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Vibration of nanotubes embedded in an elastic matrix is investigated by using the nonlocal Timoshenko beam model. Both a stress gradient and a strain gradient approach are considered. The Hamilton’s principle is adopted to obtain the frequencies of the nanotubes. The dependencies of frequency on the stiffness and mass density of the surrounding elastic matrix, the nonlocal parameter, the transverse shear stiffness and the rotary inertia of the nanotubes are obtained. The results show a significant dependence of frequencies on the surrounding medium and the nonlocal parameter. The frequencies are over-predicted by using the Euler beam model that neglects the shear stiffness and rotary inertia of the nanotubes. It is also found that the lower bound and the upper bound for the frequencies of nanotubes are, respectively, provided by the strain gradient model provides and the stress gradient theory. Explicit formulas for the frequency are obtained and therefore are easy to use by material scientists and engineers for the design of nanotubes and nanotubes based composites.

Community nurses play a crucial role in early detection and timely diagnosis of dementia. However, they are usually not prepared for the role through their formal education, particularly in low- and middle-income countries due to undeveloped nursing curriculum in dementia care. This paper describes a two-arm cluster-randomized controlled trial to improve community nurses' knowledge, attitudes, and practice changes using an innovative and interactive mobile phone applet-based activity in primary care settings. The intervention sites received dementia-specific training and control sites received care training for older people with disability. Both groups completed measures assessing dementia knowledge, attitudes, and intentions to make changes to achieve early detection and a timely diagnosis of dementia immediately after training and at 3-month follow-up. The intervention group provided feedback immediately after training and at 3-month follow-up. The main results show that the intervention group demonstrated significant improvement in dementia knowledge and attitudes from baseline immediately after training and at the 3-month follow-up. The intervention group also showed more intentions to make changes to achieve early detection of dementia. Feedback suggested the program was well-received. Overall, the program showed acceptability and feasibility in improving nurses' dementia knowledge, attitudes, and intentions to achieve early detection of dementia.

In this paper, we propose and investigate an age-structured hepatitis B virus (HBV) model with saturating incidence and spatial diffusion where the viral contamination process is described by the age-since-infection. We first analyze the well-posedness of the initial-boundary values problem of the model in the bounded domain $\Omega\subset\mathbb{R}^n$ and obtain an explicit formula for the basic reproductive number $R_0$ of the model. Then we investigate the global behavior of the model in terms of $R_0$: if $R_0\leq1$, then the uninfected steady state is globally asymptotically stable, whereas if $R_0>1$, then the infected steady state is globally asymptotically stable. In addition, when $R_0>1$, by constructing a suitable Lyapunov-like functional decreasing along the travelling waves to show their convergence towards two steady states as $t$ tends to $\pm\infty$, we prove the existence of traveling wave solutions. Numerical simulations are provided to illustrate the theoretical results.

In this paper, we investigate the complex dynamics of a reaction–diffusion S − I model incorporating demographic and epidemiological processes with zero-flux boundary conditions. By the method of Lyapunov function, the global stability of the disease free equilibrium and the epidemic equilibrium was established. In addition, the conditions of Turing instability were obtained and the Turing space in the parameters space were given. Based on these results, we present the evolutionary processes that involves organism distribution and their interaction of spatially distributed population with local diffusion, and find that the model dynamics exhibits a diffusion-controlled formation growth to “holes, holes–stripes, stripes, spots–stripes and spots” pattern replication. Furthermore, we indicate that the diseases’ spread is getting smaller with R 0 increasing, and the increasing the diffusion of infectious will increase the speed of diseases spreading. Our results indicate that the diffusion has a great influence on the spread of the epidemic and extend well the finding of spatiotemporal dynamics in the epidemic model.

The vibration behaviors of simply supported Kirchhoff and Mindlin nanoscale plates with consideration of surface effects are studied using the nonlocal elastic theory. The motion equations of the nanoplates are obtained and the closed form solutions for natural frequency are established using Navier's approach. According to the analysis, the influences of surface energy and nonlocal effect on natural frequency of the nanoplates are very significant. The surface energy increases the natural frequency but the nonlocal parameter decreases the natural frequency. The influence of nonlocal effect becomes increasingly pronounced for higher order vibration modes. On the contrast, the effect of surface energy is important at lower frequencies.

