The COVID-19 virus outbreak has affected most of the world in 2020. This paper deals with artificial intelligence (AI) methods that can address the problem of predicting scale, dynamics and sensitivity of the outbreak to preventive actions undertaken with a view to combatting the epidemic. In our study, we developed a cellular automata (CA) model for simulating the COVID-19 disease spreading. The enhanced infectious disease dynamics (Susceptible, Exposed, Infectious, and Recovered) model was applied to estimate the epidemic trends in Poland, France, and Spain. We introduced new parameters into the simulation framework which reflect the statistically confirmed dependencies such as age-dependent death probability, a different definition of the contact rate and enhanced parameters reflecting population mobility. To estimate key epidemiological measures and to predict possible dynamics of the disease, we juxtaposed crucial CA framework parameters to the reported COVID-19 values, e.g. length of infection, mortality rates and the reproduction number. Moreover, we used real population density and age structures of the studied epidemic populations. The model presented allows for the examination of the effectiveness of preventive actions and their impact on the spreading rate and the duration of the disease. It also shows the influence of structure and behavior of the populations studied on key epidemic parameters, such as mortality and infection rates. Although our results are critically dependent on the assumptions underpinning our model and there is considerable uncertainty associated with the outbreaks at such an early epidemic stage, the obtained simulation results seem to be in general agreement with the observed behavior of the real COVID-19 disease, and our numerical framework can be effectively used to analyze the dynamics and efficacy of epidemic containment methods.
Abstract. The influence of a space-dependent random mass density field on the development of solar p-modes is investigated using analytical and numerical means. Using a perturbative approach, which is valid for a weak random field and small amplitude waves, we derive a linear dispersion relation whose solutions correspond to attenuated oscillations. The real part of the frequency of these oscillations exceeds the one of waves propagating in a medium without random density. We give an interpretation of the "unphysical" nature of the frequency shift and of the amplitude attenuation which is similar to Landau damping. The analytical findings are compared with the results of the numerical solution of a model wave equation. We find that, for weak random fields and for wavelengths which are a few times the correlation length of the random density fluctuations, numerical results agree with the analytical theory. Two practical formulas for deriving the correlation spectrum of the random density field from observations are also given.
Abstract. The influence of a space-dependent random mass density field on the development of solar p-modes is investigated using analytical and numerical means. Using a perturbative approach, which is valid for a weak random field and small amplitude waves, we derive a linear dispersion relation whose solutions correspond to attenuated oscillations. The real part of the frequency of these oscillations exceeds the one of waves propagating in a medium without random density. We give an interpretation of the "unphysical" nature of the frequency shift and of the amplitude attenuation which is similar to Landau damping. The analytical findings are compared with the results of the numerical solution of a model wave equation. We find that, for weak random fields and for wavelengths which are a few times the correlation length of the random density fluctuations, numerical results agree with the analytical theory. Two practical formulas for deriving the correlation spectrum of the random density field from observations are also given.
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