Application of Differential Equations with Variable Delay in the Compartmental Models of Living Systems Научная публикация
| Журнал |
Journal of Applied and Industrial Mathematics
ISSN: 1990-4789 , E-ISSN: 1990-4797 |
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| Вых. Данные | Год: 2021, Том: 15, Номер: 3, Страницы: 466-482 Страниц : 17 DOI: 10.1134/S1990478921030091 | ||
| Ключевые слова | asymptotic stability; compartmental model; HIV-1 infection; linear differential equations with variable delay; nonsingular M-matrix; positive system; Wazewski equations | ||
| Авторы |
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| Организации |
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Информация о финансировании (1)
| 1 | Российский фонд фундаментальных исследований | 18-29-10086 |
Реферат:
Abstract: We present some approach to the construction of compartmental models of living systemsthat bases on linear nonautonomous differential equations with variable delay. The differentialequations of the dynamics of the numbers of the living system elements located in compartmentsare supplemented by a set of linear integral equations that reflect the dynamics of the number ofelements in the process of movement between compartments. The model contains somenonnegative initial data that takes into account the prehistory of the dynamics of the number ofthe living system elements. We establish the existence, uniqueness, and nonnegativity of solutionsof the model on the semi-axis and estimate the upper and lower bounds for the sum of allcomponents of the solution. The exponential stability of the trivial solution of the system ofdifferential equations is shown in the absence of an external source of influx of the living systemelements. We consider some compartmental model of the dynamics of HIV-1 infection in the bodyof an infected person. To study the model, we use the properties of nonsingular M-matrices andestablish the conditions for exponential and asymptotic stability of the trivial solution of themodel. The obtained relations are interpreted as the conditions for eradication of HIV-1 infectiondue to nonspecific factors of the human body protection. © 2021, Pleiades Publishing, Ltd.
Библиографическая ссылка:
Pertsev N.V.
Application of Differential Equations with Variable Delay in the Compartmental Models of Living Systems
Journal of Applied and Industrial Mathematics. 2021. V.15. N3. P.466-482. DOI: 10.1134/S1990478921030091 Scopus OpenAlex
Application of Differential Equations with Variable Delay in the Compartmental Models of Living Systems
Journal of Applied and Industrial Mathematics. 2021. V.15. N3. P.466-482. DOI: 10.1134/S1990478921030091 Scopus OpenAlex
Идентификаторы БД:
| Scopus: | 2-s2.0-85126370453 |
| OpenAlex: | W4232195465 |