Time delay is incorporated into a spatially explicit model for vegetation dynamics in freshwater marshes and the effect of the delay is investigated by using qualitative analysis and numerical simulation. If the specific rate of plant senescence is sufficient small then spatial homogeneity will be induced eventually for any delay, while if it is large, then a switches may occurs as time delay increases and there is a periodic oscillations if it exceed a critical value. Thus, delay time in ecosystem may be one of the important factors to induce temporal fluctuation in nature.

Although experimental and observational studies have shown that microparasites can induce the deterministic reduction, fluctuation and extinction scenarios for its host population, most existing host-parasite interaction models fail to produce such rich dynamical behaviors simultaneously. We explore the effects of explicit dynamics of parasites under logistic host growth and different infection rate function. Our results show that the explicit dynamics of parasites and standard incidence function can induce the host density fluctuation and extinction scenario in the case of logistic host growth.

Many experiments reveal that Daphnia and its microparasite populations vary strongly in density and typically go through pronounced cycles. To better understand such dynamics, we formulate a simple two dimensional autonomous ordinary differential equation model for Daphnia magna-microparasite infection with dose-dependent infection. This model has a basic parasite production number $R_0=0$, yet its dynamics is much richer than that of the classical mathematical models for host-parasite interactions. In particular, Hopf bifurcation, stable limit cycle, homoclinic and heteroclinic orbit can be produced with suitable parameter values. The model indicates that intermediate levels of parasite virulence or host growth rate generate more complex infection dynamics.

Hepatitis B virus (HBV) infection is an important health problem worldwide. In this paper, we introduce an improved HBV model with standard incidence function and cytokine-mediated ‘cure’ based on empirical evidences. By carrying out a global analysis of the modified model and studying the stability of the equilibria, we show that infection-free equilibrium is globally asymptotically stable if the basic reproduction number of virus is less than one and, conversely, the infection equilibrium is globally asymptotically stable if the basic reproduction number of virus is greater than one. The study and information derived from this model and other related models may have an important impact on preventing mortality due to hepatitis B virus in the future.

This paper considers the coevolution of phenotypic traits in a community comprising two competitive species subject to strong Allee effects. Firstly, we investigate the ecological and evolutionary conditions that allow for continuously stable strategy under symmetric competition. Secondly, we find that evolutionary suicide is impossible when the two species undergo symmetric competition, however, evolutionary suicide can occur in an asymmetric competition model with strong Allee effects. Thirdly, it is found that evolutionary bistability is a likely outcome of the process under both symmetric and asymmetric competitions, which depends on the properties of symmetric and asymmetric competitions. Fourthly, under asymmetric competition, we find that evolutionary cycle is a likely outcome of the process, which depends on the properties of both intraspecific and interspecific competition. When interspecific and intraspecific asymmetries vary continuously, we also find that the evolutionary dynamics may admit a stable equilibrium and two limit cycles or two stable equilibria separated by an unstable limit cycle or a stable equilibrium and a stable limit cycle.

Routine targeted temperature management is recommended for comatose adult patients with return of spontaneous circulation after cardiac arrest. However, the role of targeted temperature management in patients resuscitated from nonshockable cardiac arrests remains uncertain. We conducted an updated systematic review and meta-analysis to evaluate the effects of targeted temperature management in this population. Medline, EMBASE, and Cochrane databases were systematically reviewed for studies published between January 2005 and March 2016, in which targeted temperature management was compared with standard care or normothermia for adult patients resuscitated from nonshockable cardiac arrests. A total of 25 trials that included 5715 patients were identified from 10985 relevant papers. Pooled data showed that targeted temperature management not only associated with improved short-term survival (RR = 1.42, 95% CI: 1.28–1.57) and neurological function (RR = 1.63, 95% CI: 1.39–1.91) but also associated with improved long-term survival (RR = 1.64, 95% CI: 1.27–2.12) and neurological recovery (RR = 1.42, 95% CI: 1.07–1.90) in observational cohort studies. However, more frequent infectious complications were reported in hypothermia-treated patients (RR = 1.46, 95% CI: 1.26–1.70) and the quality of the evidence ranged from moderate to very low.

