Optimal Estimation of Parameters for an HIV Model

An HIV model was considered. The parameters of the model are estimated by adjoint dada assimilation method. The results showed the method is valid. This method has potential application to a wide variety of models in biomathematics.

Optimal Control Strategy for a Fully Determined HIV Model

This paper shows how mathematical methods can be implemented to formulate guidelines for clinical testing and monitoring of HIV/AIDS disease. First, a mathematical model for HIV infection is presented which the measurement of the CD4+T cells and the viral load counts are needed to estimate all its parameters. Next, through an analysis of model properties, the minimal number of measurement samples is obtained. In the sequel, the effect of Reverse Transcriptase enzyme Inhibitor (RTI) on HIV progression is demonstrated by using a control function. Also the total cost of treatment by this kind of drugs has been minimized. The numerical results are obtained by a numerical method in discretization issue, called AVK.

Mathematical Modeling of HIV Investigating the Effect of Inconsistent Treatment

HIV is a retrovirus that infects and impairs the cells and functions of the immune system. It has caused a great challenge to global public health systems and leads to Acquired Immunodeficiency Syndrome (AIDS), if not attended to in good time. Antiretroviral therapy is used for managing the virus in a patient’s lifetime. Some of the symptoms of the disease include lean body mass and many opportunistic infections. This study has developed a SIAT mathematical model to investigate the impact of inconsistency in treatment of the disease. The arising non-linear differential equations have been obtained and analyzed. The DFE and its stability have been obtained and the study found that it is locally asymptotically stable when the basic reproduction number is less than unity. The endemic equilibrium has been obtained and found to be globally asymptotically stable when the basic reproduction number is greater than unity. Numerical solutions have been obtained and analyzed to give the trends in the spread dynamics. The inconsistency in treatment uptake has been analyzed through the numerical solutions. The study found that when the treatment rate of those infected increases, it leads to an increase in treatment population, which slows down the spread of HIV and vice versa. An increase in the rate of treatment of those with AIDS leads to a decrease in the AIDS population, the reverse happens when this rate decreases. The study recommends that the community involvement in advocating for consistent treatment of HIV to curb the spread of the disease.

Mathematical Modeling of the Co-Infection Dynamics of HIV and Tuberculosis Incorporating Inconsistency in HIV Treatment

A non-linear HIV-TB co-infection has been formulated and analyzed. The positivity and invariant region has been established. The disease free equilibrium and its stability has been determined. The local stability was determined and found to be stable under given conditions. The basic reproduction number was obtained and according to findings, co-infection diminishes when this number is less than unity, and persists when the number is greater than unity. The global stability of the endemic equilibrium was calculated. The impact of HIV on TB was established as well as the impact of TB on HIV. Numerical solution was also done and the findings indicate that when the rate of HIV treatment increases the latent TB increases while the co-infected population decreases. When the rate of HIV treatment decreases the latent TB population decreases and the co-infected population increases. Encouraging communities to prioritize the consistent treatment of HIV infected individuals must be emphasized in order to reduce the scourge of HIV-TB co-infection.

