A mathematical model of COVID-19 pandemic based on a two-parameter nonlinear first-order ordinary differential equation with retarded time argument is proposed. The model uses two parameters: the time of possible dissemination of infection by an individual virus carrier and the probability of contamination of a healthy population member in a contact with an infected one per unit time. The parameters can be given functions of time, which is particularly important in describing multi-peak pandemic. The model is applicable to any community (country, city, etc.) and provides an optimal balance between the adequate description of a pandemic inherent in the known SIR model and the relative simplicity for practical estimates. Examples of the model application are in qualitative agreement with the dynamics of COVID-19 pandemic.
The calculations of vibration-rotation bound states and new metastable states of a diatomic beryllium molecule important for laser spectroscopy are presented. The problem is solved using the potential curve and the authors' software package that implements the iteration Newton method and the high-accuracy finite element method. The efficiency of the proposed approach is demonstrated by calculating vibration-rotation bound states and, for the first time, rotation-vibration metastable states with complex- valued energy eigenvalues (with negative imaginary parts of the order of (10-20 ÷ 6) cm-1) in a diatomic beryllium molecule. The existence of these metastable states is confirmed by calculating the corresponding scattering states with real-values resonance energies.
The computational scheme and calculation results of bound, metastable and Rydberg states of atomic and molecular systems important for laser spectroscopy are presented. The solution to the problem is performed using the authors' software package (see program libraries of the Computer Physics Communications journal and of the Joint Institute for Nuclear Research) that implement the high-accuracy finite element method. The FORTRAN procedure of matching tabulated potential functions with van der Waals asymptotic potential using interpolation Hermite polynomials which provides continuity of both the function itself and its derivative is presented. The efficiency of the proposed approach is demonstrated by calculated for the first time sharp metastable states with complex eigen-energies in a diatomic beryllium molecule and weakly bound Rydberg states of antiprotonic helium atom.
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