Background The determination of angiogenesis time is the key prerequisite to obtaining a balance between valid repair and excessive angiogenesis in wound healing. The aim of the investigation was to establish a bio-mathematical model predicting corneal angiogenesis time after alkali burn by back propagation neural network (BP neural network). Methods The corneas of mice in 24 groups were burned by 0.01 mol/l NaOH. Five mice in each group were sacrificed at 6 h after alkali burn. The expression levels of vegf and tsp2, determined by real-time quantitive PCR, were used as input vectors in BP neural network. Meanwhile, the corneal angiogenesis of other mice, inspected every 3 h in 24 groups till the angiogenesis time were determined, served as output vectors. The data of 18 groups were randomly chosen for network adaptation while that of other 6 groups for simulation forecasting with functions of minmax (), postreg, prepca, trapca, respectively. Results A bio-mathematical model of two-level BP neural network was established, for its purpose to predict the angiogenesis time through the expression values of vegf and tsp2. The performance index (0.00999996) was smaller than the target value (0.01) after adapting 36,557 times and the accuracy rate of this predict system was 83.33%. Furthermore, the ideal regression line and the optimization regression line were almost coincident ( R = 0.988 in network adaptation and R = 0.793 in simulation forecasting). Conclusions The investigation indicated that the bio-mathematical model had available performance of simulation and forecasting. It might provide a novel method to solve clinical problems.

The rich dynamics of a viral infection model is studied under the assumption that the immune response is retarded. It is shown that if the basic reproductive ratio of the virus is less than one, the infection-free equilibrium is globally asymptotically stable. Analytical and numerical results show that if the basic reproductive ratio of the virus is greater than one, the combined effect of the strength of the lytic component, the time delay of the immune response and the birth rate of susceptible host cells is to create a rich dynamics, which includes the occurrence of stable periodic solutions and chaotic dynamical behavior. The route from periodic oscillations to chaos is investigated. These results can be used to explain irregular real time series data on the immune state of patients.

The aim of this study is to determine the prevalence and correlates of depressive symptoms in a school-based sample of 7–17-year-old children and adolescents in west-central China. A large cross-sectional sample survey of 10657 children and adolescents was conducted in Chongqing, a municipality in west-central China. Data were collected from the Children's Depression Inventory (CDI), Adolescent Self-Rating Life Events Checklist (ASLEC) and social-demographic variables which were evaluated with a structured scale. The total prevalence of depression risk was 23.9%. The risk factors for depressive symptoms included age older than 12 years, grade lower than 10, having unmarried parents, being taken care of by people other than two parents (single parent, grandparent(s), other relatives, or others), and living in a low-income family. The pressures of health and adaptation, interpersonal relationship, and study were also strong predictors of depressive symptoms. The prevalence of depressive symptoms among children and adolescents in Chongqing of China is relatively high compared with most figures reported in other cities. There is an urgent need to develop efficacious interventions aimed at the prevention and early recognition of childhood and adolescent depression.

Electrical defibrillation, which consists of delivering a therapeutic dose of the electrical current to the fibrillating heart with the aid of a defibrillator, is still the only effective way to treat life-threatening ventricular fibrillation (VF). However, the efficacy of electrical therapy for terminating VF is highly dependent on the waveform applied. When new defibrillation waveforms or techniques are developed, their efficacy needs to be accurately evaluated and compared to those in use. A common method for the comparison of defibrillation efficacy is to estimate and compare the individual defibrillation threshold (DFT) by constructing dose response curves or using an up-and-down method. Since DFT is calculated by repetitive and sequential shocks, there will be variability for each measurement and for each individual. This creates a considerable uncertainty for paired comparison. In this paper, a novel grouped up-and-down method is developed for the comparison of defibrillation efficacy between two different defibrillation waveforms or techniques. The efficacy of two commonly used biphasic defibrillation waveforms was compared in a porcine model of cardiac arrest using the developed method. Experimental results demonstrate that the proposed method is more sensitive for efficacy comparison and requires less defibrillation attempts compared with traditional DFT methods.

In this paper, a single population model with space-limited and stage-structure is considered. Sufficient conditions for uniform persistence of the model are obtained by the theory of infinite dimensional dynamical systems. Then by applying the theory of Hopf bifurcation and the Browder fixed point theorem, sufficient conditions for the limit cycle of the model existing in small range and large range are, respectively, obtained.

