Dynamics of the HBV model with diffusion and time delay

Chronic hepatitis B infection is a major health problem,with approximately 350 million virus carriers worldwide.In Africa,about 30%-60% of children and 60%-100% of adults have

Effects of temporal variability on HBV model calibration

This study aimed to investigate the effects of temporal variability on the optimization of the Hydrologiska ByrS.ns Vattenbalansavedlning （HBV） model, as well as the calibration performance using manual optimization and average parameter values. By applying the HBV model to the Jiangwan Catchment, whose geological features include lots of cracks and gaps, simulations under various schemes were developed： short, medium-length, and long temporal calibrations. The results show that, with long temporal calibration, the objective function values of the Nash- Sutcliffe efficiency coefficient （NSE）, relative error （RE）, root mean square error （RMSE）, and high flow ratio generally deliver a preferable simulation. Although NSE and RMSE are relatively stable with different temporal scales, significant improvements to RE and the high flow ratio are seen with longer temporal calibration. It is also noted that use of average parameter values does not lead to better simulation results compared with manual optimization. With medium-length temporal calibration, manual optimization delivers the best simulation results, with NSE, RE, RMSE, and the high flow ratio being 0.563 6, 0.122 3, 0.978 8, and 0.854 7, respectively; and calibration using average parameter values delivers NSE, RE, RMSE, and the high flow ratio of 0.481 1, 0.467 6, 1.021 0, and 2.784 0, respectively. Similar behavior is found with long temporal calibration, when NSE, RE, RMSE, and the high flow ratio using manual optimization are 0.525 3, -0.069 2, 1.058 0, and 0.980 0, respectively, as compared with 0.490 3, 0.224 8, 1.096 2, and 0.547 9, respectively, using average parameter values. This study shows that selection of longer periods of temooral calibration in hvdrolouical analysis delivers better simulation in general for water balance analysis.

Mathematical Analysis on a General Delayed HBV Model with Capsids and Two Infection Routes

Considering that HBV belongs to the DNA virus family and is hepatotropic,we model the HBV DNA-containing capsids as a compartment.In this paper,a delayed HBV infection model is established,where the general incidence function and two infection routes including cell-virus infection and cell-cell infection are introduced.According to some preliminaries,including well-posedness,basic reproduction number and existence of two equilibria,we obtain the threshold dynamics for the model.We illustrate numerical simulations to verify the above theoretical results,and furthermore explore the impacts of intracellular delay and cell-cell infection on the global dynamics of the model.

A NOVEL STOCHASTIC HEPATITIS B VIRUS EPIDEMIC MODEL WITH SECOND-ORDER MULTIPLICATIVE α-STABLE NOISE AND REAL DATA

This work presents an advanced and detailed analysis of the mechanisms of hepatitis B virus(HBV)propagation in an environment characterized by variability and stochas-ticity.Based on some biological features of the virus and the assumptions,the corresponding deterministic model is formulated,which takes into consideration the effect of vaccination.This deterministic model is extended to a stochastic framework by considering a new form of disturbance which makes it possible to simulate strong and significant fluctuations.The long-term behaviors of the virus are predicted by using stochastic differential equations with second-order multiplicative α-stable jumps.By developing the assumptions and employing the novel theoretical tools,the threshold parameter responsible for ergodicity(persistence)and extinction is provided.The theoretical results of the current study are validated by numerical simulations and parameters estimation is also performed.Moreover,we obtain the following new interesting findings:(a)in each class,the average time depends on the value ofα;(b)the second-order noise has an inverse effect on the spread of the virus;(c)the shapes of population densities at stationary level quickly changes at certain values of α.The last three conclusions can provide a solid research base for further investigation in the field of biological and ecological modeling.

基于积雪数据的HBV模型改进及应用

大渡河流域内站点分布较少,历史观测数据不足,给该地区的融雪径流预报带来困难。基于欧洲中期天气预报中心提供的最新一代高分辨率陆面再分析数据集ERA5-Land,将积雪覆盖率和积雪平均深度引入度日因子雪量计算公式中,对HBV模型的积融雪模块进行改进,以提升融雪径流计算的可靠性。以大渡河上游为研究对象,选取1961—2018年的水文气象资料对模型进行率定和验证,并以2019年为例进行试预报研究。结果表明,通过引入ERA5-Land再分析数据,以及对积融雪模块进行改进,发挥了其在模拟积融雪上的优势,有效提升了融雪径流预报精度,对大渡河流域具有适用性。研究成果可为稀缺资料地区融雪径流模拟预报提供经验。

