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Reaction networks are well-known for a number of dynamical processes of natural phenomena, such as radioactive exponential decay, tumor growth, epidemics, population dynamics, to name a few. The subject of this book is extension of some classes of sigmoidal functions generated by reaction networks in the general case. The book contain some interesting results on the following topics: Some nonstandard differential model with applications to the population dynamics; Verhulst, Half-Logistic and Gompertz growth models with polynomial variable transfer; cut function of the second class with application to ''Approximation with restrictions''. The book also examines new mathematical models for controlling and approximating the data ''Corona Virus-Total Deaths-2020'' and data ''Corona Virus--Total Cases-2020''.