A system of functional differential equations is used to model the single microorganism in the chemostat environment with a periodic nutrient and antibiotic input. Based on the technique of Razumikhin, we obtain the sufficient condition for uniform persistence of the microbial population. For general periodic functional differential equations, we obtain a sufficient condition for the existence of periodic solution, therefore, the existence of positive periodic solution to the chemostat-type model is verified.

Acute burn injuries are among the most devastating forms of trauma and lead to significant morbidity and mortality. Appropriate fluid resuscitation after severe burn, specifically during the first 48 hours following injury, is considered as the single most important therapeutic intervention in burn treatment. Although many formulas have been developed to estimate the required fluid amount in severe burn patients, many lines of evidence showed that patients still receive far more fluid than formulas recommend. Overresuscitation, which is known as “fluid creep,” has emerged as one of the most important problems during the initial period of burn care. If fluid titration can be personalized and automated during the resuscitation phase, more efficient burn care and outcome will be anticipated. In the present study, a dynamic urine output based infusion rate prediction model was developed and validated during the initial 48 hours in severe thermal burn adult patients. The experimental results demonstrated that the developed dynamic fluid resuscitation model might significantly reduce the total fluid volume by accurately predicting hourly urine output and has the potential to aid fluid administration in severe burn patients.

We use the Hill function to analyze the dynamics of Tc-99m 2 methoxy-isobutyl-isonitrile (99mTc-MIBI) scintigraphy data and to examine the earlier lower extremity microvascular perfusion of diabetic patients without typical clinical symptoms and with the preserved normal ankle-brachial index (ABI). Eighty-eight participants (30 healthy control, 34 diabetic patients, and 24 diabetic patients with peripheral arterial disease [PAD]) were recruited and applied 99mTc-MIBI scintigraphy. Fourteen diabetic patients with PAD also underwent computed tomography angiography (CTA) examination and were performed endovascular interventions. Diabetic patients with normal ABI already have significantly impaired maximum 99mTc-MIBI muscle perfusion counts (P

The contribution of covalently closed circular DNA (cccDNA) and dendritic cells (DCs) to the progression of chronic hepatitis B virus (HBV) infection remains largely unknown. A dynamic model with seven cell types was proposed based on the biological mechanisms of viral replication and the host immune response. The cccDNA self-amplification rate was found to be closely related to both the basic reproduction number of the virus and the immune response. The combination of the cccDNA self-amplification rate and the initial activated DC count induces rich dynamics. Applying our model to the clinical data of untreated patients, we found that chronic patients have a high cccDNA self-amplification rate. For antiviral treatment, an overall drug effectiveness was introduced and the critical drug effectiveness was obtained. The model predicts that timely long-term therapy is needed to reduce the symptoms of HBV and to maintain the benefits of treatment.

The most frequent initial rhythm in out-of-hospital witnessed cardiac arrest is ventricular fibrillation (VF) and electrical defibrillation is still the only effective therapy for the termination of this life-threatening cardiac arrhythmia. Even though earlier defibrillation is greatly emphasized during cardiopulmonary resuscitation (CPR), unnecessary or repetitive high energy defibrillations are associated with decreased post-resuscitation myocardial function. Optimizing the timing of defibrillation is of great importance in order to discriminate patients should receive immediate defibrillation versus alternate therapies such as CPR. Since characteristics of VF waveform changes over time and with CPR, which exhibit predictable ability of defibrillation success, quantitative analysis of VF waveform has the potential to guide defibrillation. This article reviewed methods developed for VF waveform analysis (including time domain, frequency domain, time-frequency domain, nonlinear analysis, and combination analysis techniques) and their performances for the prediction of defibrillation outcomes in clinical settings. The retrospective meta-analysis confirmed that VF waveform could predict the return of organized electrical activity, restoration of spontaneous circulation, and survival reliably. Additionally, predictors based on time-frequency and nonlinear methods were superior to other methods on the whole. However, no prospective studies have been performed to identify the optimal time of defibrillation utilizing VF waveform analysis until now. Therefore, the value of VF waveform analysis to guide clinical countershock management still needs further investigation.