二阶随机扰动下HBV流行病模型全局正解的存在唯一性与平稳分布

提出一个二阶随机扰动下的乙型肝炎病毒(HBV)感染模型,并在垂直传播比例μωνC不被认为是新感染的条件下研究了该模型的动力学行为。首先,证明了该随机模型全局正解的存在唯一性。其次,通过构造合适的Lyapunov函数,证明了在Ros>1的情况下,该随机模型平稳分布的存在唯一性和遍历性,并且得到了一个当噪声等于0时与基本再生数R0相等的随机临界值Ros。

妊娠期肝内胆汁淤积症合并HBV感染孕妇妊娠不良结局风险预测模型的构建

目的:构建妊娠期肝内胆汁淤积症(ICP)合并乙型肝炎病毒(HBV)感染孕妇妊娠不良结局风险模型并制定相应护理措施。方法:回顾性选取2021年5月—2022年3月在我院接受治疗的108例妊娠期ICP合并HBV孕妇作为研究对象,根据是否发生妊娠不良结局分为良好结局组和不良结局组。采用多因素Logistic回归分析不良结局发生的影响因素并构建妊娠期ICP合并HBV孕妇妊娠不良结局的风险模型。另外,选取2022年5月—2023年3月在我院符合纳入标准的62例妊娠期ICP合并HBV孕妇作为验证组。结果:良好结局组62例(57.41%),不良结局组46例(42.59%),多因素分析结果显示,丙氨酸氨基转移酶(ALT)、HBV的脱氧核糖核酸(HBV-DNA)、门冬氨酸氨基转移酶(AST)及总胆汁酸(TBA)是ICP合并HBV孕妇妊娠不良结局发生的独立影响因素(P<0.05);在此基础上建立风险预测模型,其受试者工作特征曲线(ROC)下面积(AUC)为0.859,95%CI(0.786,0.931),敏感度为71.7%,特异度为85.5%。验证模型AUC为0.842,Hosemer-Lemeshow检验显示,χ^(2)=6.391,P=0.603。结论:妊娠期ICP合并HBV孕妇妊娠不良结局的风险预测模型具有较好的预测效能,ALT、HBV-DNA、AST及TBA均是病人发生不良结局的主要影响因素,护理人员应注意孕妇各项指标的定期监测,及时调整治疗方案,降低妊娠不良结局的发生风险。

合并MAFLD的慢性HBV感染者显著肝纤维化的无创模型建立与验证

目的 探究合并代谢相关性脂肪性肝病(metabolic associated fatty liver disease,MAFLD)的慢性HBV感染患者发生显著肝纤维化的危险因素,构建并验证预测肝组织显著肝纤维化的无创模型,为临床启动抗纤维化治疗提供思路。方法 回顾性收集2015年1月至2020年12月就诊于广东省中医院肝病科收治的合并MAFLD的慢性HBV感染患者445例,根据入院时间分为训练队列(n=274)和验证队列(n=171)。训练队列中根据病理结果分为无/轻微肝纤维化组(<S_(2)期,n=106)和显著肝纤维化组(≥S_(2)期,n=168),比较两组患者临床指标,多因素Logistic回归方法筛选显著肝纤维化的危险因素,ROC曲线评价无创模型的预测效能,并在验证队列中验证。结果 445例患者中,肝组织显著纤维化287例(63.08%),其中训练队列168例(61.31%)、验证队列119例(69.59%)。训练队列中,≥S_(2)期组患者的年龄、ALT、AST、ALP、GGT、PT、HBsAg、HBV DNA、LSM均高于<S_(2)组,WBC、RBC、PLT、TG、Urea均低于<S_(2)组(P<0.05)。多因素分析显示,年龄、GGT、HBV DNA、LSM均是显著肝纤维化的独立危险因素(P<0.05),Urea是保护因素(P<0.05)。根据年龄、GGT、Urea、HBV DNA和LSM建立无创模型Y=0.063×年龄(岁)+0.016×GGT(U/L)+0.246×HBV DNA(lg IU/L)+0.245×LSM(kPa)-0.484×Urea(mmol/L)-3.578,在训练队列中预测肝组织显著纤维化预测效能均高于APRI、FIB-4(P<0.05),取敏感度与特异度最大时的点的临界值Y=0.70,此时预测敏感度为62.5%,特异度为92.5%;在验证队列中,预测效能均高于APRI、FIB-4(P<0.05)。结论 年龄、GGT、Urea、HBV DNA和LSM是合并MAFLD的慢性HBV感染患者发生显著肝纤维化的危险因素,由这些参数建立的无创模型对预测该人群发生显著肝纤维化有一定准确性。

DYNAMICAL BEHAVIOR OF A STOCHASTIC HBV INFECTION MODEL WITH LOGISTIC HEPATOCYTE GROWTH

This paper is concerned with a stochastic HBV infection model with logistic growth. First, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HBV infection model. Then we obtain sufficient conditions for extinction of the disease. The stationary distribution shows that the disease can become persistent in vivo.

