Delay-driven phase transitions in an epidemic model on time-varying networks.

A complex networked system typically has a time-varying nature in interactions among its components, which is intrinsically complicated and therefore technically challenging for analysis and control. This paper investigates an epidemic process on a time-varying network with a time delay. First, an averaging theorem is established to approximate the delayed time-varying system using autonomous differential equations for the analysis of system evolution. On this basis, the critical time delay is determined, across which the endemic equilibrium becomes unstable and a phase transition to oscillation in time via Hopf bifurcation will appear. Then, numerical examples are examined, including a periodically time-varying network, a blinking network, and a quasi-periodically time-varying network, which are simulated to verify the theoretical results. Further, it is demonstrated that the existence of time delay can extend the network frequency range to generate Turing patterns, showing a facilitating effect on phase transitions.

Modeling the Impact of Vaccination on COVID-19 and Its Delta and Omicron Variants.

Vaccination is an important means to fight against the spread of the SARS-CoV-2 virus and its variants. In this work, we propose a general susceptible-vaccinated-exposed-infected-hospitalized-removed (SVEIHR) model and derive its basic and effective reproduction numbers. We set Hong Kong as an example and calculate conditions of herd immunity for multiple vaccines and disease variants. The model shows how the number of confirmed COVID-19 cases in Hong Kong during the second and third waves of the COVID-19 pandemic would have been reduced if vaccination were available then. We then investigate the relationships between various model parameters and the cumulative number of hospitalized COVID-19 cases in Hong Kong for the ancestral, Delta, and Omicron strains. Numerical results demonstrate that the static herd immunity threshold corresponds to one percent of the population requiring hospitalization or isolation at some point in time. We also demonstrate that when the vaccination rate is high, the initial proportion of vaccinated individuals can be lowered while still maintaining the same proportion of cumulative hospitalized/isolated individuals.

A stochastic SEIHR model for COVID-19 data fluctuations.

Although deterministic compartmental models are useful for predicting the general trend of a disease's spread, they are unable to describe the random daily fluctuations in the number of new infections and hospitalizations, which is crucial in determining the necessary healthcare capacity for a specified level of risk. In this paper, we propose a stochastic SEIHR (sSEIHR) model to describe such random fluctuations and provide sufficient conditions for stochastic stability of the disease-free equilibrium, based on the basic reproduction number that we estimated. Our extensive numerical results demonstrate strong threshold behavior near the estimated basic reproduction number, suggesting that the necessary conditions for stochastic stability are close to the sufficient conditions derived. Furthermore, we found that increasing the noise level slightly reduces the final proportion of infected individuals. In addition, we analyze COVID-19 data from various regions worldwide and demonstrate that by changing only a few parameter values, our sSEIHR model can accurately describe both the general trend and the random fluctuations in the number of daily new cases in each region, allowing governments and hospitals to make more accurate caseload predictions using fewer compartments and parameters than other comparable stochastic compartmental models.

Modeling the COVID-19 Pandemic Using an SEIHR Model With Human Migration.

The 2019 novel coronavirus disease (COVID-19) outbreak has become a worldwide problem. Due to globalization and the proliferation of international travel, many countries are now facing local epidemics. The existence of asymptomatic and pre-symptomatic transmissions makes it more difficult to control disease transmission by isolating infectious individuals. To accurately describe and represent the spread of COVID-19, we suggest a susceptible-exposed-infected-hospitalized-removed (SEIHR) model with human migrations, where the "exposed" (asymptomatic) individuals are contagious. From this model, we derive the basic reproduction number of the disease and its relationship with the model parameters. We find that, for highly contagious diseases like COVID-19, when the adjacent region's epidemic is not severe, a large migration rate can reduce the speed of local epidemic spreading at the price of infecting the neighboring regions. In addition, since "infected" (symptomatic) patients are isolated almost immediately, the transmission rate of the epidemic is more sensitive to that of the "exposed" (asymptomatic) individuals. Furthermore, we investigate the impact of various interventions, e.g. isolation and border control, on the speed of disease propagation and the resultant demand on medical facilities, and find that a strict intervention measure can be more effective than closing the borders. Finally, we use some real historical data of COVID-19 caseloads from different regions, including Hong Kong, to validate the modified SEIHR model, and make an accurate prediction for the third wave of the outbreak in Hong Kong.