To quantitatively study the effect of delay on selection dynamics in long-term sphere culture of cancer stem cells (CSCs), a selection dynamic model with time delay is proposed. Theoretical results show that the ubiquitous time delay in cell proliferation may be one of the important factors to induce fluctuation, and numerical simulations indicate that the proposed selection dynamical model with time delay can provide a better fitting effect for the experiment of a long-term sphere culture of CSCs. Thus, it is valuable to consider the delay effect in the future study on the dynamics of nongenetic heterogeneity of clonal cell populations.

In this paper, mathematical analysis of the global dynamics of a viral infection model in vivo is carried out. Though the model is originally to study hepatitis C virus (HCV) dynamics in patients with high baseline viral loads or advanced liver disease, similar models still hold significance for other viral infection, such as hepatitis B virus (HBV) or human immunodeficiency virus (HIV) infection. By means of Volterra-type Lyapunov functions, we know that the basic reproduction number [Formula: see text] is a sharp threshold para-meter for the outcomes of viral infections. If [Formula: see text], the virus-free equilibrium is globally asymptotically stable. If [Formula: see text], the system is uniformly persistent, the unique endemic equilibrium appears and is globally asymptotically stable under a sufficient condition. Other than that, for the global stability of the unique endemic equilibrium, another sufficient condition is obtained by Li–Muldowney global-stability criterion. Using numerical simulation techniques, we further find that sustained oscillations can exist and different maximum de novo hepatocyte influx rate can induce different global dynamics along with the change of overall drug effectiveness. Finally, some biological implications of our findings are given.

Human immunodeficiency virus 1 (HIV-1) drug resistance is a grave problem in highly active antiretroviral therapy (HAART) and neutral mutation is an important factor in the evolution of HIV-1. We consider the process of HIV-1 quasispecies transition in HAART to be transformation among three viral phenotypes: wild-type HIV-1, neutral-type HIV-1 and resistant-type HIV-1. A new model is proposed to study the transition dynamics of resistant-type HIV-1 induced by neutral mutation. The colonized time, the stable time and the stable size of the resistant species are simulated with the model. The results indicate that neutral mutation is closely related to the colonized pattern of resistant-type HIV-1 quasispecies which may lead to important strategies for predicting or checking HIV-1 drug resistance. Key words: Human immunodeficiency virus -1, neutral mutation, drug resistance, highly active antiretroviral therapy, stability delay, stability.

On the ecological timescale, two predator species with linear functional responses can stably coexist on two competing prey species. In this paper, with the methods of adaptive dynamics and critical function analysis, we investigate under what conditions such a coexistence is also evolutionarily stable, and whether the two predator species may evolve from a single ancestor via evolutionary branching. We assume that predator strategies differ in capture rates and a predator with a high capture rate for one prey has a low capture rate for the other and vice versa. First, by using the method of critical function analysis, we identify the general properties of trade-off functions that allow for evolutionary branching in the predator strategy. It is found that if the trade-off curve is weakly convex in the vicinity of the singular strategy and the interspecific prey competition is not strong, then this singular strategy is an evolutionary branching point, near which the resident and mutant predator populations can coexist and diverge in their strategies. Second, we find that after branching has occurred in the predator phenotype, if the trade-off curve is globally convex, the predator population will eventually branch into two extreme specialists, each completely specializing on a particular prey species. However, in the case of smoothed step function-like trade-off, an interior dimorphic singular coalition becomes possible, the predator population will eventually evolve into two generalist species, each feeding on both of the two prey species. The algebraical analysis reveals that an evolutionarily stable dimorphism will always be attractive and that no further branching is possible under this model.

Objectives: Fluctuation profile has been observed in chronic hepatitis B patients who are untreated or interrupt therapy. A mathematical model and its parameters could be used to diagnose the assumption of superinfection of hepatocytes and to understand the causes for the spontaneous fluctuation pattern of HBV DNA loads in chronically infected patients. Methods: We propose a new conceptual model in terms of chemical kinetics, which is based on the assumption that hepatocytes can be superinfected with hepatitis B virus (HBV). Minimizing the sum of squares of the deviations, we fitted the model to the HBV DNA trajectories from clinical data and obtained the model parameters. Results: The model with the fitted parameters can capture the tendency of HBV DNA trajectories. The mean value of the fitted number of virions that enter a single hepatocyte at the beginning stage of an invasion is 2.10 ± 0.18. The dynamics patterns may correlate with the clinical phenotypes of patients and the value of clinical parameters, such as α-fetoprotein, hepatitis B e-antigen, hepatitis B e-antibody, total bilirubin and alanine transaminase. Conclusions: The superinfection scenario is possible in HBV infection and it may induce HBV DNA fluctuation in the host.