Projection of future streamflow of the Hunza River Basin,Karakoram Range(Pakistan)using HBV hydrological model

Hydrologiska Byrans Vattenbalansavdeling(HBV) Light model was used to evaluate the performance of the model in response to climate change in the snowy and glaciated catchment area of Hunza River Basin. The study aimed to understand the temporal variation of streamflow of Hunza River and its contribution to Indus River System(IRS). HBV model performed fairly well both during calibration(R2=0.87, Reff=0.85, PBIAS=-0.36) and validation(R2=0.86, Reff=0.83, PBIAS=-13.58) periods on daily time scale in the Hunza River Basin. Model performed better on monthly time scale with slightly underestimated low flows period during bothcalibration(R2=0.94, Reff=0.88, PBIAS=0.47) and validation(R2=0.92, Reff=0.85, PBIAS=15.83) periods. Simulated streamflow analysis from 1995-2010 unveiled that the average percentage contribution of snow, rain and glacier melt to the streamflow of Hunza River is about 16.5%, 19.4% and 64% respectively. In addition, the HBV-Light model performance was also evaluated for prediction of future streamflow in the Hunza River using future projected data of three General Circulation Model(GCMs) i.e. BCC-CSM1.1, CanESM2, and MIROCESM under RCP2.6, 4.5 and 8.5 and predictions were made over three time periods, 2010-2039, 2040-2069 and 2070-2099, using 1980-2010 as the control period. Overall projected climate results reveal that temperature and precipitation are the most sensitiveparameters to the streamflow of Hunza River. MIROC-ESM predicted the highest increase in the future streamflow of the Hunza River due to increase in temperature and precipitation under RCP4.5 and 8.5 scenarios from 2010-2099 while predicted slight increase in the streamflow under RCP2.6 during the start and end of the 21 th century. However, BCCCSM1.1 predicted decrease in the streamflow under RCP8.5 due to decrease in temperature and precipitation from 2010-2099. However, Can ESM2 predicted 22%-88% increase in the streamflow under RCP4.5 from 2010-2099. The results of this study could be useful for decision making and effective future strategic plans for water management and their sustainability in the region.

Modelling and Simulation of the Spread of HBV Disease with Infectious Latent

This paper studies the global behavior of the spread of HBV using a SEIR model with a constant vaccination rate. The infectivity during the incubation period is considered as a second way of transmission. The basic reproduction number R0 is derived as a function of the two contact rates?β1?and β2?. There is a disease free equilibrium point (DFE) of our model. When R0 R0 > 1, there is a unique endemic equilibrium. We proved that the endemic equilibrium was globally asymptotically stable when R0 > 1 and that the disease persisted in the population. These results are original for our model with vaccination and two contact rates.

HBV模型在玛纳斯河流域的适用性

新疆天山北坡山区流域水文气象资料稀缺,融雪径流模拟比较困难。为研究HBV模型在新疆天山北坡玛纳斯河流域径流模拟的适用性,通过分析流域积雪覆盖率与径流的相关性,并基于中国地面降水与气温日值0.5°×0.5°格点数据集,经空间插值得到研究区多年平均降水和气温的空间分布,运用HBV模型模拟了玛纳斯河流域2000—2013年日尺度和月尺度径流过程,与SRM的模拟效果进行对比分析。结果表明:①多年月平均积雪覆盖率与多年月平均流量呈负相关,相关系数R^(2)=0.67,流域内积雪融水对径流的补给作用明显;②数据集经空间插值得到研究区多年平均降水和气温的空间分布能基本反映流域的垂直气候差异性,数据集可作为玛纳斯河流域缺乏气象资料的高山区径流模拟的输入数据;③HBV模型与SRM在玛纳斯河流域日尺度和月尺度的径流模拟效果评价等级均为良好,且HBV模型对洪峰流量模拟效果更好,整体的模拟值与实测值偏差更小,HBV模型在玛纳斯河流域具有较好的适用性。

