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.     

一类具有感染年龄SIRS模型的分析

根据乙肝的传播特点,通过假设感染率依赖于个体的生理年龄及感染年龄.接种免疫有一定的有效期,建立了具有生理年龄和感染年龄的模型,并研究了地方病平衡点的存在条件.     

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.     

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.     

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.     

Epidemic dynamics model with delay and impulsive vaccination control base on variable population

Pulse vaccination is an effective strategy for the elimination of infectious diseases. In this paper, we considered an SEIR epidemic model with delay and impulsive vaccination direct at a variable population and analyzed its dynamic behaviors. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection‐free periodic solution of the impulsive epidemic system, further, prove that the infection‐free periodic solution is globally attractive if the vaccination rate is larger than θ* or the length of latent period of disease is larger than τ* or the length of period of impulsive vaccination is smaller than T*. We also prove that a short latent period of the disease (with τ) or a long period of pulsing (with T) or a small pulse vaccination rate (with θ) is sufficient to bring about the disease is uniformly persistent. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

脉冲免疫作用某一年龄群体的SIV模型

讨论带脉冲免疫的传染病模型,脉冲免疫作用于一特定年龄段的易感人群.我们研究了模型无病周期解的存在性.     

带有脉冲免疫和传染年龄的SIV传染病模型解的存在性

我们建立带有脉冲免疫和传染年龄的SIV传染病模型,这类传染病在潜伏期具有传染性,总人口规模依赖时间,并且传染类的康复率和传染年龄有关.我们证明此类模型解存在唯一.     

Qualitative analysis of the SICR epidemic model with impulsive vaccinations

Control of epidemic infections is a very urgent issue today. To develop an appropriate strategy for vaccinations and effectively prevent the disease from arising and spreading, we proposed a modified Susceptible‐Infected‐Removed model with impulsive vaccinations. For the model without vaccinations, we proved global stability of one of the steady states depending on the basic reproduction number R₀. As typically in the epidemic models, the threshold value of R₀ is 1. If R₀ is greater than 1, then the positive steady state called endemic equilibrium exists and is globally stable, whereas for smaller values of R₀, it does not exist, and the semi‐trivial steady state called disease‐free equilibrium is globally stable. Using impulsive differential equation comparison theorem, we derived sufficient conditions under which the infectious disease described by the considered model disappears ultimately. The analytical results are illustrated by numerical simulations for Hepatitis B virus infection that confirm the theoretical possibility of the infection elimination because of the proper vaccinations policy. Copyright © 2012 John Wiley & Sons, Ltd.     

按比例接种情况下的乙肝流行模型及研究

研究了按比例接种情况下的乙肝这种流行病的数学模型，给出了对疾病传播有重要影响的再生数R0，得到了无病平衡点和地方病平衡点的局部渐近稳定性，并对不同的参数进行了数值模拟．     

带有脉冲免疫和传染年龄的传染病模型的全局吸引性

讨论了带有脉冲免疫和传染年龄的传染病模型.传染类的恢复率是传染年龄的函数,当染病再生数小于1时,文章得到无病周期解是全局吸引的.如果总人口规模变化,也可得到类似的结论.最后,提出了带有脉冲免疫和传染年龄传染病模型待解决的问题.     

GLOBAL STABILITY OF SIVS MODEL WITH SATURATION INCIDENCE, INFECTION AGE AND IMPULSIVE VACCINATED RATE

In this paper, an impulsive vaccinated strategy to eradicate SIVS epidemic model is studied. Since infection age is an important factor of epidemic progression, we incorporate the infection age into the model. In this model, we analyze the dynamic behaviors of this model and obtain that there exists an infection-free periodic solution which is globally asymptotically stable under a sufficient condition. Our results indicate that a short period of pulse or a large pulse vaccination rate is the sufficient con...     

Three kinds of TVS in a SIR epidemic model with saturated infectious force and vertical transmission

Three different vaccination and treatment strategies in the SIR epidemic model with saturated infectious force and vertical transmission are analyzed. The dynamics of epidemic models are globally investigated by using Floquet theory and comparison theorem of impulsive differential equation. Thresholds are identified and global stability results are proved. For every treatment and vaccination strategy, the disease-free periodic solution of impulsive system has been obtained and is found to be globally asymptotically stable when the basic reproduction number is less than one, equivalently the cure rate is larger than the threshold value, whereas the disease is persistent when the basic reproduction number is larger than one. These results indicate that a large cure rate will lead to the eradication of a disease.     

The effect of impulsive vaccination on an SIR epidemic model

In this paper, an SIR epidemic model is constructed and analyzed. We get the result that if the parameters satisfy the condition β>α+γ+b, then the disease will be ultimately permanent. Under this condition, we consider how the impulsive vaccination affects the original system. The sufficient condition for the global asymptotical stability of the disease-eradication solution is obtained. We also get that if the impulsive vaccination rate is less than some value, the disease will be permanent, and the disease cannot be controlled. People can select appropriate vaccination rate according to our theoretical result to control diseases.     

两类易感者具垂直传染和预防接种的SIRS传染病模型

讨论了具有连续预防接种和脉冲预防接种且具有垂直传染的双线性SIRS传染病模型,分别给出了SIRS传染病模型基本再生数.利用Liapunov函数方法和LaSalle不变原理证明了连续预防接种下无病平衡点和正平衡点的全局稳定性;利用脉冲微分方程的Floquet 乘子理论和比较定理,证明了无病周期解的存在性和全局稳定性.     

非线性接触率SIR模型脉冲接种策略研究

建立了具有非线性接触率脉冲预防接种的SIR传染病模型,利用脉冲微分方程理论,对模型的动力学性态进行了分析,给出了模型的阀值,证明了无病周期解的存在性及全局渐近稳定性.     

具脉冲预防接种的SIRS传染病模型中地方病周期解的存在性

对具脉冲预防接种的SIRS传染病模型进行分析,利用分支理论得到了系统中地方病周期解的存在性,并利用数值模拟的方法验证了所得结论的正确性,完善了对该系统的讨论结果     

Optimal Impulsive Control Problem with Application to Human Immunodeficiency Virus Treatment

This paper describes an optimal control problem involving a nonlinear impulsive control system, together with a nonlinear objective function and nonlinear control and state constraints. Both the magnitude of the impulses as well as the instants at which the impulses are applied can be regarded as decision variables. A computational method is described for solving the problem. To illustrate the usefulness of our method for real-life applications, we solve a Human Immunodeficiency Virus (HIV) treatment problem. The numerical results obtained clearly illustrate the efficiency of our method.     

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.