Behavior of Trajectories of a Four-Dimensional Model of HIV Infection

Capa

Citar

Texto integral

Acesso aberto Acesso aberto
Acesso é fechado Acesso está concedido
Acesso é fechado Somente assinantes

Resumo

A model of interaction between the human immunodeficiency virus and the human immune system is considered. Equilibria in the state space of the system and their stability are analyzed, and the ultimate bounds of the trajectories are constructed. It has been proved that the local asymptotic stability of the equilibrium corresponding to the absence of disease is equivalent to its global asymptotic stability. The loss of stability is shown to be caused by a transcritical bifurcation.

Sobre autores

A. Kanatnikov

Bauman Moscow State Technical University, Moscow, 105005, Russia

Email: skipper@bmstu.ru
Москва, Россия

O. Tkacheva

Bauman Moscow State Technical University, Moscow, 105005, Russia

Autor responsável pela correspondência
Email: tkolga17@gmail.com
Москва, Россия

Bibliografia

  1. Kirschner D., Lenhart S., Serbin S. Dynamics of HIV infection of CD4+T cells // Math. Biosci. 1993. V. 114. P. 81-125.
  2. Perelson A.S., Nelson P.W. Mathematical analysis of HIV-1 dynamics in vivo // SIAM Rev. 1999. V. 41. P. 3-44.
  3. Elaiw A.M. Global properties of a class of HIV models // Nonlin. Anal. Real World Appl. 2010. V. 11. P. 2253-2263.
  4. Hadjiandreou M., Conejeros R., Vassiliadis V.S. Towards a long-term model construction for the dynamic simulation of HIV infection // Math. Biosci. Eng. 2007. V. 4. P. 489-504.
  5. De Leenheer P., Smith H.L. Virus dynamics: a global analysis // SIAM J. Appl. Math. 2003. V. 63. P. 1313-1327.
  6. Nowak M., May R.M. Virus Dynamics: Mathematical Principles of Immunology and Virology. Oxford, 2000.
  7. Dehghan M., Nasri M., Razvan M.R. Global stability of a deterministic model for HIV infection in vivo // Chaos, Solitons and Fractals. 2007. V. 34. P. 1225-1238.
  8. Kirschner D., Lenhart S., Serbin S. Optimal control of the chemotherapy of HIV // J. Math. Biol. 1997. V. 35. P. 775-792.
  9. Малинецкий Г.Г. Математические основы синергетики. М., 2017.
  10. Крищенко А.П. Локализация инвариантных компактов динамических систем // Дифференц. уравнения. 2005. V. 41. № 12. С. 1597-1604.
  11. Канатников А.Н., Крищенко А.П. Инвариантные компакты динамических систем. М., 2011.
  12. Крищенко А.П. Поведение траекторий автономных систем // Дифференц. уравнения. 2018. Т. 54. № 11. С. 1445-1450.
  13. Халил Х.К. Нелинейные системы. М.; Ижевск, 2009.
  14. Starkov K.E., Kanatnikov A.N. Eradication conditions of infected cell populations in the 7-order HIV model with viral mutations and related results // Math. 2021. V. 9. Art. 1862.
  15. Kanatnikov A.N., Krishchenko A.P. Iteration procedure of localization in a chronic Leukemia model // AIP Conf. Proc. 2020. Art. 210004-1.
  16. Четаев Н.Г. Устойчивость движения. М., 1965.

Arquivos suplementares

Arquivos suplementares
Ação
1. JATS XML
Baixar

Declaração de direitos autorais © Russian Academy of Sciences, 2023