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In this paper, we consider the combined effects of cytotoxic T lymphocyte (CTL) responses on the competition dynamics of two Simian immunodeficiency virus (SIV) strains model. One of strains concerns a relatively slowly replicating and mildly cytopathic virus in the early infection (SIVMneCL8), the other is faster replicating and more cytopathic virus at later stages of the infection (SIVMne170). It is shown that the global dynamics of the ordinary differential equations can be determined by several threshold parameters, and we prove the global stability of the equilibria by rigorous mathematical analysis. To account for a series of infection mechanism leading to viral production, we incorporate time delays in the infection term. Using the methods of constructing suitable Lyapunov functionals and LaSalle’s invariance principle, we obtain the sufficient conditions for the global attractiveness of infection-free equilibrium with both virus strains going extinct, single-infection equilibrium with one of two virus strains out-competing the other one and the two strains coexisting infection equilibrium. We establish that the intracellular delays can destabilize the single-infection equilibrium leading to Hopf bifurcation and periodic oscillations. We show that introduction of immune responses is responsible for the coexistence of two virus strains and the intracellular delays may alter the two-strain competition results. Numerical simulations are presented to illustrate the theoretical conclusions. [ABSTRACT FROM AUTHOR]

The mass action infection law, the most frequently used transmission process in the theoretical studies of disease dynamics, has been challenged in various ways. Hill type infection rate is supposed to be a better alternative to mass action law. In the first phase of this paper, we study a basic HIV model with Hill type infection rate. In the second phase, we modify our basic model with intracellular delay τ that measures the time between the first effective contact between a virus and a healthy CD4 + T cell and the latter becomes productively infective. Mathematical results like well-posedness, permanence, local stability and global stability of both the delayed and non-delayed systems are studied. It is observed that the endemic equilibrium is locally and globally asymptotically stable if the virus replication factor is greater than a threshold value and unstable otherwise. In the latter case, the disease-free steady state occurs and is proved to be globally asymptotically stable. Our simulation results shed different insights on drug therapy when various perturbations are given to the system. It is shown that multi-blockers drug therapy is more appropriate in the treatment of HIV patients in comparison to any mono-blocker drug therapy. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a mathematical model for HILV-I infection of CD4+ T-cells is investigated. The force of infection is assumed be of a function in general form, and the resulting incidence term contains, as special cases, the bilinear and the saturation incidences. The model can be seen as an extension of the model [Wang et al. Mathematical analysis of the global dynamics of a model for HTLV-I infection and ATL progression, Math. Biosci. 179 (2002) 207-217; Song, Li, Global stability and periodic solution of a model for HTLV-I infection and ATL progression, Appl. Math. Comput. 180(1) (2006) 401-410]. Mathematical analysis establishes that the global dynamics of T-cells infection is completely determined by a basic reproduction number . If , the infection-free equilibrium is globally stable; if , the unique infected equilibrium is globally stable in the interior of the feasible region. [Copyright &y& Elsevier]