A viral infection model with a nonlinear infection rate is constructed based on empirical evidences. Qualitative analysis shows that there is a degenerate singular infection equilibrium. Furthermore, bifurcation of cusp-type with codimension two (i.e., Bogdanov-Takens bifurcation) is confirmed under appropriate conditions. As a result, the rich dynamical behaviors indicate that the model can display an Allee effect and fluctuation effect, which are important for making strategies for controlling the invasion of virus. This work is supported by the National Natural Science Fund of China nos. 30770555 and 10571143, the Natural Science Foundation Project of CQ CSTC 2007BB5012, and the Science Fund of Third Military Medical University 06XG001 SI

In this paper we model and analyze the hepatitis B virus (HBV) infection in a diffusion model confined to a finite domain, induced by intracellular time delay between infection of a cell and production of new virus particles. The equilibrium solutions are obtained and the stability is analyzed if the space is assumed as homogeneous. When the space is inhomogeneous, the effects of diffusion and intracellular time delay are obtained by computer simulations.

A mathematical model is proposed to simulate the hepatitis B virus (HBV) infection with spatial dependence. The existence of traveling waves is established via the geometric singular perturbation method. Numerical simulations show that the model admits non-monotone traveling profiles. Influences of various parameters on the minimum wave speed are also discussed.

The influence of surface effects on the energy-generating performance of piezoelectric circular nanomembrane energy harvesters under blood pressure is studied. The effects of surface elasticity, surface piezoelectricity, residual surface stress and geometry nonlinear strain are incorporated in the present model. An approximated closed-form solution for the electrical energy of the nanomembrane is derived by using the energy method. Results show that positive surface elasticity and residual surface stress reduce the electrical energy and the surface piezoelectricity effect increases the electrical energy. The influence of surface effect on the energy-generating performance of piezoelectric circular membranes is more significant for a membrane with a small thickness and a large radius-to-thickness ratio.

To study the transition dynamics of resistant-type human immunodeficiency virus 1 (HIV-1) in highly active antiretroviral therapy (HAART) and the affect of neutral mutation in the evolution of HIV-1, a mathematical model is proposed when mutation occurs mainly during reproduction. The derived results show that the resistant-type will certainly colonize in patients once mutation occurs. Furthermore, a neutral mutation is closely related to the colonized pattern of resistant-type HIV-1 quasispecies and there are some changes in the pattern of transmission dynamics when mutation occurs mainly during reproduction or in the absence of reproduction, which may lead to significant strategies for predicting or checking HIV-1 drug resistance in HAART.

The influence of the surface and small-scale effects on electromechanical coupling behavior of a piezoelectric nanowire is studied by using the beam bending model. An explicit formula for the electromechanical coupling (EMC) coefficient of the piezoelectric nanowire is obtained based on the nonlocal electroelasticity theory. It is found that the inclusion of the nonlocal effect in the model produces a significant difference from the past model which ignores the nonlocal effect in the prediction of the EMC coefficient and the electric field in the nanowire, confirming the significance of including the surface and small-scale effects in the analysis of piezoelectric nanowires. In particular, the influence of surface effects on the electric field is dominant for smaller nonlocal parameters. If the nanowire is subjected to an applied concentrated load and without surface effect, the nonlocal effect has no effect on its bending and electric field. This study might be helpful for understanding the size-dependent electromechanical properties of piezoelectric nanowires and design of piezoelectric-beam–based nanogenerators.

This paper investigates the dynamics of an HTLV-I infection model with intracellular delay and immune activation delay. The primary objective of the study is to consider the effect of the time delay on the stability of the infected equilibrium. Two sharp threshold parameters $\Re_{0}$ and $\Re_{1}$ are identified as the basic reproduction number for viral infection and for CTLs response, respectively, which determine the long time behaviors of the viral infection. In particular, our mathematical analysis reveals that a Hopf bifurcation occurs when immune activation delay passes through a critical value. Using the normal form theory and center manifold arguments, the explicit formulae which determine the stability, the direction, and the period of bifurcating periodic solutions are derived. Numerical simulations are given to support the theoretical results.