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Applied mathematics, Statistics, Probability
The paper introduces and discusses the evolution equation, and, based exclusively on this equation, considers random walk models for the time series available on the daily confirmed Covid-19 cases for different countries. It is shown that a conventional random walk model is not consistent with the current global pandemic time series data, which exhibits non-ergodic properties. A self-affine random walk field model is investigated, derived from the evolutionary equation for a specified memory function which provides the non-ergodic fields evident in the available Covid-19 data. This is based on using a spectral scaling relationship of the type 1/ωα where ω is the angular frequency and α ∈ (0, 1) conforms to the absolute values of a normalised zero mean Gaussian distribution. It is shown that α is a primary parameter for evaluating the global status of the pandemic in the sense that the pandemic will become extinguished as α → 0 for all countries. For this reason, and based on the data currently available, a study is made of the variations in α for 100 randomly selected countries. Finally, in the context of the Bio-dynamic Hypothesis, a parametric model is considered for simulating the three-dimensional structure of a spike protein which may be of value in the development of a vaccine.
Blackledge J.M. (2021) On the Evolution Equation for Modelling the Covid-19 Pandemic. In: Agarwal P., Nieto J.J., Ruzhansky M., Torres D.F.M. (eds) Analysis of Infectious Disease Problems (Covid-19) and Their Global Impact. Infosys Science Foundation Series. Springer, Singapore. https://doi.org/10.1007/978-981-16-2450-6_4