Successive waves of COVID 19: confinement effects on virus-prevalence with a mathematical model.

BACKGROUND: A pandemic outbreak of severe acute respiratory syndrome coronavirus 2 (COVID 19) incidence data are largely available online. Until August 17, COVID 19 has hit more than 22 million individuals all over the globe. So, it is urged to get clear information about the prevalence of the virus. Therefore, one can manipulate easily a suitable mathematical model to fit these published data. METHODS: We propose a mathematical model that considers the total population, in 25 countries, either infected by COVID 19 or confined (safe) during the period from November 17, 2019, to August 17, 2020. The model considers the total population as a complex number; the imaginary part is the number of infected individuals and the real part is the number of confined individuals. This classification combined with mathematical treatments leads to a transmission dynamics of the virus to be as wave-like motion. The virus can hit any country either by one wave or by successive waves (up to 11 waves). FINDINGS: We find net discrimination between the 25 countries investigated in this report. The immediate response to the first attack is a substantial parameter to determine whether the epidemic attack will be in one wave or it can be in successive waves. For example, the best case was such as individuals in China hit by one wave while the individuals in the USA were attacked by nine waves; it is the worst case all over the globe. In addition, the model differentiates between the daily reproduction numbers (Rd0) and the median reproduction number (R0). We have found that Rd0 decreases exponentially with time from high values down to zero at the wave maximum point; and R0 varies from a country to another. For example, the virus hit individuals in Germany in R0 = 1.39 (96% CI 1.01-3.87) and in the USA R0 = 3.81 (91% CI 1.71-5.15). We have found that twice the virus has hit both the USA and Iran. The great protestation of black matter lives in the USA and the great assemblage of the new Iranian year, on March 21, 2020, have been the cause of the second epidemic attack in both countries. INTERPRETATION: Our results show that COVID 19 transmission depends on the prompt reaction against the first viral-wave. The reaction depends on both the social behaviour of individuals and on the swift system-decision by the governmental decision-maker(s). The Chinese strictly follow the decision-maker and therefore the virus hit by only one wave; while in the USA, the system-decision was different and the American-responses were different, therefore ten waves followed the first wave.

Photocatalytic activity of V doped ZnO nanoparticles thin films for the removal of 2- chlorophenol from the aquatic environment under natural sunlight exposure.

Vanadium doped ZnO powders were used as precursors to deposit thin films of V(5+) incorporated ZnO nanoparticles on glass substrates by the pulsed laser deposition technique. The observed variations in Raman signals, visible region shift in the diffuse reflectance spectra along with a small shift in the (101) reflections of the X-ray diffraction (XRD) confirmed the insertion of V(5+) ions in ZnO lattice. No other additional reflection in the XRD results other than ZnO further endorsed the occupation of lattice positions by V entities rather than independent oxide formation. The asymmetric XPS peaks of Zn2p and V2p core levels confirmed the existence of both in the vicinity. The existence of minimal proportion of V(3+) along with V(5+) states varied the alteration of the oxidation states V in the synthetic route. The SEM images at various resolutions displayed the uniform distribution identical nanoparticles without the presence of additional phases in the deposited films. The SEM cross-section measurements revealed the uniform thickness of ∼90 nm of each film, whereas the surface studies of the films were performed by AFM. The as-synthesized films were tested for photocatalytic activity in sunlight illumination for the removal of 2-chlorophenol. The unique feature of the study was the estimation of the photocatalytic activity 20 ppm of 2-chlorophenol by exposing the low exposed area. The degradation of the substrate was measured by liquid phase UV-vis spectroscopy, whereas total organic carbon measurement revealed the mineralization of the substrate. The released Cl(-) ions were also measured by ion chromatography. The estimated flatband potentials and pHzpc values of the V doped materials, by Mott-Schottky analysis and zeta potential measurements respectively, were correlated with the photocatalytic activity. The kinetics of the photocatalytic degradation/mineralization process was estimated and results were correlated with the plausible mechanism.