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Viral infection model with diffusion and state-dependent delay: a case of logistic growth

Rezounenko, Alexander V. (2017)

Proceedings of Equadiff 14

We propose a virus dynamics model with reaction-diffusion and logistic growth terms, intracellular state-dependent delay and a general non-linear infection rate functional response. Classical solutions with Lipschitz in-time initial functions are investigated. This type of solutions is adequate to the discontinuous change of parameters due to, for example, drug administration. The Lyapunov functions approach is used to analyse stability of interior infection equilibria which describe the cases of...

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

Kateryna Fedoryshyna, Alexander Rezounenko (2021)

Mathematica Bohemica

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...

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