Corrigendum: Multiplicity of Mathematical Modeling Strategies to Search for Molecular and Cellular Insights into Bacteria Lung Infection

Review of Mathematical Modeling of the Inflammatory Response in Lung Infections and Injuries

“…Mathematical modeling addresses scales that include subcellular and molecular interactions, communication between individual cells, interaction between various cell types and other signals at the tissue level, up to host and population levels. Various types of interactions within the immune system can be modeled using mathematical techniques, providing predictions and simulations for real-life scenarios and suggesting interventions, including development and testing of new personalized treatments [62,63]. Figure 1 gives an overview of the immune response in the lungs and highlights the mathematical modeling methods used to research diseases that trigger lung inflammation.…”

“…The model can be calibrated by fitting to time series data. A variety of mathematical and computational techniques have been developed for ODE models, including uncertainty and sensitivity analysis, optimal control methods, bifurcation analysis, and parameter estimation and identifiability [62,65].…”

“…These agents interact on a defined two-or three-dimensional space based on a set of rules informed by the behavior of the biological system. The stochastic component is a strength of these types of models, since deterministic models such as ODEs and PDEs may lose accuracy when the molecules or cells being modeled have low total counts and randomness effects their interaction rates [62]. Using a set of simple rules, highly complex behavior can emerge.…”

“…Boolean models may be pruned to exclude nodes and interactions that are discovered to be unimportant by the data and can incorporate multiple scales. Boolean models do not include spatial dynamics and do not capture non-linearities well [62,74]. Methods have been developed to analyze these large signaling networks.…”

“…Mathematical research of the effects of aging on the immune system, coinfections, and use of vaccinations could improve the treatment of influenza. Complex mechanisms such as activation of different phenotypes of immune cells like macrophages should be studied further, as well as the positive and negative feedback loops that, when dysregulated, can exacerbate inflammation or contribute to the reappearance of infection [62]. ABMs, "omics" data, systems-based approaches, and high-performance computing have been suggested for future modeling efficacy [98,109,112].…”