| Abstract: |
| Allergy is an incurable immune disorder with symptoms that can be controlled by medication. Usually, if allergy occurs, there exists a disbalance in Th1-Th2 helper lymphocytes concentrations with an increased activity of Th2 helper cells. In this work, we created a nonlinear control model of allergy that describes the dynamics of naive helper cells, Th1 cells, Th2 cells, the allergen and medication intake. One of the ways to prevent allergic reaction, can be to find the way of balancing the concentrations of Th1 and Th2 lymphocytes. Using optimal control theory and Pontryagin maximum principle we stated and solved an optimal control problem and obtained the best optimal drug intake scenario that by balancing T helper cells appears to be less harmful for a hypothetical patient. |
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