A recursive model of the spread of COVID-19: Modelling study

Background: The major medical and social challenge of the 21st century is COVID-19, caused by the novel coronavirus SARS-CoV-2. Critical issues include the rate at which the coronavirus spreads and the effect of quarantine measures and population vaccination on this rate. Knowledge of the laws of the spread of COVID-19 will enable assessment of the effectiveness and reasonableness of the quarantine measures used, as well as determination of the necessary level of vaccination needed to overcome this crisis. Objective: This study aims to establish the laws of the spread of COVID-19 and to use them to develop a mathematical model to predict changes in the number of active cases over time, possible human losses, and the rate of recovery of patients, to make informed decisions about the number of necessary beds in hospitals, the introduction and type of quarantine measures, and the required threshold of vaccination of the population. Methods: This study analyzed the onset of COVID-19 spread in countries such as China, Italy, Spain, the United States, the United Kingdom, Japan, France, and Germany based on publicly available statistical data. The change in the number of COVID-19 cases, deaths, and recovered persons over time was examined, considering the possible introduction of quarantine measures and isolation of infected people in these countries. Based on the data, the virus transmissibility and the average duration of the disease at different stages were evaluated, and a model based on the principle of recursion was developed. Its key features are the separation of active (nonisolated) infected persons into a distinct category and the prediction of their number based on the average duration of the disease in the inactive phase and the concentration of these persons in the population in the preceding days. Results: Specific values for SARS-CoV-2 transmissibility and COVID-19 duration were estimated for different countries. In China, the viral transmissibility was 3.12 before quarantine measures were implemented and 0.36 after these measures were lifted. For the other countries, the viral transmissibility was 2.28-2.76 initially, and it then decreased to 0.87-1.29 as a result of quarantine measures. Therefore, it can be expected that the spread of SARS-CoV-2 will be suppressed if 56%-64% of the total population becomes vaccinated or survives COVID-19. Conclusions: The quarantine measures adopted in most countries are too weak compared to those previously used in China. Therefore, it is not expected that the spread of COVID-19 will stop and the disease will cease to exist naturally or owing to quarantine measures. Active vaccination of the population is needed to prevent the spread of COVID-19. Furthermore, the required specific percentage of vaccinated individuals depends on the magnitude of viral transmissibility, which can be evaluated using the proposed model and statistical data for the country of interest

COVID-19 spreading: a recursive model

Abstract This communication describes a recursive mathematical model of the spreading COVID-19 infection, which allows estimating the effectiveness of quarantine measures. This model takes into account the contagiousness of infected people during the incubation period of the disease and the conditionally non-contagiousness of sick people due to their isolation. The model was used to analyze the situation in eight countries and to find the viral transmissibility, which made it possible to give a brief prediction of the COVID-19 spreading

Hot-Melt and Pressure-Sensitive Adhesives Based on Styrene-Isoprene-Styrene Triblock Copolymer, Asphaltene/Resin Blend and Naphthenic Oil

Asphaltene/resin blend (ARB) extracted from heavy crude oil was used to modify poly(styrene-block-isoprene-block-styrene) (SIS) to make it an adhesive. There were prepared double and triple mixtures containing 10–60% SIS, 10–40% ARB, and 10–50% naphthenic oil used as an additional plasticizer. The viscoelasticity of the mixtures at 25 °C and 120 °C was studied, their flow curves were obtained, and the temperature dependences of the loss tangent and the components of the complex modulus were measured. In addition, the mixtures were used as hot-melt adhesives (HMAs) and pressure-sensitive adhesives (PSAs) in the shear, peel, and pull-off tests of the adhesive bonds that they formed with steel. Both naphthenic oil and ARB act as plasticizers for SIS and make it sticky. However, only the combined use of ARB and the oil allows for achieving the best set of adhesive properties of the SIS-based mixture. High-quality HMA requires low oil content (optimal SIS/ARB/oil ratio is 50/40/10, pull-off adhesion strength (τt) of 1990 kPa), whereas a lot of the oil is needed to give SIS characteristics of a PSA (SIS/ARB/oil is 20/40/40, τt of 100 kPa). At the same time, the resulting PSA can be used as a hot-melt pressure-sensitive adhesive (HMPSA) that has many times lower viscosity than HMA (13.9 Pa·s versus 2640 Pa·s at 120 °C and 1 s−1) but provides a less strong adhesive bond (τt of 960 kPa)

Asphaltene-Stabilized Polyisobutylene Pressure-Sensitive Adhesives for Ultraviolet Protection and Surface Bonding

