Influenza A virus is recognized today as one of the most challenging viruses that threatens both human and animal health worldwide. Understanding the control mechanisms of influenza infection and dynamics is crucial and could result in effective future treatment strategies. Many kinetic models based on differential equations have been developed in recent decades to capture viral dynamics within a host. These models differ in their complexity in terms of number of species elements and number of reactions. Here, we present a new approach to understanding the overall structure of twelve influenza A virus infection models and their relationship to each other. To this end, we apply chemical organization theory to obtain a hierarchical decomposition of the models into chemical organizations. The decomposition is based on the model structure (reaction rules) but is independent of kinetic details such as rate constants. We found different types of model structures ranging from two to eight organizations. Furthermore, the model’s organizations imply a partial order among models entailing a hierarchy of model, revealing a high model diversity with respect to their long-term behavior. Our methods and results can be helpful in model development and model integration, also beyond the influenza area.

The restrained captive domination number (RCDN), denoted by γ Rca ( G ) , is a new definition of domination number in graphs introduced in this article. If D is a captive dominating set and G [ V − D ] has no isolated vertex, then D is a restrained captive dominating set (RCDS) of graph G . Furthermore, some properties, theorems, and propositions are determined. The inverse RCDN is introduced too. The RCDN in complement graphs is discussed. Finally, the RCDS of some graphs is determined. We have explained that if the graph has pendent vertex, then it has no RCDN.