Search

This paper proposes and analyzes an adaptive immunity HIV infection model. The model describes the interaction between healthy CD 4 + T cells, silent (latent) infected cells, active infected cells, free HIV particles, Cytotoxic T lymphocytes (CTLs) and antibodies. The healthy CD 4 + T cells can be infected when they are contacted by one of the following: (i) free HIV particles, and this is known as virus-to-cell (VTC) transmission (ii) silent infected cells, and we call this mode of infection as silent HIV-infected cell-to-cell (CTC) transmission, and (iii) active infected cells, and we call this mechanism active HIV-infected CTC transmission. The incidence rates of the healthy CD 4 + T cells with free HIV particles, silent infected cells, and active infected cells are given by general functions. Moreover, the production/proliferation and removal/death rates of all compartments are represented by general functions. The model is an improvement of the existing HIV infection models which have neglected the incidence between the silent infected cells and healthy CD 4 + T cells. We first show that the model is well-posed. Then, we show that the model has five equilibria and their existence are governed by five threshold parameters. Under a set of conditions on the general functions and the threshold parameters, we have proven the global asymptotic stability of all equilibria by using Lyapunov's method. We have illustrated the theoretical results via numerical simulations. We have studied the effect of CTC transmission on the dynamical behavior of the system. We have shown that inclusion of CTC transmission decreases the concentration of the healthy CD4 + T cells and increases the concentrations of the infected cells and free HIV particles. [ABSTRACT FROM AUTHOR]

• We propose a mathematical model for examining the consequence of adaptive immune responses to the viral mutation to control disease transmission. • We consider three populations, namely, the uninfected epithelial cells, infected cells, and the SARS-CoV-2 virus. • We also take into account combination drug therapy on the dynamics of COVID-19 and its effect. • We present a fractional-order model representing COVID-19/SARS-CoV-2 infection of epithelial cells. • Here we explore the effect of adaptive immune response using fractional order operator to monitor the memory on the cell-biological aspects. A novel coronavirus disease (COVID-19) appeared in Wuhan, China in December 2019 and spread around the world at a rapid pace, taking the form of pandemic. There was an urgent need to look for the remedy and control this deadly disease. A new strain of coronavirus called Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was considered to be responsible for COVID-19. Novel coronavirus (SARS-CoV-2) belongs to the family of coronaviruses crowned with homotrimeric class 1 fusion spike protein (or S protein) on their surfaces. COVID-19 attacks primarily at our throat and lungs epithelial cells. In COVID-19, a stronger adaptive immune response against SARS-CoV-2 can lead to longer recovery time and leads to several complications. In this paper, we propose a mathematical model for examining the consequence of adaptive immune responses to the viral mutation to control disease transmission. We consider three populations, namely, the uninfected epithelial cells, infected cells, and the SARS-CoV-2 virus. We also take into account combination drug therapy on the dynamics of COVID-19 and its effect. We present a fractional-order model representing COVID-19/SARS-CoV-2 infection of epithelial cells. The main aim of our study is to explore the effect of adaptive immune response using fractional order operator to monitor the influence of memory on the cell-biological aspects. Also, we have studied the outcome of an antiviral drug on the system to obstruct the contact between epithelial cells and SARS-CoV-2 to restrict the COVID-19 disease. Numerical simulations have been done to illustrate our analytical findings. [ABSTRACT FROM AUTHOR]

• A general adaptive immunity viral infection model with multiple delays is developed and rigorously analyzed. • Two routes of infection and multi-stages of infected cells have been incroporated. • Well-possedness of the model and existence of equilibria are established. • Global stability of the equilibria are established by means of Lyapunov functionals. This paper proposes and analyzes a viral infection model that characterizes the interactions of the viruses, susceptible host cells, n -stages of infected cells, B cells and CTL cells. We consider both virus-to-cell and cell-to-cell transmissions and n + 1 intracellular distributed time delays. The incidence rate of infection as well as the generation and removal rates of all compartments are described by general nonlinear functions. We derive five threshold parameters which determine the existence of the equilibria of the model under consideration. A set of conditions on the general functions has been established which is sufficient to investigate the global stability of the five equilibria of the model. The global asymptotic stability of all equilibria is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations of the model with specific forms of the general functions. Effect of antiviral treatment, time delays and cellular infection on the dynamical behavior of the system is addressed. [ABSTRACT FROM AUTHOR]