Structure and Hierarchy of Influenza Virus Models Revealed by Reaction Network Analysis

Abstract

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.

Structure and Hierarchy of SARS-CoV-2 Infection Dynamics Models Revealed by Reaction Network Analysis

“…Our method is an extension of that used in [ 19 ] to analyze Influenza A virus modeling. We will briefly describe our method for the example of the in-host ODE model from Almocera [ 1 ] (see Figure 1 ).…”

“…Finally, different models with different reaction networks can be analyzed, compared and related to each other in a hierarchy as it was done for Influenza-A virus (IAV) infections [ 19 ] and also incorporating the PDEs analysis [ 25 ].…”

“…Note that the Smith Influenza-A model is the only one that considers co-infection by bacteria X . For more information about the COT analysis of the Influenza-A infection models see [ 19 ].…”

“…The signature of a model gives a brief overview of its potential dynamical behavior, which allows for relating several models to each other and combining them in a hierarchy. Finally, we link the respective hierarchy of SARS-CoV-2 with that from Influenza A from [ 19 ]. In the Conclusions, we summarize our findings and the benefits of the technique applied herein.…”

Trends in mathematical modeling of host–pathogen interactions

“…Only a high investment is effective and leads to the global maximum. For further explanations, see section "Molecular mimicry and crypsis" and Lang et al [77] employed to study the dynamics of bacteria [19,88], fungi [79], viruses (for review, see [8,12,25,52,101,139]), and has also been applied to other areas such as cell division mechanisms (e.g., [53, 63, 65-67, 129, 130]).…”