or with a stable chronic health condition, at 31 sites in five countries (Belgium, Brazil, Colombia, Philippines, and South Africa). The participants were randomly assigned 1:1 using a centralised internet randomisation system to receive two 0·5 mL intramuscular doses of SCB-2019 (30 µg, adjuvanted with 1·50 mg CpG-1018 and 0·75 mg alum) or placebo (0·9% sodium chloride for injection supplied in 10 mL ampoules) 21 days apart. All study staff and participants were masked, but vaccine administrators were not. Primary endpoints were vaccine efficacy, measured by RT-PCR-confirmed COVID-19 of any severity with onset from 14 days after the second dose in baseline SARS-CoV-2 seronegative participants (the per-protocol population), and the safety and solicited local and systemic adverse events in the phase 2 subset. This study is registered on EudraCT (2020-004272-17) and ClinicalTrials.gov (NCT04672395). FINDINGS: 30 174 participants were enrolled from March 24, 2021, until the cutoff date of Aug 10, 2021, of whom 30 128 received their first assigned vaccine (n=15 064) or a placebo injection (n=15 064). The per-protocol population consisted of 12 355 baseline SARS-CoV-2-naive participants (6251 vaccinees and 6104 placebo recipients). Most exclusions (13 389 [44·4%]) were because of seropositivity at baseline. There were 207 confirmed per-protocol cases of COVID-19 at 14 days after the second dose, 52 vaccinees versus 155 placebo recipients, and an overall vaccine efficacy against any severity COVID-19 of 67·2% (95·72% CI 54·3-76·8), 83·7% (97·86% CI 55·9-95·4) against moderate-to-severe COVID-19, and 100% (97·86% CI 25·3-100·0) against severe COVID-19. All COVID-19 cases were due to virus variants; vaccine efficacy against any severity COVID-19 due to the three predominant variants was 78·7% (95% CI 57·3-90·4) for delta, 91·8% (44·9-99·8) for gamma, and 58·6% (13·3-81·5) for mu. No safety issues emerged in the follow-up period for the efficacy analysis (median of 82 days [IQR 63-103]). The vaccine elicited higher rates of mainly mild-to-moderate injection site pain than the placebo after the first (35·7% [287 of 803] vs 10·3% [81 of 786]) and second (26·9% [189 of 702] vs 7·4% [52 of 699]) doses, but the rates of other solicited local and systemic adverse events were similar between the groups. INTERPRETATION: Two doses of SCB-2019 vaccine plus CpG and alum provides notable protection against the entire severity spectrum of COVID-19 caused by circulating SAR-CoV-2 viruses, including the predominating delta variant. FUNDING: Clover Biopharmaceuticals and the Coalition for Epidemic Preparedness Innovations.

Dynamics of the Kuramoto-Sakaguchi oscillator network with asymmetric order parameter.

We study the dynamics of a generalized version of the famous Kuramoto-Sakaguchi coupled oscillator model. In the classic version of this system, all oscillators are governed by the same ordinary differential equation (ODE), which depends on the order parameter of the oscillator configuration. The order parameter is the arithmetic mean of the configuration of complex oscillator phases, multiplied by some constant complex coupling factor. In the generalized model, we consider that all oscillators are still governed by the same ODE, but the order parameter is allowed to be any complex linear combination of the complex oscillator phases, so the oscillators are no longer necessarily weighted identically in the order parameter. This asymmetric version of the K-S model exhibits a much richer variety of steady-state dynamical behavior than the classic symmetric version; in addition to stable synchronized states, the system may possess multiple stable (N-1,1) states, in which all but one of the oscillators are synchronized, as well as multiple families of neutrally stable states or closed orbits, in which no two oscillators are synchronized. We present an exhaustive description of the possible steady state dynamical behaviors; our classification depends on the complex coefficients that determine the order parameter. We use techniques from group theory and hyperbolic geometry to reduce the dynamic analysis to a 2D flow on the unit disc, which has geometric significance relative to the hyperbolic metric. The geometric-analytic techniques we develop can in turn be applied to study even more general versions of Kuramoto oscillator networks.

Cluster synchronization in networks of identical oscillators with α-function pulse coupling.

