Department of Biological Sciences

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Author: search.filters.author.Dubey, Uma S.Subject: search.filters.subject.Virus dynamics model

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    Modeling the role of acquired immune response and antiretroviral therapy in the dynamics of HIV infection
    (Elsiever, 2018-02) Dubey, Uma S.; Dubey, Balram
    This paper deals with the study of a virus dynamics model in order to get better insights into HIV infection within the body. The model incorporates therapeutic modalities such as reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs). RTIs prevent viral replication/entry within the infected CD4 T cells while PIs block the virus assembly and thus further propagation and production of new virions. The proliferation of uninfected CD4 T cells has been assumed to be as full logistic growth term to capture the dynamics of HIV virus. The model also considers two important components of the acquired immune response, namely the cytotoxic T lymphocyte (CTL) immune response (self stimulation due to infection and stimulation due to infected cells have been considered) and antibody immune response. Critical threshold conditions for the existence of equilibrium points have been determined. We studied the analytical behavior of these equilibrium points locally as well as globally using Lasalle’s invariance principle and Lyapunov’s direct method. We explored the sensitivity of the therapeutic drugs on the model system. Further, the behavior of the proposed model system has been studied numerically through simulation tools.
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    Modeling the dynamics of viral–host interaction during treatment of productively infected cells and free virus involving total immune response
    (VUP, 2021) Dubey, Uma S.; Dubey, Balram
    Virus dynamics models are useful in interpreting and predicting the change in viral load over the time and the effect of treatment in emerging viral infections like HIV/AIDS, hepatitis B virus (HBV). We propose a mathematical model involving the role of total immune response (innate, CTL, and humoral) and treatment for productively infected cells and free virus to understand the dynamics of virus–host interactions. A threshold condition for the extinction or persistence of infection, i.e. basic reproductive number, in the presence of immune response (RI) is established. We study the global stability of virus-free equilibrium and interior equilibrium using LaSalle’s principle and Lyapunov’s direct method. The global stability of virus-free equilibrium ensures the clearance of virus from the body, which is independent of initial status of subpopulations. Central manifold theory is used to study the behavior of equilibrium points