MATHEMATICAL MODELING OF CHEMICAL SIGNALS IN INFLAMMATORY PATHWAYS

Mechanistic, autonomous, ordinary differential equations represent a powerful way to crystalize and reproduce the dynamics of complex, nonlinear interactions. Design and calibration of these models, however, represent a challenge to the construction of fully validated models. Various parameter techniques are employed, evaluated and improved upon for the purpose of fitting in a nonlinear setting. Cells communicate with other cells and their environment by producing and receiving chemical signals. In the context of pathogen response, these signals regulate how the collective of cells reacts. One such undifferentiated response to signal is known as inflammation, and it is an important mediator of pathogen clearance as well as tissue healing; however, it also has the potential to damage the surrounding tissue when regulatory mechanisms break down. Models are built using the mechanisms of these interactions to produce a high level effect, and to predict what measures can be taken, as in influenza, to prevent dysregulation. The models developed for inflammatory response first take into consideration the production and reception of immune factors, cytokines, and then put these mechanisms into the context of tissue level response to external signals and internal signals in the form of system damage. This is incorporated into a nonlinear model of immune response to Influenza A Virus, with innate, adaptive, and humoral immunity components. The model is calibrated against data for both sublethal and lethal initial dosages. A model of mosquito response to exogenous cytokine as immune stimulation is also explored. Successful model fitting using Metropolis-Hastings methods yields multi-objective results for nonlinear deterministic models