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This article aims to study a hepatitis B virus (HBV) infection model incorporating two nonlinear incidences and spatial diffusion in capsids, virus, and cytotoxic T lymphocyte (CTL) immune response. Three equilibria which are infection-free, immune-free, and infection with CTL immunity are calculated under rational assumptions. Furthermore, two reproduction numbers are verified to assert the global stability of the HBV model. In the end, the theoretical results on HBV dynamics are further illustrated by performing numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behaviors of a multiple delayed HIV-1 infection model which describes the interactions of humoral, cytotoxic T lymphocyte (CTL) immune responses, and two modes of transmission that are the classical virus-to-cell infection and the direct cell-to-cell transmission are investigated. The model incorporates three delays, including the delays of cell infection, virus production and activation of immune response. We first prove the well-posedness of the model, and calculate the biological existence of equilibria and the reproduction numbers, which contain virus infection, humoral immune response, CTL immune response, CTL immune competition, and humoral immune competition. Further, the threshold conditions for the local and global stability of the equilibria for infection-free, immune-free, antibody response, CTL response, and interior are established by utilizing linearization method and the Lyapunov functionals. The existence of Hopf bifurcation with immune delay as a bifurcation parameter is investigated by using the bifurcation theory. Numerical simulations are carried out to illustrate the theoretical results and reveal the effects of some key parameters on viral dynamics. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behaviors for a diffusive virus infection model with two general nonlinear incidence functions, CTL immune impairment and discrete delays, are investigated. Cell-to-cell transmission plays a more important role in virus spreading in addition to virus-to-cell infection. Nonnegativity and boundcedness properties of the solutions are proven to show the well-posedness of the model. Five reproduction numbers are calculated and verified to be thresholds determining the global properties of the virus model. A significant impact of cell-to-cell transmission is that they increase the basic reproduction number. If one neglects either the cell-to-cell transmission or virus-to-cell infection, the basic reproduction number of the model is underevaluated. Numerical simulations are carried out to illustrate the dynamical behavior of the model. [ABSTRACT FROM AUTHOR]

Letandbe two nests withandcomplemented inandwheneverand, respectively. Assume thatis a unital additive surjection. In this paper, all additive mapspreserving commutativity up to a factor() in both directions (i.e.satisfiesif and only iffor all) are characterized. [ABSTRACT FROM AUTHOR]

Abstract: Let be a nest algebra associated with the nest on a (real or complex) Banach space . Assume that every is complemented whenever . Let be an additive map. It is shown that the following three conditions are equivalent: (1) is derivable at zero point, i.e., whenever ; (2) is Jordan derivable at zero point, i.e., whenever ; (3) has the form for some additive derivation and some scalar . It is also shown that is generalized derivable at zero point, i.e., whenever , if and only if is an additive generalized derivation. Finer characterizations of above maps are given for the case . [Copyright &y& Elsevier]

Abstract: Let and be nest algebras associated with the nests and on Banach Spaces. Assume that and are complemented whenever and . Let be a unital additive surjection. It is shown that preserves Jordan zero-products in both directions, that is , if and only if is either a ring isomorphism or a ring anti-isomorphism. Particularly, all unital additive surjective maps between Hilbert space nest algebras which preserves Jordan zero-products are characterized completely. [Copyright &y& Elsevier]

In this paper, the dynamical behaviors for multiple delayed latent virus model with virus-to-cell infection and cell-to-cell transmissions and humoral immunity are investigated. The virus-to-cell and cell-to-cell incidence rates are modeled by general nonlinear functions. The basic reproduction number R 0 and the humoral immune response number R 1 are calculated and proved to be threshold conditions determining the local and global properties of the virus model. The existence of Hopf bifurcation with immune delay as a bifurcation parameter is presented, and the effects of some key parameters on viral dynamics are revealed by numerical simulations. [ABSTRACT FROM AUTHOR]

No abstract available. [ABSTRACT FROM AUTHOR]