The population‐level impact of HBV and its vaccination on HIV transmission dynamics

Hepatitis B virus (HBV) and its vaccination strategy may affect human immunodeficiency virus (HIV) transmission dynamics because both viruses have synergistic effects. To quantitatively assess the potential impact of HBV and its vaccination strategy on HIV transmission dynamics at the population level, in this paper, we formulate a deterministic compartmental model that describes the joint dynamics of HBV and HIV. We first derive the explicit expressions for the basic reproduction numbers of HIV and HBV and analyze the dynamics of HIV and HBV subsystems, respectively. Then a systematic qualitative analysis of the full system is also provided, which includes the local and global behavior. By using a set of reasonable parameter values, the full system is numerically investigated to assess the potential impact of HBV and its vaccination strategy on HIV transmission. The direct and indirect population level impact of HBV on HIV is demonstrated by calculating the fraction of HIV infections attributable to HBV and the difference between HIV prevalence in the presence and absence of HBV, respectively. The findings imply that the increase of HBV vaccination rate may unusually accelerate HIV epidemics indirectly, although the direct effect of HBV on HIV transmission decreases as HBV vaccination rate increases. Finally, the potential impact of HIV on HBV transmission dynamics is investigated by way of parenthesis. Copyright © 2016 John Wiley & Sons, Ltd.     

Global asymptotical properties for a diffused HBV infection model with CTL immune response and nonlinear incidence

This article proposes a diffused hepatitis B virus (HBV) model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained. Global stability of the positive equilibrium of the model is also considered. The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.     

Global properties of an improved hepatitis B virus model

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.     

The analysis and application of an HBV model

A mathematical model is formulated to describe the spread of hepatitis B. The stability of equilibria and persistence of disease are analyzed. The results shows that the dynamics of the model is completely determined by the basic reproductive number ρ₀. If ρ₀ < 1, the disease-free equilibrium is globally stable. When ρ₀ > 1, the disease-free equilibrium is unstable and the disease is uniformly persistent. Furthermore, under certain conditions, it is proved that the endemic equilibrium is globally attractive. Numerical simulations are conducted to demonstrate our theoretical results. The model is applied to HBV transmission in China. The parameter values of the model are estimated based on available HBV epidemic data in China. The simulation results matches the HBV epidemic data in China approximately.     

Use of discrete-event simulation to evaluate strategies for the prevention of mother-to-child transmission of HIV in developing countries

HIV/AIDS affects over 40 million people worldwide, and more than 70% of these people live in Africa. Mother-to-child transmission of HIV accounts for over 90% of all HIV infections in children under the age of 15 years. However, implementing HIV prevention policies in Africa is extremely difficult because of the poor medical and socio-economic infrastructure. In this paper, we present a discrete-event simulation model that evaluates the relative benefits of two potentially affordable interventions aimed at preventing mother-to-child transmission of HIV, namely anti-retroviral treatment at childbirth and/or bottlefeeding strategies. The model uses rural Tanzanian data and compares different treatment policies. Our results demonstrate that strategic guidelines about breastfeeding are highly dependent on the assumed increase in infant mortality due to bottlefeeding, the efficacy of anti-retroviral treatment at childbirth, and the maternal health stage. The cost of averted infections, though low by Western standards, may represent significant obstacles to policy implementation in developing countries.     

Analysis of an SVIC model with age-dependent infection and asymptomatic carriers

In this paper,we formulated an age-dependent model for the transmission dynamics of HBV with vaccination. The class of acutely infectious individuals,asymptomatic carrier of host population is stratified by age. Mathematically, we established that basic reproduction number can govern the global stability of equilibria. Biologically, we verify the impacts of the asymptomatic carriers and the effectiveness of vaccination on the disease transmission through numerical simulation. Our results indicated that the more number of infectious individuals specific to frequently progressed to asymptomatic carriers, the more likely the disease can be eradicated by continuous vaccination strategies.     

Global dynamics for an age-structured epidemic model with media impact and incomplete vaccination

Some studies show that the efficacy of vaccines may decline and the vaccine-induced immunity wanes with time elapsed since vaccination (e.g., BCG, HBV vaccines). Meanwhile, the use of media can effectively contain the emerging epidemics. In our work, an SVEIR epidemic model with media impact, age-dependent vaccination and latency is proposed, where the efficacy of vaccines depends on the time since vaccination. Uniform persistence and the sharp threshold dynamics are established, that is, the vaccination reproduction number completely determines the global dynamics of the model system. Our main results established can be extended to the SVEIR model with the general nonlinear infectious force function of monotonicity and concavity.     

Hepatitis C. New guidelines on precautions, follow-up

An OR team has a greater chance of operating on a patient infected with hepatitis C than on a patient with HIV or hepatitis B. Many patients with HCV aren't critically ill, and the team may not know a patient is infected. HCV is more common than many think--an estimated 3.5 million people in the US are infected. The consequences are grave. For most, infection is lifelong. At least 85% become chronically infected. Chronically infected individuals are at risk for cirrhosis and liver cancer. Unfortunately, not much can be done to prevent transmission. There is no vaccine and not much in the way of treatment. In recent weeks, the Centers for Disease Control and Prevention (CDC) and professional societies have tried to address workers' concerns with new recommendations that, although they don't provide easy answers, offer added guidance.     

