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.

Spectroscopic ellipsometry of Zn(1-x)Cu(x)O thin films based on a modified sol-gel dip-coating technique.

Nanocrystalline Zn(1-x)Cu(x)O thin films (x=0, 0.01, 0.02, 0.03, 0.04 and 0.05) were synthesized by sol-gel dip-coating technique on a quartz substrate. These films were annealed at 350°C for 2 h. The X-ray diffraction showed a hexagonal crystal structure with high intensity peak for the (002) reflection plane indicating preferential growth along the c-axis of the crystal lattice. The peak position related to the (002) peak was shifted as a result of the copper ion incorporation, confirming the interstitial substitution of the zinc ions by the copper ions. This interstitial substitution leads to a decrease of an average crystallite size and lattice constants and an increase of the micro-strain up to 2 at.% of the copper amount. The surface morphology was explored by scanning electron microscopy which confirmed the homogenous distribution of nanoparticles in the deposited films along the quartz substrates. The energy dispersion X-ray spectroscopy revealed absence of impurities in the as-deposited films. The high resolution electron microscopy and selected area electron diffraction depicted that the films have polycrystalline nature. The film thickness and optical constants of the Zn(1-x)Cu(x)O thin films were estimated by fitting the spectroscopic ellipsometric data (ψ and Δ) using three different models. The refractive index was fitted using harmonic oscillator model from which the oscillator and the dispersive energies were found. The dielectric constant, dielectric loss, energy loss functions were also determined.