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As a preliminary overview, this work provides first a broad tutorial on the fluidization of discrete event dynamic models, an efficient technique for dealing with the classical state explosion problem. Even if named as continuous or fluid, the relaxed models obtained are frequently hybrid in a technical sense. Thus, there is plenty of room for using discrete, hybrid and continuous model techniques for logical verification, performance evaluation and control studies. Moreover, the possibilities for transferring concepts and techniques from one modeling paradigm to others are very significant, so there is much space for synergy. As a central modeling paradigm for parallel and synchronized discrete event systems, Petri nets (PNs) are then considered in much more detail. In this sense, this paper is somewhat complementary to David and Alla (2010). Our presentation of fluid views or approximations of PNs has sometimes a flavor of a survey, but also introduces some new ideas or techniques. Among the aspects that distinguish the adopted approach are: the focus on the relationships between discrete and continuous PN models, both for untimed, i.e., fully non-deterministic abstractions, and timed versions; the use of structure theory of (discrete) PNs, algebraic and graph based concepts and results; and the bridge to Automatic Control Theory. After discussing observability and controllability issues, the most technical part in this work, the paper concludes with some remarks and possible directions for future research.

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The coronavirus disease 2019 (COVID-19) pandemic caused by the new coronavirus (SARS-CoV-2) is currently responsible for more than 3 million deaths in 219 countries across the world and with more than 140 million cases. The absence of FDA-approved drugs against SARS-CoV-2 has highlighted an urgent need to design new drugs. We developed an integrated model of the human cell and SARS-CoV-2 to provide insight into the virus’ pathogenic mechanism and support current therapeutic strategies. We show the biochemical reactions required for the growth and general maintenance of the human cell, first, in its healthy state. We then demonstrate how the entry of SARS-CoV-2 into the human cell causes biochemical and structural changes, leading to a change of cell functions or cell death. A new computational method that predicts 20 unique reactions as drug targets from our models and provides a platform for future studies on viral entry inhibition, immune regulation, and drug optimisation strategies. The model is available in BioModels (https://www.ebi.ac.uk/biomodels/MODEL2007210001) and the software tool, findCPcli, that implements the computational method is available at https://github.com/findCP/findCPcli.