基于Bayes时空模型分析HIV/AIDS晚发现的时空分布特征及其影响因素

【目的】旨在分析兰州市HIV/AIDS晚发现的时空聚集性特征及相关影响因素,明确兰州市HIV/AIDS晚发现高风险地区和时间趋势,为兰州市因地制宜地制定HIV/AIDS防治策略措施提供参考依据。【方法】选择兰州市2011-2018年间新报告的成年HIV/AIDS病例作为研究对象,研究中所需的数据资料来自兰州市疾病预防控制中心和兰州市统计年鉴。采用Bayes时空模型分析HIV/AIDS晚发现相对风险(RR)的时空分布特征及其影响因素。【结果】2011-2018年间兰州市新报告的HIV/AIDS病例共计1984例,其中HIV/AIDS晚发现者有982例(49.5%),平均年龄为39.67岁,男性占90.9%。老年人和女性HIV/AIDS病例中晚发现的比例更高;城关区(51.1%)、安宁区(50.3%)和榆中县(51.9%)具有高于平均水平的HIV/AIDS晚发现比例;2011-2018年间兰州市总体的晚发现比例呈波动上升趋势。Bayes时空模型分析结果显示,兰州市HIV/AIDS晚发现风险在2011-2015年间波动变化,而在2015年后迅速上升,其RR(95%CI)从1.01(0.84,1.23)上升到1.11(0.77,1.97);红古区和三个县的晚发现风险变化趋势与兰州市的总体变化趋势相似,而城关区和七里河区的晚发现风险呈下降趋势;晚发现相对风险大于1的区县包括:永登县(RR=1.07,95%CI:0.55,1.96)、西固区(RR=1.04,95%CI:0.67,1.49)、城关区(RR=2.41,95%CI:0.85,6.16)和七里河区(RR=2.03,95%CI:1.10,3.27)。冷热点分析结果显示城关区和七里河区为热点区。影响因素分析结果显示,随着人均GDP(RR=0.65,95%CI:0.35,0.90)和HIV/AIDS病例中的男性比例(RR=0.53,95%CI:0.19,0.92)的增高,HIV/AIDS晚发现的相对风险越低;而人口密度(RR=1.35,95%CI:1.01,1.81)越大,晚发现风险越高。【结论】兰州市的HIV/AIDS晚发现风险呈上升趋势,并且存在明显的地区差异特征;人均GDP、HIV/AIDS中男性比例和人口密度是HIV/AIDS晚发现的影响因素。因此,对于晚发现风险高和存在相关风险因素的区县,应重视并制定有针对性的HIV筛查和防治服务,降低HIV/AIDS晚发现比例和风险。

献血者HIV检测策略的成本效果分析

目的以多中心HIV残余风险研究为基础,分析不同HIV检测策略的成本与效果,为血站采用适宜的HIV检测策略提供参考依据。方法依据安徽省3家血站献血者HIV检测、确认情况,估算HIV不同检测方法的残余风险。建立决策树模型,分析国内现行政策下的3种不同检测策略的成本效果差异。结果本研究调查地区,抗-HIV-1+2 ELISA、HIV Ag/Ab1+2 ELISA、ELISA+NAT技术的残余风险分别为1.17×10^(-6)、0.84×10^(-6)、0.59×10^(-6);经决策树模型分析,在无核酸检测时,HIV Ag/Ab1+2 ELISA较抗-HIV-1+2 ELISA方案更具成本效果优势,但加上1遍NAT后,HIV Ag/Ab1+2 ELISA的优势消失;HIV试剂成本、HIV治疗成本以及假阳性报废成本,是模型的敏感因素。结论本研究调查地区,采用1遍抗HIV-1+2 ELISA加1遍NAT方案,具有成本效果优势。血站在决定采用何种HIV检测策略前,需对使用的酶免试剂,进行确认和评估,在保证灵敏度的前提下,综合考虑关键因素为试剂成本及试剂假阳性率。

具有非局部感染和周期治疗的HIV感染模型的时空动力学分析

该文建立了一类非自治反应扩散HIV细胞模型来研究周期治疗、非局部感染对HIV感染时空动力学的影响.具体地,首先推导出模型基本再生数R0,其由下一代再生算子R的谱半径所定义.然后对模型的动力学行为进行分析,其中包括无感染平衡态的全局稳定性、HIV感染的一致持久性以及周期正平衡态的存在性.最后,通过数值模拟验证了理论结果的正确性并分析了相关重要因素对HIV感染进程的影响,为HIV的临床治疗提供有价值的参考建议.

On the Bifurcations and Multiple Endemic States of a Single Strain HIV Model Dedicated to Professor Toshikazu Sunada on the Occasion of his 60th Birthday

The dynamics of a single strain HIV model is studied. The basic reproduction number R0 used as a bifurcation parameter shows that the system undergoes transcritical and saddle-node bifurcations. The usual threshold unit value of R0 does not completely determine the eradication of the disease in an HIV infected person. In particular, a sub-threshold value Rc is established which determines the system＇s number of endemic states： multiple if Rc 〈 Ro 〈 1, only one if Rc=Ro = 1, and none if R0 〈 Rc 〈 1.