The usual way to protect indoor areas from solar UV radiation is to use UV-absorbing materials, which are applied as a thin film on the surface of the windowpane. Asphaltenes are useless wastes from crude oil refining that absorb UV radiation well, which gave the idea of their use in protective coatings. Pressure-sensitive adhesives based on polyisobutylene containing from 5 to 30 wt% of asphaltenes were obtained. Deterioration of the adhesive properties with the introduction of 5–20 wt% of asphaltenes was shown by adhesion tests, which can be associated with the plasticization of the polymer matrix. At the same time, the use of 30 wt% of asphaltenes leads to the polymer matrix reinforcement with the restoration of adhesive properties to the original level or even slightly higher. The rheological study of adhesives at 25 °C and 120 °C showed the structural network formation by asphaltenes at a content of 30 wt%, explaining the increase in adhesion performance. According to microscopy, asphaltenes are flat brown glass shards in a polymer matrix. They absorb electromagnetic radiation, predominantly in the UV range, while maintaining relative translucency in the visible range. This makes it possible to obtain thin films from the asphaltene-filled adhesive for bonding glass sheets to produce UV-blocked and tinted windowpanes

The Use of Branching Agents in the Synthesis of PBAT

Biodegradable polyesters represent an advanced alternative to polyolefin plastics in various applications. Polybutylene adipate terephthalate (PBAT) can compete with polyolefins in terms of their mechanical characteristics and melt processing conditions. The properties of PBAT depend on the molecular weight, dispersity, and architecture of the copolymer. Long-chain branching (LCB) of the PBAT backbone is an efficient method for the improvement of the copolymer characteristics. In the present work, we studied branching agents (BAs) 1–7 of different structures in the two-stage polycondensation of 1,4-butanediol, dimethyl terephthalate, and adipic acid and investigated the composition and melt rheology of the copolymers. According to the results of the research, 1,1,1-tris(hydroxymethyl)ethane 2 and 3-hydroxy-2-(hydroxymethyl)-2-methylpropanoic acid 5 outperformed glycerol 1 as BAs in terms of shear thinning behavior and viscoelasticity

The Effect of Non-Solvent Nature on the Rheological Properties of Cellulose Solution in Diluted Ionic Liquid and Performance of Nanofiltration Membranes

The weak point of ionic liquids is their high viscosity, limiting the maximum polymer concentration in the forming solutions. A low-viscous co-solvent can reduce viscosity, but cellulose has none. This study demonstrates that dimethyl sulfoxide (DMSO), being non-solvent for cellulose, can act as a nominal co-solvent to improve its processing into a nanofiltration membrane by phase inversion. A study of the rheology of cellulose solutions in diluted ionic liquids ([EMIM]Ac, [EMIM]Cl, and [BMIM]Ac) containing up to 75% DMSO showed the possibility of decreasing the viscosity by up to 50 times while keeping the same cellulose concentration. Surprisingly, typical cellulose non-solvents (water, methanol, ethanol, and isopropanol) behave similarly, reducing the viscosity at low doses but causing structuring of the cellulose solution and its phase separation at high concentrations. According to laser interferometry, the nature of these non-solvents affects the mass transfer direction relative to the forming membrane and the substance interdiffusion rate, which increases by four-fold when passing from isopropanol to methanol or water. Examination of the nanofiltration characteristics of the obtained membranes showed that the dilution of ionic liquid enhances the rejection without changing the permeability, while the transition to alcohols increases the permeability while maintaining the rejection

Effect of Chain Structure on the Rheological Properties of Vinyl Acetate–Vinyl Alcohol Copolymers in Solution and Bulk

Bulk and solution studies revealed a strongly pronounced effect of chain structure on the rheological and relaxation behavior of well-characterized vinyl acetate–vinyl alcohol copolymers of similar composition and polymerization degree. The frequency–temperature superposition principle is fully applicable to the random copolymers, which demonstrate all expected relaxation states, whereas a divergence of the reduced dynamic moduli–frequency dependences is observed for the multiblock copolymers. In the latter case, the terminal zone is sensitive to the self-assembling of vinyl alcohol blocks into (depending on the copolymer composition) crystalline or amorphous microstructures. The monomer unit distribution particularly affects properties of the copolymer solutions in <i>N</i>,<i>N</i>-dimethylformamide (DMF). 5% solutions behave as simple viscoelastic liquids at 20 °C and show viscoplastic behavior at −20 °C, where more blocky chains are characterized by up to 4 orders of magnitude higher yield stress values. The multiblock copolymer solutions demonstrate a pronounced viscosity hysteresis in the heating–cooling cycle, being absent in the random copolymers. 10% solutions of multiblock copolymers are practically gelatinous even at room temperature. The observed effects are explained by examining the peculiarities of hydrogen bonding in vinyl acetate–vinyl alcohol copolymers using FTIR spectroscopy. The multiblock copolymers are characterized by stronger hydroxyl–hydroxyl H-bonds and greater fraction of interchain hydroxyl–acetyloxy H-bonds providing aggregation of chains and high viscosity of the corresponding samples, whereas the random copolymers more strongly interact with the residual solvent. Dynamic light scattering studies prove that the relaxation of concentration fluctuations is completely diffusive, being bimodal in the random copolymers and trimodal in the multiblock ones. The fast mode in the latter case demonstrates anomalous concentration behavior. In the dilute regime, up to very low concentrations, multiblock copolymer chains form stable aggregates, and this fact correlates with an unusual growth of the reduced viscosity in the corresponding rheological experiments