This work provides a mathematical technique for analyzing and comparing infection dynamics models with respect to their potential long-term behavior, resulting in a hierarchy integrating all models. We apply our technique to coupled ordinary and partial differential equation models of SARS-CoV-2 infection dynamics operating on different scales, that is, within a single organism and between several hosts. The structure of a model is assessed by the theory of chemical organizations, not requiring quantitative kinetic information. We present the Hasse diagrams of organizations for the twelve virus models analyzed within this study. For comparing models, each organization is characterized by the types of species it contains. For this, each species is mapped to one out of four types, representing uninfected, infected, immune system, and bacterial species, respectively. Subsequently, we can integrate these results with those of our former work on Influenza-A virus resulting in a single joint hierarchy of 24 models. It appears that the SARS-CoV-2 models are simpler with respect to their long term behavior and thus display a simpler hierarchy with little dependencies compared to the Influenza-A models. Our results can support further development towards more complex SARS-CoV-2 models targeting the higher levels of the hierarchy.

In this work we characterize the set of persistent species in dynamical systems related to chemical reaction networks. Chemical reaction networks consist of a set of species and a set of reaction r...

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.

This review explores how intuitive processes drive innovation, which we define as novel ideas, inventions, or artistic creations that cannot be logically derived from existing knowledge or sensory data. Although intuitive processes are not yet fully recognized as a formal area of scientific research, this paper examines current approaches to their study and modeling. It highlights the necessity of integrating unconventional modeling methods with neuroscience to gain deeper insights into these processes. Key experimental studies investigating extrasensory abilities—such as remote viewing, precognition, and telepathy—are reviewed, emphasizing their potential relevance to innovation. We propose that combining these unconventional modeling approaches with insights from systems neurology can provide new perspectives on the neural mechanisms underpinning intuition and creativity. This review emphasizes the critical need for further research into intuitive processes to address complex global challenges. It calls for a more open, interdisciplinary approach to scientific inquiry, promoting the exploration of unconventional forms of knowledge generation and their neural correlates.

Background: The regulation of cellular proliferation and genomic integrity is controlled by complex surveillance mechanisms known as cell cycle checkpoints. Disruptions in these checkpoints can lead to developmental defects and tumorigenesis. Methods: To better understand these mechanisms, computational modeling has been employed, resulting in a dataset of 414 mathematical models in the BioModels database. These models vary significantly in detail and simulated processes, necessitating a robust analytical approach. Results: In this study, we apply the chemical organization theory (COT) to these models to gain insights into their dynamic behaviors. COT, which handles both ordinary and partial differential equations (ODEs and PDEs), is utilized to analyze the compartmentalized structures of these models. COT’s framework allows for the examination of persistent subsystems within these models, even when detailed kinetic parameters are unavailable. By computing and analyzing the lattice of organizations, we can compare and rank models based on their structural features and dynamic behavior. Conclusions: Our application of the COT reveals that models with compartmentalized organizations exhibit distinctive structural features that facilitate the understanding of phenomena such as periodicity in the cell cycle. This approach provides valuable insights into the dynamics of cell cycle control mechanisms, refining existing models and potentially guiding future research in this area.