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"Математическо моделиране и числен анализ"

ще се състои на 27.07.2016 г., сряда, от 10:00 часа в зала 403 на Института по математика и информатика.

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Mathematical model for the dynamics of the autoimmune disease alopecia areata in cycling hair follicles

 ще изнесе Dr. Atanaska Dobreva, Department of Mathematics, Florida State University.

Резюме. Alopecia areata is an autoimmune condition which causes distinct patterns of hair loss. The disease development mechanisms are still not completely understood, and treatment is often difficult. Hair follicles are organs that constantly cycle through phases of growth, regression, and rest. A main feature of alopecia areata is that it interrupts and makes the growth stage very short. We first construct a model of ordinary differential equations to describe how the condition develops over time in a small cluster of homogeneous growing follicles. The model incorporates interactions between hair follicles and the immune system in accordance with the immune privilege collapse hypothesis for disease pathogenesis. As a next step, we elaborate the dynamical system by including the underlying hair cycle and provide simulations for states of health, disease, and treatment. In addition, we apply parameter sensitivity analysis to determine how the processes reflected in the model influence the growth phase length.