Overflow models for the admission of intensive care patients.

An earlier article, inspired by overflow models in telecommunication systems with multiple streams of telephone calls, proposed a new analytical model for a network of intensive care units (ICUs), and a new patient referral policy for such networks to reduce the blocking probability of external emergency patients without degrading the quality of service (QoS) of canceled elective operations, due to the more efficient use of ICU capacity overall. In this work, we use additional concepts and insights from traditional teletraffic theory, including resource sharing, trunk reservation, and mutual overflow, to design a new patient referral policy to further improve ICU network efficiency. Numerical results based on the analytical model demonstrate that our proposed policy can achieve a higher acceptance level than the original policy with a smaller number of beds, resulting in improved service for all patients. In particular, our proposed policy can always achieve much lower blocking probabilities for external emergency patients while still providing sufficient service for internal emergency and elective patients. In addition, we provide new accurate and computationally efficient analytical approximations for QoS evaluation of ICU networks using our proposed policy. We demonstrate numerically that our new approximation method yields more accurate, robust and conservative results overall than the traditional approximation. Finally, we demonstrate how our proposed approximation method can be applied to solve resource planning and optimization problems for ICU networks in a scalable and computationally efficient manner.

Randomized controlled trial of vitamin D supplement on endothelial function in patients with type 2 diabetes.

BACKGROUND: Suboptimal vitamin D status is associated with endothelial dysfunction and an increased risk of cardiovascular diseases but it is unclear whether vitamin D supplementation is beneficial. The aim was to investigate the effect of vitamin D supplementation on endothelial function in patients with type 2 diabetes mellitus (DM). METHODS: In a double-blind, placebo-controlled trial, we randomized 100 type 2 DM patients to vitamin D supplement (5000 IU/day, n = 50) or placebo (controls, n = 50) for 12 weeks. Assessment of vascular function with brachial artery flow-mediated dilatation (FMD), circulating levels of endothelial progenitor cells (EPCs) and brachial-ankle pulse wave velocity, and metabolic parameter, high-sensitivity C-reactive protein (hsCRP) and oxidative stress markers were performed before and after the supplementation. RESULTS: After 12 weeks, vitamin D treated patients had significant increases in serum 25-hydroxyvitamin D [25(OH)D] concentration (treatment effect 34.7 ng/mL, 95% CI 26.4-42.9, P < 0.001) and serum ionized calcium (treatment effect 0.037 mmol/L, 95% CI 0.007-0.067, P = 0.018); decreased serum parathyroid hormone concentration (treatment effect -0.55 pmol/L, 95% CI -1.08 to -0.02, P = 0.042) compared to patients who received placebo. Nevertheless, vitamin D supplementation did not improve vascular function as determined by FMD, circulating EPC count or baPWV (all P > 0.05). Furthermore, hsCRP, oxidative stress markers, low- and high-density lipoprotein and glycated hemoglobin were also similar between two groups (all P > 0.05). CONCLUSION: In patients with type 2 DM, 12 weeks oral supplementation of vitamin D did not significantly affect vascular function or serum biomarkers of inflammation and oxidative stress. CLINICAL TRIAL NUMBER: HKCTR-867, www.hkclinicaltrials.com.

Molecular logic gates using surface-enhanced Raman-scattered light.

A voltage-activated molecular-plasmonics device was created to demonstrate molecular logic based on resonant surface-enhanced Raman scattering (SERS). SERS output was achieved by a combination of chromophore-plasmon coupling and surface adsorption at the interface between a solution and a gold nanodisc array. The chromophore was created by the self-assembly of a supramolecular complex with a redox-active guest molecule. The guest was reversibly oxidized at the gold surface to the +1 and +2 oxidation states, revealing spectra that were reproduced by calculations. State-specific SERS features enabled the demonstration of a multigate logic device with electronic input and optical output.

