Analysis of latent CHIKV dynamics models with general incidence rate and time delays

In this paper, we study the stability analysis of latent Chikungunya virus (CHIKV) dynamics models. The incidence rate between the CHIKV and the uninfected monocytes is modelled by a general nonlinear function which satisfies a set of conditions. The model is incorporated by intracellular discrete or distributed time delays. Using the method of Lyapunov function, we established the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.     

Dynamical behavior of a hepatitis B virus transmission model with vaccination

Hepatitis B virus (HBV) infection is a globally health problem. In 2005, the WHO Western Pacific Regional Office set a goal of reducing chronic HBV infection rate to less than 2% among children five years of age by 2012, as an interim milestone towards the final goal of less than 1%. Many countries made some plans (such as free HBV vaccination program for all neonates in China now) to control the transmission HBV. We develop a model to explore the impact of vaccination and other controlling measures of HBV infection. The model has simple dynamical behavior which has a globally asymptotically stable disease-free equilibrium when the basic reproduction number R₀≤1, and a globally asymptotically stable endemic equilibrium when R₀>1. Numerical simulation results show that the vaccination is a very effective measure to control the infection and they also give some useful comments on controlling the transmission of HBV.     

Transient kinetics of thermodynamic buffering

The transient response of mitochondrial ATP production towards perturbations was studied by analyzing the trajectories leading from arbitrary initial conditions of the adenine nucleotide pool to the final steady state. These trajectories were calculated from differential equations based on linear relations between flows and thermodynamic forces of the adenylate kinase system including oxidative phosphorylation. The motion of the system along the trajectories consists of two phases: (1) a rapid phase leading from initial states to a common relaxation curve; and (2) a slow phase leading along the relaxation curve to the final steady state. The first phase corresponds to a motion close to the loci of constant adenylic energy charge. In line with this observation is the finding that the energy charge is a constant of motion of the adenylate kinase reaction. The second phase corresponds to a motion along a relaxation curve characterized by minimal Lyapunov exponents in the concentration space of the adenine nucleotides. Thus, both phases of the transient kinetics can be approximated in terms of thermodynamic functions to a high degree of precision. Incubations with isolated rat liver mitochondria were in excellent agreement with the theoretical predictions. In summary, these studies show that the adenylate kinase system not only optimizes the efficiency of oxidative phosphorylation through thermodynamic buffering but, in addition, also deeply influences the transient response of the whole system.     

Temporal more than spatial regulation of sway is important for posture in response to an ultra-compliant surface

Background and aim: Many people use balance training as a rehabilitation or habilitation modality. Although the time course of changes to temporal and spatial aspects of postural sway over the initial weeks of such training is as yet unclear. Particularly, we sought to explore the effects of training on sway during a dynamic task of stance on an ultra-compliant surface. Such a task provides different mechanical, and thus sensorimotor, constraints compared to stance on a solid surface.

Methods: Center of pressure (COP) was measured on an ultra-compliant surface atop a force plate at the start of each of 18?days of a 6-week balance training program. Range and standard deviation quantified amount of sway while velocity and Lyapunov exponent (LyE) quantify speed and rhythmicity of sway, respectively.

Results: Trend analysis indicated quadratic changes in COP range and standard deviation, with initial reductions followed by returns to initial values by the end of training. Linear reduction of movement velocity and LyE continued through the duration of the program. Reduced LyE indicates regular (self-similar) structure of the COP path.

Conclusions: These results provide insight to the developing postural strategy necessary for maintaining upright stance within the dynamics created by interactions with an ultra-compliant surface. Participants showed sensitivity to surface properties, moving both more slowly and with a more regular movement pattern; suggesting that they were able to develop a more feed-forward approach to the maintenance of balance by exploiting task constraints.     

HIV/AIDS dynamics: Impact of economic classes with transmission from poor clinical settings

We formulate and analyze a nonlinear deterministic HIV/AIDS model with two social classes, namely the poor and the rich including transmission from poor clinical settings with a randomly variable population. Four sub-models are derived from the full model, the disease threshold parameters are computed, and it is shown that the disease will die down if these initial threshold parameters are less than unity and will persist if they exceed unity. The impact of economic classes (along with transmission from poor/inadequate clinical settings) on the disease dynamics is assessed, and we observe that even with a single sexual partner, the reproduction number is slightly greater than unity, implying that the additional transmission can only be from clinical settings. Stability (local and global) of both the disease-free and endemic equilibria are then investigated using various techniques of dynamical systems such as Centre Manifold theory and Lyapunov's second method. Analysis on the bifurcation parameter is carried out to assess the impact of related HIV transmission from poor clinical settings. We estimate some of the model parameter values and numerical simulations of the model are represented graphically. Our results show that the prevalence of HIV in rich communities seems to be higher than that in the poor, but the disease develops faster in impoverished individuals.     

广义Lyapunov函数与微分系统关于两种量度的相对稳定性(Ⅲ)

讨论具有性质（V）的广义Lyapunov函数的确定与判别，从而基本上完成利用广义Lyapunov函数研究微分系统关于两种量度的相对稳定性问题．     

Kinematic Analysis of the Neck and Upper Extremities During Walking in Healthy Young Adults

The objective of this paper is to quantify the local stabilities of the neck and upper extremities (right/left shoulders and right/left elbows), and investigate differences between linear and nonlinear measurements of the associated joint motions and differences in the local stability between the upper and lower extremities. This attempt involves the calculation of a nonlinear parameter, Lyapunov Exponent (LE), and a linear parameter, Range of Motion (ROM), during treadmill walking in conjunction with a large population of healthy subjects. Joint motions of subjects were captured using a three-dimensional motion-capture system. Then mathematical chaos theory and the Rosenstein algorithm were employed to calculate LE of joints as the extent of logarithmic divergence between the neighboring state-space trajectories of flexion-extension angles. LEs computed over twenty males and twenty females were 0.037±0.023 for the neck, 0.043±0.021 for the right shoulder, 0.045±0.030 for the left shoulder, 0.032±0.021 for the right elbow, and 0.034±0.026 for the left elbow. Although statistically significant difference in the ROM was observed between all pairs of the neck and upper extremity joints, differences in the LE between all pairs of the joints as well as between males and females were not statistically significant. Between the upper and lower extremities, LEs of the neck, shoulder, and elbow were significantly smaller than those of the hip (∼0.064) and the knee (∼0.062). These results indicate that a statistical difference in the local stability between the upper extremity joints is not significant. However, the different result between the ROM and LE gives a strong rationale for applying both linear and nonlinear tools together to the evaluation of joint movement. The LEs of the joints calculated from a large population of healthy subjects could provide normative values for the associated joints and can be used to evaluate the recovery progress of patients with joint related diseases.