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In this paper, a deterministic model characterizing the within-host infection of Hepatitis C virus (HCV) in intrahepatic and extrahepatic tissues is presented. In addition, the model also includes the effect of the cytotoxic T lymphocyte (CTL) immunity described by a linear activation rate by infected cells. Firstly, the non-negativity and boundedness of solutions of the model are established. Secondly, the basic reproduction number R 01 and immune reproduction number R 02 are calculated, respectively. Three equilibria, namely, infection-free, CTL immune response-free and infected equilibrium with CTL immune response are discussed in terms of these two thresholds. Thirdly, the stability of these three equilibria is investigated theoretically as well as numerically. The results show that when R 01 < 1 , the virus will be cleared out eventually and the CTL immune response will also disappear; when R 02 < 1 < R 01 , the virus persists within the host, but the CTL immune response disappears eventually; when R 02 > 1 , both of the virus and the CTL immune response persist within the host. Finally, a brief discussion will be given. [ABSTRACT FROM AUTHOR]

The aim of this work is to investigate the existence and uniqueness of μ-pseudo almost periodic (resp. μ-pseudo compact almost automorphic) weak solutions for the following partial functional differential inclusion: x ′ (t) + A x (t) ∋ f (t , x t) f o r t ∈ R , where A : H ⟶ 2 H is a strongly maximal monotone operator on a real Hilbert space H , f : R × C ⟶ H is a Stepanov μ-pseudo almost periodic (resp. μ-pseudo compact almost automorphic) function of class r, C = C ([ − r , 0 ] , H) is the Banach space of all continuous functions from [ − r , 0 ] to H and the history function x t is defined by x t (θ) = x (t + θ) for θ ∈ [ − r , 0 ]. Two examples are given for parabolic and subdifferential systems. [ABSTRACT FROM AUTHOR]

In this article, for a diffusive population model describing interaction of pioneer-climax species, we explore the issues of spreading speed, linear determinacy and traveling wave fronts. Applying the theory developed by Weinberger et al. [J. Math. Biol. 2002;45:183–218], we identify some ranges of model parameters within which, the model is shown to have a single spreading speed which is linearly determinate and coincides with the corresponding minimal speed for the traveling wave fronts connecting two relevant equilibria, one being a boundary equilibrium and the other being a coexistence equilibrium. [ABSTRACT FROM AUTHOR]