New methods for proving the existence and stability of periodic solutions in singularly perturbed delay systems

2007 ◽  
Vol 259 (1) ◽  
pp. 101-127 ◽  
Author(s):  
A. Yu. Kolesov ◽  
E. F. Mishchenko ◽  
N. Kh. Rozov
Keyword(s):  
Periodic Solutions ◽  
Singularly Perturbed ◽  
Delay Systems ◽  
New Methods ◽  
Existence And Stability

scholarly journals Modelling chronic hepatitis B using the Marchuk-Petrov model

2021 ◽  
Vol 2099 (1) ◽  
pp. 012036
Author(s):  
M Yu Khristichenko ◽  
Yu M Nechepurenko ◽  
D S Grebennikov ◽  
G A Bocharov
Keyword(s):  
Time Delay ◽  
Hepatitis B ◽  
Immune Responses ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Stable Periodic ◽  
Delay Differential ◽  
Parameter Values

Abstract Systems of time-delay differential equations are widely used to study the dynamics of infectious diseases and immune responses. The Marchuk-Petrov model is one of them. Stable non-trivial steady states and stable periodic solutions to this model can be interpreted as chronic viral diseases. In this work we briefly describe our technology developed for computing steady and periodic solutions of time-delay systems and present and discuss the results of computing periodic solutions for the Marchuk-Petrov model with parameter values corresponding to the hepatitis B infection.

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