@MASTERSTHESIS\{IMM2016-06933,
    author       = "E. O. Bangsgaard",
    title        = "Mathematical Modelling of the Dynamic Role of the {HPA} Axis in the Immune System",
    year         = "2016",
    school       = "Technical University of Denmark, Department of Applied Mathematics and Computer Science",
    address      = "Richard Petersens Plads, Building 324, {DK-}2800 Kgs. Lyngby, Denmark, compute@compute.dtu.dk",
    type         = "",
    note         = "Supervisor: Poul G. Hjorth, pghj@dtu.dk, {DTU} Compute",
    url          = "http://www.compute.dtu.dk/English.aspx",
    abstract     = "The aim of the thesis is to formulate a model describing the dynamic role of the Hypothalamic-Pituitary-Adrenal (HPA) axis in the immune system. The two subsidiary goals of the thesis are the formulation of two models describing the acute inflammatory response and the dynamics of the hormones of the {HPA} axis, respectively. All three models are compared to available data.

In the first part of the thesis, information of existent models in the literature, describing the acute inflammatory response is collected after which a minimal, mathematical model is formulated. The model is a reduced and modified version of a model proposed by Roy et al. (2009). The model is compared to the model proposed by Roy et al. (2009) and data measured in rats. Existence and uniqueness of the solutions to the system together with the existence of an attracting trapping region is proved. The model is simulated for rats exposed to three different doses of the endotoxin (lipopolysaccharides, {LPS}).

The second part of the thesis deals with the formulation of a mathematical model describing the interactions of the hormones in the {HPA} axis. The model is formulated on the basis of a model proposed by Ottesen (2011) and the work accomplished by Rasmussen et al. (2015). Existence and uniqueness of the solutions to the system together with the existence of an attracting trapping region is proved. A good approximation of the model is fitted convincingly to {ACTH} and cortisol concentration data from eight individuals.

In the last part of the thesis, biological reasoning and mathematical modelling is used to formulate a model describing the dynamical role of the {HPA} axis in the immune system, by coupling the two studied models. The parameters are estimated using concentration data of {TNF-}a, {ACTH} and cortisol after injection of endotoxin. Finally, the model is compared to a model recently proposed by Malek et al. (2015) and simulated for different dosing and timing scenarios."
}