脉冲输入免疫因子的HBV模型的稳定性和持久性分析

提出了一个数学模型,用于研究脉冲投放免疫因子对HBV传染病动力学的影响.通过利用脉冲微分不等式和比较定理,证明了HBV模型的无病周期解的存在性,给出了无病周期解的全局渐近稳定性和系统的持续性的充分条件.研究结果表明:短的投放周期或适当的免疫因子投放量可以导致HBV的清除.     

乙肝疫苗接种后体液免疫应答的数学模型

接种乙肝疫苗是预防和控制乙型肝炎的有效措施,接种后乙肝表面抗体的持久性以及记忆细胞的长期免疫机制一直是人们关注的焦点.在维持长期免疫应答的长寿命浆细胞假说的基础之上,我们提出了一个接种乙肝疫苗后机体的体液免疫应答模型来描述接种人群乙肝表面抗体滴度的变化过程.通过选择模型中一些参数的值,模拟接种重组疫苗和血源疫苗后机体的免疫应答过程,之后又模拟了持续存在的抗原与长寿命浆细胞共同作用下维持长期免疫应答的过程,模型的模拟结果与实际抗体滴度拟合的很好.还分析了模型的几个参数对免疫效果的影响.模型及结果可以帮助人们更好地理解免疫机制.     

Global stability and a non-standard finite difference scheme for a diffusion driven HBV model with capsids

A diffusion driven model for hepatitis B virus (HBV) infection, taking into account the spatial mobility of both the HBV and the HBV DNA-containing capsids is presented. The global stability for the continuous model is discussed in terms of the basic reproduction number. The analysis is further carried out on a discretized version of the model. Since the standard finite difference (SFD) approximation could potentially lead to numerical instability, it has to be restricted or eliminated through dynamic consistency. The latter is accomplished by using a non-standard finite difference (NSFD) scheme and the global stability properties of the discretized model are studied. The results are numerically illustrated for the dynamics and stability of the various populations in addition to demonstrating the advantages of the usage of NSFD method over the SFD scheme.     

A non-standard finite difference scheme for a diffusive HBV infection model with capsids and time delay

In this paper, a non-standard finite difference (NSFD) scheme for a delayed diffusive hepatitis B virus (HBV) infection model with intracellular HBV DNA-containing capsids is proposed. Dynamic consistency of this NSFD scheme is achieved by showing that the scheme preserves the non-negativity and boundedness of the solutions and the global stability of the homogeneous steady states of the corresponding continuous model without any restriction on spatial and temporal grid sizes. We prove the global stability of the steady states by constructing suitable discrete Lyapunov functions.     

Global dynamics and cost-effectiveness analysis of HIV pre-exposure prophylaxis and structured treatment interruptions based on a multi-scale model

Structured treatment interruptions (STI) were proposed to reduce costs and side effects for HIV infected individuals, but whether the possible viral rebound within hosts after treatment interruption would lead to more new infections and additional costs among the population remains unknown. Oral pre-exposure prophylaxis (PrEP) is shown as an effective but expensive strategy to prevent the acquisition of HIV infection. To investigate the effectiveness and cost-effectiveness of STI and PrEP, we develop a multi-scale model linking within-host and between-host dynamics in the presence of drug resistance. Lyapunov functionals are constructed to analyze the global dynamics of the coupled system. We fit this model to the annual AIDS incidence and death data from 1980 to 2014 among men who have sex with men (MSM) in San Francisco and compare the impact of six various intervention scenarios (low, medium, high PrEP coverage with or without STI) on new infections and cost-effectiveness over the next 20 years. We estimate the PrEP efficacy needed to eliminate the disease for different fraction of acquired drug resistance under the above six scenarios. Numerical simulations show that expanding PrEP coverage is very cost-effective, but whether implementing STI is cost-saving depends on the efficacy of second-line drugs. That is to say, STI could always save money, but it may lead to more (less) new infections than continuous therapy and thus less (more) health benefit for high (low) efficacy of second-line drugs. These results provide insights about the long-term effect of STI and PrEP on the disease control and cost-effectiveness.     

Modeling the progression of articular erosion in rheumatoid arthritis (RA): Initial mathematical models

Rheumatoid Arthritis (RA) is a chronic inflammatory disease of unknown cause that affects around 1% of the adult population in the U.S. Women are more often affected than men by a ratio of 3 to 1, and although the disease can appear at any age in adult life, the incidence and prevalence increase with age. The inflammatory process that characterizes RA, centers in and around articular structures and is characterized by destruction that progresses over time. Attempts to apply curve fitting to the analysis of the progression of radiographie damage in RA have lead to numerous forms of mathematical models (linear, quadratic, cubic, square root, first-order kinetics, etc.). None of these models has been very successful in that a signficiant degree of ambiguity of the appropriate model form still remains. A mathematical model of the progression of RA would be useful to evaluate the effect of interventions to ameliorate joint destruction. In this paper, we present a rigorously derived second-order kinetics model and propose

• 1.(a) a possible explanation for the ambiguity found in prior analyses, and
• 2.(b) present a potentially clinically useful model for RA disease progression based upon radiographic assessment of joint damage.

