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Optimal strategies for achieving immune balance in a mathematical model of allergy treatmentстатья
- Авторы: Grigorieva E.V., Khailov E.N.
- Журнал: Pure and Applied Functional Analysis
- Том: 6
- Номер: 2
- Год издания: 2021
- Первая страница: 317
- Последняя страница: 351
- Аннотация: Allergy is immune disorder that changes the code in action of T-helper cells. It is known that people showing allergy symptoms have a predominant concentration of inflammatory Th2-cells than thosewithout symptoms. Our aim is to create realistic control models of allergy and find possible way to prevent its symptoms by optimal treatment.Firstly, on a given time interval, we considered and investigated a system of differential equations describing interaction between naiveT-helper cells, Th1- and Th2-cells, and of allergen. The model equilibria, their stability and bifurcation analysis are conducted. Secondly,three bounded controls reflecting the impact of drugs and other direct and indirect measures during anti-allergenic therapy are introduced intothis system. The bounded controls may reflect the types of treatment related to a) the intake of antihistamine that suppresses the dominanceof Th2-cells by blocking histamine receptors, b) stimulation of Th1-cells, c) isolation from the allergen or taking a drug inhibiting the release of histamine from mast cells. The objective of this study is to eliminate allergy symptoms by balancing Th1-Th2 immune cells and to minimizethe cost of the treatment. The results of analytical analysis and numerical calculations are presented. Optimal strategies leading to theminimization of the objective function and its interpretation and possible application to allergy treatment are discussed.
- Добавил в систему: Хайлов Евгений Николаевич