Vitamin D deficiency is associated with depletion of circulating endothelial progenitor cells and endothelial dysfunction in patients with type 2 diabetes.

CONTEXT: Vitamin D (Vit-D) deficiency is associated with type 2 diabetes mellitus (DM) and endothelial dysfunction. The relationship of Vit-D deficiency with circulating endothelial progenitor cells and endothelial dysfunction in type 2 DM patients nonetheless remains unclear. OBJECTIVE: We aimed to investigate the cross-sectional association of Vit-D status with brachial flow-mediated dilation (FMD) and circulating endothelial progenitor cell (EPC) numbers in type 2 DM patients. DESIGN, SETTING, AND PARTICIPANTS: We conducted a cross-sectional study of 280 patients (59% male, aged 68 ± 10 yr) with type 2 DM recruited in outpatient clinics during the winter period. MAIN OUTCOME MEASURE: We measured serum 25-hydroxyvitamin D [25(OH)D] by an ELISA kit, circulating CD34+/kinase insert domain-containing receptor (KDR)+ and CD133+/KDR+ EPCs by flow cytometry and brachial artery FMD by vascular ultrasound, respectively. RESULTS: The mean serum 25(OH)D concentration was 25.00 ± 9.17 ng/ml, and 34.3% of patients had Vit-D deficiency [25(OH)D < 20 ng/ml]. Serum 25(OH)D concentration had a significant correlation with hemoglobin A1c level [B = -0.018, 95% confidence interval (CI) -0.035 to -0.002, P = 0.032]. Patients with Vit-D deficiency status had significantly lower brachial FMD (mean difference -1.43%, 95% CI -2.31 to -0.55, P = 0.001) and CD133+/KDR+EPC counts (mean difference -0.12%, 95% CI -0.21 to -0.019, P = 0.022) than those with sufficient Vit-D status after adjustment for age, sex, and cardiovascular risk factors, including hemoglobin A1c levels. CONCLUSIONS: Our results demonstrate that serum 25(OH)D status was significantly associated with brachial artery FMD and circulating CD133+/KDR+EPCs. This suggests that Vit-D deficiency might contribute to depletion of EPCs and endothelial dysfunction in patients with type 2 DM.

Turning on resonant SERRS using the chromophore-plasmon coupling created by host-guest complexation at a plasmonic nanoarray.

An active molecular plasmonics system is demonstrated where a supramolecular chromophore generated in a host-guest binding event couples with the localized surface plasmon resonance (LSPR) arising from gold nanodisc gratings. This coupling was achieved by wavelength-matching the chromophore and the LSPR with the laser excitation, thus giving rise to surface-enhanced resonance Raman scattering (SERRS). The chromophore is a broad charge-transfer (CT) band centered at 865 nm (epsilon = 3500 M(-1) cm(-1)) generated by the complexation of cyclobis(paraquat-p-phenylene) (CBPQT(4+)) and the guest molecule tetrathiafulvalene (TTF). The substrates consist of sub-1-microm gold nanodisc arrays which display dimension-tunable plasmon wavelengths (600-1000 nm). The vibrational spectra of the complex arising from SERRS (lambda(exc) = 785 nm) were generated by irradiating an array (lambda(LSPR) = 765 nm) through the solution to give a chromophore-specific signature with the intensities surface enhanced by approximately 10(5). Surface adsorption of the empty and complexed CBPQT(4+) is also implicated in bringing the chromophore into the electric field arising from the surface-localized plasmon. In a titration experiment, the SERRS effect was then used to verify the role of resonance in turning on the spectrum and to accurately quantify the binding between surface-adsorbed CBPQT(4+) and TTF. The use of a nonpatterned gold substrate as well as a color mismatched complex did not show the enhancement, thus validating that spectral overlap between the chromophore and plasmon resonance is key for resonance surface enhancement. Simulations of the electric fields of the arrays are consistent with interdisc plasmon coupling and the observed enhancement factors. The creation of a responsive plasmonic device upon the addition of the guest molecule and the subsequent coupling of the CT chromophore to the plasmon presents favorable opportunities for applications in molecular sensing and active molecular plasmonics.