     

Peer interactions in a computer lab: reflections on results of a case study involving web-based dynamic geometry sketches

A case study, originally set up to identify and describe some benefits and limitations of using dynamic web-based geometry sketches, provided an opportunity to examine peer interactions in a lab. Since classes were held in a computer lab, teachers and pairs faced the challenges of working and communicating in a lab environment.Research has shown that particular teacher interventions provide motivation for the consideration of new ideas, and help uncover misunderstandings that may interfere with student progress [Towers, J. (1999). In what ways do teachers interventions interact with and occasion the growth of students’ mathematical understanding. Doctoral Dissertation, University of British Columbia, Unpublished]. Examples of student discourse presented here suggest that certain peer interactions act in similar ways—helping propel students towards new understanding. On the other hand, they also show that some peer interactions, although superficially similar to teacher interventions, may hamper student progress.     

PLANNING MARINE PROTECTED AREAS: A MULTIPLE USE GAME

Abstract The EU Marine Strategy Directive (MSD) has a regional focus in its implementation. The directive obliges countries to take multiple uses and the marine strategies of neighboring countries into account when formulating marine strategies and when designating marine protected areas (MPAs). We use game theoretical analysis both to find the optimal size of MPAs with multiple uses by multiple countries and to investigate the influences of multiple uses on cooperation. To this end, we develop a model in which two specific uses, fisheries and nature conservation, by multiple countries are considered in a strategic framework. The results of the paper suggest that EU marine policy such as the MSD and the coming Maritime Policy may help to secure the highest possible benefits from these MPAs if these policies induce cooperation among countries, but only if policies force countries to consider all possible benefits of MPAs. In fact cooperation on a single issue may give a worse outcome than the noncooperative equilibrium. The results also indicate that cooperation may be hard to achieve because of defector incentives, and therefore policy measures should be strict in enforcing cooperation on all possible uses of MPAs.     

Evolutionary dynamics of the spatial Prisoner’s Dilemma with self-inhibition

In this paper we study the influence of interventions on self-interactions in a spatial Prisoner’s Dilemma on a two-dimensional grid with periodic boundary conditions and synchronous updating of the dynamics. We investigate two different types of self-interaction modifications. The first type (FSIP) is deterministic, effecting each self-interaction of a player by a constant factor, whereas the second type (PSIP) performs a probabilistic interventions. Both types of interventions lead to a reduction of the payoff of the players and, hence, represent inhibiting effects. We find that a constant but moderate reduction of self-interactions has a very beneficial effect on the evolution of cooperators in the population, whereas probabilistic interventions on self-interactions are in general counter productive for the coexistence of the two different strategies.     

Quantitative modeling of risk management strategies: Stochastic reserving and hedging of variable annuity guaranteed benefits

Variable annuities are enhanced life insurance products that offer policyholders participation in equity investment with minimum return guarantees. There are two well-established risk management strategies in practice for variable annuity guaranteed benefits, namely, (1) stochastic reserving based on risk measures such as value-at-risk (VaR) and conditional-tail-expectation (CTE); (2) dynamic hedging using exchange-traded derivatives. The latter is increasingly more popular than the former, due to a common perception of its low cost. While both have been extensively used in the insurance industry, scarce academic literature has been written on the comparison of the two approaches. This paper presents a quantitative framework in which two risk management strategies are mathematically formulated and where the basis for decision making can be determined analytically. Besides, the paper proposes dynamic hedging of net liabilities as a more effective and cost-saving alternative to the common practice of dynamic hedging of gross liabilities. The finding of this paper does not support the general perception that dynamic hedging is always more affordable than stochastic reserving, although in many cases it is with the CTE risk measure.     

Systemic cost-effectiveness analysis of food hazard reduction – Campylobacter in Danish broiler supply

An integrated microbiological–economic framework for policy support is developed to determine the cost-effectiveness of alternative intervention methods and strategies to reduce the risk of Campylobacter in broilers. Four interventions at the farm level and four interventions at the processing stage are considered. Cost analyses are conducted for different risk reduction targets and for three alternative scenarios concerning the acceptable range of interventions. Results demonstrate that using a system-wide policy approach to risk reduction can be more cost-effective than a policy focusing purely on farm-level interventions. Allowing for chemical decontamination methods may enhance cost-effectiveness of intervention strategies further.     

ESTIMATION OF PARAMETERS IN A CLOSED PYGMY POPULATION IN CAMEROON

Inspired by Kouakep [16], we consider in this note a wellposed model with differential susceptibility and infectivity adding continuous age structure to an ODE model for a "Baka" pygmy group in the East of Cameroon(Africa).Assuming a very low contribution of carriers to infection compared to acute infection, we estimate a probability p(a)(to develop symptomatic Hepatitis B state at age a) and acute carriers' transmission rate. The value R_0= 2:67 1 of the basic reproduction number estimated from data in the east of Cameroon confirms that HBV is endemic in the Baka pygmy group.