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In this book particular attention was paid to the study of new dynamic models based on modifications of existing ones, with the interesting and insufficiently studied hypothesis of a possible "polynomial variable transfer" and their use in the analysis of up-to-date and still insufficiently analyzed world data - "Corona Virus" COVID-19 (sickness, mortality, etc.). We did not neglect the known statistics and analyzes of the spread of previous epidemics SARS-CoV, Cholera, Ebola and others. As a result of these studies, a coherent methodology for analysis and modeling of a predictive model of the distribution of COVID-19 in Bulgaria was formed. Due to the fact that the "forecast data" (worldwide) were highly exponential in nature, and that the existing epidemiological mathematical models do not give reliable forecast results (due to the many unknowns accompanying this pandemic, the pointless study of heavy stratified systems from differential equations and research for stability of components of its solution ...) we stopped at a modification of the classic Half-Logistic model with the so-called by us - "Polynomial Variable Transfer".