In this article we combine the novel mathematical concept of a hierachical hypergraph with the idea of ruled-based stochastic processes. The hierachical hypergraph structural concept is immensely important when dealing with the mathematical abstraction of the idea of 'multi-scale composition' in general. Classical graphs as systems descriptions, and therefore also network theory, lack the ability to describe the structure of multi-scale systems. However, hierachical hypergraphs can describe such a system completely in a consistent way. A typical multi-scale description starts from the lowest level, the basic system components, like atoms in chemistry, or individuals in a sociological or epidemiological context. As upper levels in this hierachy, we can then define molecules, molecules of molecules (chemistry, biochemistry), or groups, and groups of groups (ecology, sociology, economy) etc. The hierachical hypergraph covers the static description of such a multi-scale complex system, but not the dynamical part, the time evolution. For the time evolution we define a process (both deterministic and stochastic) which is event-driven, and defined for each level of the hierachy. A typical such event structure are collision events, leading to classical reaction kinetics for chemical systems in case of a single level hierachy only. But we also consider deterministic updates, like a daily update of information, like stock prices, for example, or a mix of updates for different rules.
We discuss also some applications, mostly those related to novel models of the Covid-19 pandemic.