Determination of binding strengths of a host-guest complex using resonance Raman scattering.

The detection of analyte-binding events by receptors is drawing together the fields of Raman spectroscopy and supramolecular chemistry. This study is intended to facilitate this cohering by examining a model in the solution phase. The resonance Raman scattering (RRS) spectra of the complexation between tetrathiafulvalene (TTF) and cyclobis(paraquat-p-phenylene) (CBPQT(4+)) has been used as the model system to characterize the binding event of a host-guest system. RRS spectra are generated by excitation (lambda(exc) = 785 nm) within the lowest-energy charge-transfer (CT) transition (lambda(max) = 865 nm) of the TTF subsetCBPQT(4+) complex. The paired binding curves from the RRS and UV-vis-NIR titration data agrees with prior work, and a DeltaG of -5.7 +/- 0.6 kcal mol(-1) (MeCN, 298 K) was obtained for the complexation of TTF with CBPQT(4+). Computations on the complex and its components reproduce the energy shifts and resonance enhancements of the Raman band intensities, providing a basis to identify the structural and vibrational changes occurring upon complexation. The changes in bond lengths coincide with partial depopulation of a TTF-based HOMO and population of a CBPQT(4+)-based LUMO through CT mixing in the ground state of 0.46e(-). The structural changes upon complexation generally lead to lower wavenumber vibrations and to changes in the normal mode descriptions.

Electromechanical carbon nanotube switches for high-frequency applications.

We describe the fabrication and characterization of a nanoelectromechanical (NEM) switch based on carbon nanotubes. Our NEM structure consists of single-walled nanotubes (SWNTs) suspended over shallow trenches in a SiO(2) layer, with a Nb pull electrode beneath. The nanotube growth is done on-chip using a patterned Fe catalyst and a methane chemical vapor deposition (CVD) process at 850 degrees C. Electrical measurements of these devices show well-defined ON and OFF states as a dc bias up to a few volts is applied between the CNT and the Nb pull electrode. The CNT switches were measured to have speeds that are 3 orders of magnitude higher than MEMS-based electrostatically driven switches, with switching times down to a few nanoseconds, while at the same time requiring pull voltages less than 5 V.

Performance evaluation of an optical hybrid switch with circuit queued reservations and circuit priority preemption.

We provide here a new loss model for an optical hybrid switch that can function as an optical burst switch and/or optical circuit switch. Our model is general as it considers an implementation whereby some of the circuits have preemptive priority over bursts and others are allowed to queue their reservations. We first present an analysis based on a 3-dimension state-space Markov chain that provides exact results for the blocking probabilities of bursts and circuits, the proportion of circuits that are delayed and the mean delay of the circuits that are delayed. Because it is difficult to exactly compute the blocking probability in realistic scenarios with a large number of wavelengths, we derive computationally a scalable and accurate approximations based on reducing the 3-dimension state space into a single dimension. These scalable approximations that can produce performance results in a fraction of a second can readily enable switch dimensioning. Extensive numerical results are presented to demonstrate the accuracy and the use of the new approximations.

Carbon nanotube Schottky diodes using Ti-Schottky and Pt-Ohmic contacts for high frequency applications.

We have demonstrated Schottky diodes using semiconducting single-walled nanotubes (s-SWNTs) with titanium Schottky and platinum Ohmic contacts for high-frequency applications. The diodes are fabricated using angled evaporation of dissimilar metal contacts over an s-SWNT. The devices demonstrate rectifying behavior with large reverse bias breakdown voltages of greater than -15 V. To decrease the series resistance, multiple SWNTs are grown in parallel in a single device, and the metallic tubes are burnt-out selectively. At low biases these diodes showed ideality factors in the range of 1.5 to 1.9. Modeling of these diodes as direct detectors at room temperature at 2.5 terahertz (THz) frequency indicates noise equivalent powers (NEP) potentially comparable to that of the state-of-the-art gallium arsenide solid-state Schottky diodes, in the range of 10(-13) W/ radical Hz.