HBV相关肝纤维化小鼠模型的建立及关键表型深度分析研究

目的 探索HBV感染所致肝纤维化小鼠模型形成条件及表型分析。方法 以18只CBA/CaJ小鼠为研究对象,随机分为对照组(n=4)和实验组(n=14),实验组按照每只2μg的剂量、通过高压水动力方法进行尾静脉注射cccDNA,对照组注射等体积PBS,转染68周后采样。通过qPCR方法检测肝中HBV DNA及HBV cccDNA,ELISA方法检测血清HBsAg、HBeAg,免疫组化检测肝组织中HBsAg、HBcAg,用一代测序法检测HBeAg+/HBsAg-及HBeAg-/HBsAg+组织DNA基因测序,生化分析ALT和AST,HE染色、天狼星染色及Masson染色分析肝组织病理。结果 实验组中,100%的小鼠HBV-DNA拷贝数高于1000 copies/mL;小鼠肝组织cccDNA拷贝数显著高于空白组(P<0.05);42.9%的小鼠血清HBsAg和HBeAg呈阳性;60%的小鼠肝HBsAg呈阳性和26.7%的小鼠肝HBcAg呈阳性;HBeAg-/HBsAg+样本中出现A1762T/G1764A和G1896A/G1899A位点突变,HBeAg+/HBsAg-样本出现前S2区及S区多位点突变;小鼠ALT值异常率为57.1%,AST值异常率为7.1%;HE染色观察到所以实验组小鼠肝组织损伤及肝炎症浸润,天狼星染色、Masson染色观察到92.9%的肝组织发生纤维化。结论 通过尾静脉高压水动力注射CBA/CaJ小鼠HBV cccDNA 68周后,HBV主要DNA、HBV cccDNA、血清及肝组织HBsAg、HBeAg仍然阳性,HBV感染可引起小鼠肝纤维化,甚至可模拟临床HBV BCP/PC基因突变表型。

考虑病毒DNA核衣壳和细胞间传播的一般HBV扩散模型

该文综合考虑了诱发HBV感染的两类途径、一般发生率函数和HBV病毒及其核衣壳的扩散效应,建立了一般性的HBV扩散模型.证明了模型解的适定性,两类平衡态的存在唯一性和模型的一致持久性,然后通过构造Lyapunov函数,得出模型的阈值动力学行为.最后结合数值模拟验证理论结果的同时,揭示了扩散对各状态变量的影响,结果显示:扩散影响HBV感染,且扩散系数越大,HBV感染的空间区域越大.

基于CMIP6气候模式和两种水文模型综合集成预估的黄河源区未来40年流量变化

基于两个共享社会经济低碳路径(SSP1-2.6、SSP2-4.5)下的CMIP6中的8个GCMs气候模式进行黄河源区2021—2060年平均气温和降水量预估。在此基础上,利用CMIP6中的8个GCMs气候模式分别驱动HBV、SWAT水文模型综合集成预估了黄河源区2021—2060年流量的年代际变化。结果表明:SSP1-2.6、SSP2-4.5情景下,2021—2060年黄河源区呈暖湿化趋势,平均气温较基准期(1995—2014年)分别上升1.3℃、1.6℃,年降水量分别增加11.6%、11.5%。SSP1-2.6、SSP2-4.5情景下2021—2060年黄河源区年平均流量分别增多8.6%、8.5%;两种情景下黄河源区21世纪各年代际流量均增加,其中21世纪20年代和30年代流量增幅小于40年代、50年代流量增幅。SSP1-2.6、SSP2-4.5情景下黄河源区2021—2060年6—8月流量减幅在1%以下,而3—5月和9—12月流量增幅为0.1%~2.1%。SSP1-2.6、SSP2-4.5情景下黄河源区蓄水期(9—11月)极端丰水流量增加2.5%~2.7%,SSP1-2.6情景下黄河源区2021—2060年汛期(6—8月)极端丰水流量总体增加0.1%,SSP2-4.5情景下黄河源区汛期极端丰水流量减少1.3%,SSP1-2.6、SSP2-4.5情景下黄河源区枯水期(12至次年5月)极端丰水流量减少0.7%~1.0%;黄河源区汛期(SSP1-2.6和SSP2-4.5情景)及枯水期(SSP1-2.6情景)极端枯水流量较基准期增加0.8%~1.9%,两种情景下黄河源区蓄水期极端枯水流量减少1.8%~2.3%。

