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Given that HIV/AIDS infection is characterized by long and variable periods of infectiousness, variable infectivity, and age heterogeneity, this work focuses on the global behavior of a PDE HIV/AIDS model structured by ages of susceptibility, treatment, and multi-stage infection. Local stability of the model is demonstrated. Its uniform persistence is ingeniously solved. Particularly, global asymptotic stability of unique positive equilibrium is addressed by a concise method in which the highlight lies in determining the 'kernel function' in the Lyapunov functional to derive the semi-negative definiteness of its time derivative. Numerical experiments are also shown to reinforce our theoretical results. These results can contribute to a better understanding of the impacts of class age on the evolution of AIDS in a population and inform the development of AIDS prevention strategies. [ABSTRACT FROM AUTHOR]

As the prevalence of viral infection in body, human T‐cell leukemia virus type 1 (HTLV‐1) is receiving increasing attention. Research on the corresponding virus models is of great significance to tackle the challenges of understanding HTLV‐1 development and treatment. This paper focuses on the dynamic analysis for a stochastic model with nonlinear cytotoxic T lymphocyte (CTL) response, which is driven by Ornstein–Uhlenbeck (OU) process to model the progression of HTLV‐1 in vivo. Rich dynamic behaviors such as the extinction of infected CD4+ T cells (ITCs), stationary distribution (SD), probability density, and finite‐time stability (FTS) of the model are established to reveal the interaction of cell populations. The optimal therapeutic strategy based on the cost‐benefit viewpoint is further obtained. Finally, illustrative numerical simulations are represented to corroborate the effectiveness of treatment and the ambient perturbation's impact that strengthening the noise strength can lead to rapid virus clearance. [ABSTRACT FROM AUTHOR]

It is beyond dispute that cytotoxic T-lymphocytes (CTLs) exert a vital function in the host's antiviral defense mechanism. With the idea of the above factor and the logistic proliferation of CD4 + T-cells, we establish a HTLV-I (human T-cell leukemia virus type-I) mathematical model. First, two threshold parameters ℛ 0 and ℛ c (the basic reproduction numbers for viral infection and CTL immune response, respectively) are obtained. Second, sufficient criteria for local and global asymptotic stabilities of the feasible equilibria of the model are deduced, respectively. Third, the sensitivity analyses of ℛ 0 and ℛ c are performed to better understand the effective strategies for HTLV-I infection. Finally, not only numerical simulations are given to illustrate the stability conclusions, but also the biological significance is stated. [ABSTRACT FROM AUTHOR]

Achieving high strength and ductility for Ti alloys and their composites has been a key objective and also a great challenge for their engineering applications. Herein, we designed TiC/(TC18 + TC4) composites with bionic and heterogeneously lamella structures, achieving an exceptional combination of high strength and ductility. This is attributed to the formation of alternative layers of TC18-coarse grains and TC4-fine grains with TiC precipitated at their interfaces. Plastic incompatibility of these three-phases produces significant hetero-deformation-induced hardening, induced by mutual interactions of heterogeneous grains and TiC precipitates, as well as activation of extensive < c + a > slip groups. An optimal yield strength of ∼ 1168 MPa and a uniform elongation of ∼ 6% have been achieved, which are much higher than those of the TC4 matrix (i.e. ∼919 MPa and ∼2%). This study provides a new strategy for composite designs to overcome the trade-off dilemma for strength-ductility. [ABSTRACT FROM AUTHOR]

This paper is devoted to proposing a mathematical model in order to explore the dynamics of HTLV-Ⅰ (human T-cell leukemia virus type-Ⅰ) infection, in which the closely related target cell-virus-immune system interaction and the time-delay cytotoxic T lymphocyte (CTL) immune response are taken into consideration. Firstly, we give the relevant lemma for the existence of feasible equilibrium points of the model, and then further certify the global asymptotic stabilities of the infection-free equilibrium (IFFE) $ E_1 $ and the immune-free equilibrium (IMFE) $ E_2 $. Furthermore, we research the existence of Hopf bifurcation (HB) occurring at the immune equilibrium (IE) $ E^* $ due to the influence of the delay bifurcation parameter. Also, the numerical simulations confirm this fact. In addition, we obtain the explicit expressions which determine the direction and stability of HB. Finally, a succinct discussion shows that the delay in CTL response can destabilize $ E^* $ and generate HB, but not affect stabilities of $ E_1 $ and $ E_2 $. [ABSTRACT FROM AUTHOR]

The outbreak of a disease can lead to behavioral changes in the healthy to avert infection. We first establish a nonlinear SEIR epidemic model that incorporates the impact of individuals' behavioral response owe to information of the disease prevalence. Both the existence of equilibria and sharp sufficient conditions on stable equilibria are verified. Whereafter, the local and global sensitivity analyses are carried out to assess the relative effects of parameters on the basic reproduction number. Therewith the optimal control problem is considered to provide a theoretical basis for disease prevention and control, and the existence and uniqueness consequences for optimal control paths are demonstrated. Some numerical examples and discussions are given to support and visualize our analytical results, which can be derived that the combined use of three control measures is more effective than any single adopted control strategy to curb the spread of diseases. We also find that the information plays a crucial role in controlling infection. [ABSTRACT FROM AUTHOR]