We study a network of N identical leaky integrate-and-fire model neurons coupled by α-function pulses, weighted by a coupling parameter K. Studies of the dynamics of this system have mostly focused on the stability of the fully synchronized and the fully asynchronous splay states, which naturally depends on the sign of K, i.e., excitation vs inhibition. We find that there is also a rich set of attractors consisting of clusters of fully synchronized oscillators, such as fixed (N-1,1) states, which have synchronized clusters of sizes N-1 and 1, as well as splay states of clusters with equal sizes greater than 1. Additionally, we find limit cycles that clarify the stability of previously observed quasiperiodic behavior. Our framework exploits the neutrality of the dynamics for K=0 which allows us to implement a dimensional reduction strategy that simplifies the dynamics to a continuous flow on a codimension 3 subspace with the sign of K determining the flow direction. This reduction framework naturally incorporates a hierarchy of partially synchronized subspaces in which the new attracting states lie. Using high-precision numerical simulations, we describe completely the sequence of bifurcations and the stability of all fixed points and limit cycles for N=2-4. The set of possible attracting states can be used to distinguish different classes of neuron models. For instance from our previous work [Chaos 24, 013114 (2014)CHAOEH1054-150010.1063/1.4858458] we know that of the types of partially synchronized states discussed here, only the (N-1,1) states can be stable in systems of identical coupled sinusoidal (i.e., Kuramoto type) oscillators, such as θ-neuron models. Upon introducing a small variation in individual neuron parameters, the attracting fixed points we discuss here generalize to equivalent fixed points in which neurons need not fire coincidently.

Classification of attractors for systems of identical coupled Kuramoto oscillators.

We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For [Formula: see text] oscillators, there are four possible types of attractors: completely synchronized fixed points or limit cycles, and fixed points or limit cycles where all but one of the oscillators are synchronized. The case N = 3 is exceptional; systems of three identical Kuramoto oscillators can also posses attracting fixed points or limit cycles with all three oscillators out of sync, as well as chaotic attractors. Our results rely heavily on the invariance of the flow for such systems under the action of the three-dimensional group of Möbius transformations, which preserve the unit disc, and the analysis of the possible limiting configurations for this group action.

Rhythm-induced spike-timing patterns characterized by 1D firing maps.

We explore patterns in the spike timing of neurons receiving periodic inputs, with an emphasis on stable characteristics which are realized in both models and in-vitro whole-cell recordings. We report on whole-cell recordings of pyramidal CA1 cells from rat hippocampus and entorhinal cortex and compare this data to model simulations. Cells were injected with a constant current to induce a steady firing rate and then a modest rhythm was added which altered the spike times and their corresponding phases relative to the rhythm. For both experiment and theory the relationship between consecutive spike phases is characterized by a probability distribution with peaks concentrated near a one-dimensional firing map. As is well-known, stable fixed points of this map correspond to the neuron phase-locking to the rhythm. We show that the interaction between noise and sufficiently steep maps can also cause a new kind of spike-time organization, in which consecutive spike time pairs organize into discrete clusters, with transitions between these clusters proceeding in a fixed sequence. This structure is not just a vestige of the noise-free dynamics. This slow dynamics and temporal organization in the relationship between consecutive spike phases is not evident in either the neuron's voltage traces or single phase or interspike interval histograms. Furthermore, the consecutive spike relationship is also evident in consecutive ISIs, and hence this ordering can be observed without detailed knowledge of the rhythm (e.g. without concurrent LFP recordings).

Structure of long-term average frequencies for Kuramoto oscillator systems.

We study the long-term average frequency as a function of the natural frequency for Kuramoto oscillators with periodic coefficients. Unlike the case for more general periodically forced oscillators, this function is never a "devil's staircase"; it may have plateaus at integer multiples of the forcing frequency, but we prove it is strictly increasing between these plateaus. The proof uses the fact that the flow maps for Kuramoto oscillators extend to Möbius transformations on the complex plane, and that Möbius transformations have particularly simple dynamics that rule out p:q mode locking except in the case of fixed points (q=1). We also give a criterion for the degeneration of an integer plateau to a single point and use it to explain the absence of plateaus at even multiples of the collective frequency for a Kuramoto system with a bimodal frequency distribution.

Dynamical phase transitions in periodically driven model neurons.

Transitions between dynamical states in integrate-and-fire neuron models with periodic stimuli result from tangent or discontinuous bifurcations of a return map. We study their characteristic scaling laws and show that discontinuous bifurcations exhibit a kind of phase transition intermediate between continuous and first order. In the model-independent spirit of our analysis we show that a six-dimensional (6D) gating variable model with an attracting limit cycle has similar phase transitions, governed by a 1D return map. This reduction to 1D map dynamics should extend to real neurons in a periodic current clamp setting.