Abstract
In this paper, we study the stability analysis of two within-host virus dynamics models with antibody immune response. We assume that the virus infects n classes of target cells. The second model considers two types of infected cells: (i) latently infected cells; and (ii) actively infected cells that produce the virus particles. For each model, we derive a biological threshold number R0. Using the method of Lyapunov function, we establish the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.
Highlights
Many mathematicians have proposed several mathematical models to describe the interaction between viruses and human target cells
We have studied two within-host virus dynamics models with antibody immune response and with n classes of target cells
We have investigated the global stability of the steady states of the model by using Lyapunov method and LaSalle’s invariance principle
Summary
Many mathematicians have proposed several mathematical models to describe the interaction between viruses (such as HIV, HCV, HBV, HTLV and CHIKV) and human target cells (see, e.g., [1–36]). The infected cells and free virus particles die at rates eI and rV, respectively. In 2017, Wang and Liu [36] presented a mathematical model for in host virus infection by considering a constant production rate of the B cells in addition to their proliferation rate. The model in Equations (1)–(4) assumes that the virus infects only one category of target cells. There are several models for viral infections that have included two categories of target cells (see, e.g., [38–47]). To model the virus dynamics with multiple categories of target cells, Elaiw [53]. Several mathematical models have been proposed which take the antibody immune response into account (see, e.g., [29–35]) These models have included one target cell population. The antibody immune response is considered where the population dynamics of the B cells is described by Equation (5). We construct Lyapunov function using the method of Korobeinikov [55]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
