Mathematica Bohemica, Vol. 146, No. 1, pp. 91-114, 2021


Viral in-host infection model with two state-dependent delays: stability of continuous solutions

Kateryna Fedoryshyna, Alexander Rezounenko

Received Febuary 23, 2019.   Published online March 5, 2020.

Abstract:  A virus dynamics model with two state-dependent delays and logistic growth term is investigated. A general class of nonlinear incidence rates is considered. The model describes the in-host interplay between viral infection and CTL (cytotoxic T lymphocytes) and antibody immune responses. The wellposedness of the model proposed and Lyapunov stability properties of interior infection equilibria which describe the cases of a chronic disease are studied. We choose a space of merely continuous initial functions which is appropriate for therapy, including drug administration.
Keywords:  evolution equation; state-dependent delay; Lyapunov stability; virus infection model
Classification MSC:  93C23, 34K20, 97M60


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Affiliations:   Kateryna Fedoryshyna, Intego Group LLC, 23 Bahhovutivska Str., Kyiv 04107, Ukraine, e-mail: fedoryshyna.kateryna@gmail.com; Alexander Rezounenko (corresponding author), V. N. Karazin Kharkiv National University, 4 Svobody Sqr., Kharkiv 61022, Ukraine, e-mail: rezounenko@gmail.com


 
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