The use of dynamic models is essential in science and also in everyday life when we want to define or influence the relationships between quantities that vary in space/time. Dynamic nonlinearities cannot be ignored in a large part of practical problems. Within nonlinear systems, so-called nonnegative (positive) models play an important role in such applications where the state variables can naturally be represented in a nonnegative coordinates system with quantities such as pressure, concentration, absolute temperature, or composition. According to , "One is tempted to assert that positive systems are the most often encountered systems in almost all areas of science and technology, except electro mechanics ... ". Kinetic systems (also called chemical reaction networks) developed as a mathematical abstraction of dynamical models describing chemical transformations belong to the family of nonnegative systems, and they can be considered as universal descriptors of nonlinear dynamics [2,3]. It is interesting and useful that kinetic models can also be interpreted and applied in a stochastic discrete event context, equivalently, e.g. to Petri nets. In this contribution, two groups of related results are summarized. Firstly, optimization based methods are shown for computing possible reaction graph structures realizing given dynamics which also allows the design of feedback controllers for nonlinear systems . Secondly, the application of kinetic systems' theory will be illustrated for the analysis of compartmental models including (generalized) flow models originally obtained from the spatial discretization of partial differential equations , and epidemic models used for data reconstruction and prediction during the COVID-19 pandemics .
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