基于HBV模型确定沁河流域洪涝致灾临界雨量

对暴雨洪涝较为严重的沁河流域进行暴雨洪涝风险评估需要致灾临界雨量。运用半分布式水文模型HBV,选取以润城水文站为控制站的沁河流域1977—1988年逐日气象数据和水文数据,在率定和验证水文模型HBV的基础上,结合水位—流量关系,对沁河流域洪涝致灾临界雨量进行确定,并且运用1982年洪涝灾情的实测水文数据和降水量数据,验证致灾临界降水量的合理性。结果表明:沁河流域的三级致灾临界降水量是合理的,可作为判断该流域在不同前期水位条件下是否发生暴雨洪涝灾害的依据。

基于HBV模型的尼洋曲流域上游洪水致灾临界面雨量研究

[目的]建立工布江达以上尼洋曲流域的降水—径流关系,构建该流域的致洪临界雨量指标,以期为开展山洪气象预警工作提供参考。[方法]根据流域暴雨洪水致灾机制,利用地面气象观测和CMORPH资料,基于HBV水文模型进行计算分析。[结果]利用2007—2011年观测数据对HBV水文模型的参数优化和率定,模拟数据与观测数据的确定性系数为0.91,NASH效率系数为0.89;采用2012—2014年观测数据进行验证,确定性系数为0.86,NASH效率系数为0.85,率定期和验证期的平均相对误差均为3.1%,表明经过率定的HBV模型对尼洋曲上游流域具有较好的适用性。[结论]尼洋曲流域的洪水过程不仅与实时降水的面雨量有关,还与前期基础水位有关,致灾临界面雨量随前期基础水位升高而减小,并且随着前期水位的变化,临界雨量值呈现了非线性响应特征。

基于HBV模型的淮河流域洪水致灾临界雨量研究

根据流域暴雨洪水致灾机制,文章提出了考虑前期基础水位的动态致灾临界雨量指标,并以淮河上游地区为例,基于HBV水文模型建立了降水-流量-水位关系,并根据这种关系确立了临界雨量确定的方法流程。首先基于历史水文数据率定和验证模型,得到适用于研究区的最优化模型参数,然后构建洪水上涨期水位流量关系,最后以是否达到致灾水位为标准,通过模型试算并结合水位流量关系曲线反推出致灾临界雨量值。在淮河上游地区的研究中,利用2002-2009年逐日气象水文数据对HBV模型进行了参数率定和检验,并针对洪水过程进行了参数优化,经过率定后HBV模型对王家坝以上流域具备较好的适用性,对典型洪水过程模拟的确定性系数和NASH效率系数均在0.8以上;根据王家坝站实测流量水位数据,构建了概化的单一关系曲线;结合HBV模型和水位流量关系得到了王家坝以上流域的动态致灾临界雨量指标,临界雨量值随前期基础水位升高而减小,并且随着前期水位的变化,临界雨量值呈现了明显的非线性响应特征。

HBV模型的改进与应用

在HBV模型原理及其特点的基础上,结合广东省所处的暴雨径流地区的水文特征,去掉冰雪融水量对产汇流的影响,增加了坡面产流和汇流模块,并把河网线性汇流改成马斯京根河网汇流。将改进的模型应用于韩江棠荆流域做进一步的研究,并把原模型及改进模型所得到的结果分别与实测结果进行比较分析,从而为今后继续拓展HBV模型在该流域的应用提供有益的研究经验。

HBV水文模型在玉树巴塘河流域洪水临界雨量阈值研究中的应用

区域气象灾害的评估在防灾减灾中具有很重要的地位,它不仅是认识灾情、进行灾害区划、实行灾害预测、制定防治对策、进行损失评估、实施防治措施和进行项目管理的基础,对政府的辅助决策都具有重要意义。基于玉树县社会经济统计资料、水文资料、巴塘河洪水灾情资料的基础上,应用HBV模型尝试性的研究暴雨诱发的中小河流洪水临界风险雨量阈值研究,结果表明:1)近11a来新寨站平均流量23.2m3/s,2001年、2003年、2005年汛期流量较大,2006—2011年流量明显偏少;2)在率定期HBV模型对新寨站日径流深模拟的确定性系数达0.678 2,Nash效率系数为0.604 4,验证期确定性系数超过了0.770,Nash效率系数为0.530 5;3)根据不同的基础水位,有效划分了24h玉树巴塘河流域洪水面雨量预警指标,为今后玉树县巴塘河流域提高灾害防御能力提供研究基础。