Bifurcation and Stability Analysis of HIV Infectious Model with Two Time Delays

The HIV problem is studied by version of delay mathematical models which consider the apoptosis of uninfected CD4+ T cells which cultured with infected T cells in big volume. The opportunistic infection and the apoptosis of uninfected CD4+ T cells are caused directly or indirectly by a toxic substance produced from HIV genes. Ubiquitously, the nonlinear incidence rate brings forth the increasing number of infected CD4+ T cells with introduction of small time delay, and in addition, there also exists a natural time delay factor during the process of virus replication. With state feedback control of time delay, the bifurcating periodical oscillating phenomena is induced via Hopf bifurcation. Mathematically, with the geometrical criterion applied in the stability analysis of delay model, the critical threshold of Hopf bifurcation in multiple delay differential equations which satisfy the transversal condition is derived. By applying reduction dimensional method combined with the center manifold theory, the stability of the bifurcating periodical solution is analyzed by the perturbation near Hopf point.

Approximate Solutions for a Class of Fractional-Order Model of HIV Infection via Linear Programming Problem

In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of HIV infection of CD4+T cells with therapy effect. The fractional derivative in our approach is in the sense of Riemann-Liouville. To solve the problem, we reduce the system of FDE to a discrete optimization problem. By obtaining the optimal solutions of new problem by minimization the total errors, we obtain the approximate solution of the original problem. The numerical solutions obtained from the proposed approach indicate that our approximation is easy to implement and accurate when it is applied to a systems of FDEs.

How to Effectively Detect and Manage People Living with HIV/AIDS in China:Establishment of a Community-based Model

This study explored a novel systemic community-based model for detecting and manag-ing people living with HIV/AIDS (PLWHA). Both quantitative and qualitative research methods were used in this study. A quantitative questionnaire investigation was conducted in a sample of 1192 subjects which were randomly selected from two areas with high HIV prevalence, Xiangfan City and Shiyan City of Hubei Province, China. Twenty-two medical and health service staffs were inter-viewed by semi-structured questionnaire focusing on awareness, status, problems, and suggestions about community-based Voluntary Counseling and Testing and Provider Initiated Testing and Coun-seling (VCT/PITC). And they were organized to discuss about the aforementioned issues in Xiangfan City and Shiyan City, respectively. Our results showed that the accessibility and availability of the general VCT/PITC were bad. About 28.3% had known and only 4.9% had made use of VCT/PITC. Developing community-based VCT/PITC had some special advantages that can overcome some ex-isting problems to remedy the aforementioned defects. We are led to conclude that, to maximize the availability and uptake rate of the VCT/PITC, we plan to detect PLWHA by developing the commu-nity-based VCT/PITC through 4 paths. Then we establish the community HIV health care center con-stituted of 8 sectors to provide an overall management. Thus, we can effectively detect and manage the PLWHA with a new systemic community-based model.

The Changing Trends of HIV/AIDS in An Ethnic Minority Region of China: Modeling the Epidemic in Liangshan Prefecture, Sichuan Province

Objective This study was to investigate the HIV current situation in Liangshan prefecture, in order to predict prevalence and transmission trends. Methods Region-specific population, behavior, serosurveillence, and policy/program data （from 1995 to 2020） were gathered from various local and national organizations and applied to the Asian Epidemic Model （AEM） and used to derive estimates of future HIV prevalence, epidemic trends, and outcomes of intervention strategies. Results The AEM projections for 2020 included increased number of people living with HIV （PLHIV; to 136 617）, increased HIV prevalence （2.51%）, and 8037 deaths from acquired immunodeficiency syndrome （AIDS） in this region. However, the overall HIV incidence rate （per 10 000） was projected to decline from 27 in 2015 to 22 in 2020, largely due to a predicted decrease in HIV infection rate （per 10 000） from 658 in 2013 to 621 in 2020 among intravenous drug users. In contrast, the cases of HIV infection per i0 000 was projected to increase from 420 in 2010 to 503 in 2020 among men who have sex with men, and from 8 in 2010 to 15 in 2020 among the general population. The predominant risk factor for HIV transmission over the next decade in Liangshan was casual sex. Community-based outreach strategies to reduce injected drug use and casual sex, and to promote condom use, were predicted as effective interventions to decrease HIV transmission. Conclusion Implementation of a comprehensive public health program, with targeting to the region-specific at-risk populations, will help to mitigate HIV/AIDS spread in Liangshan.

Stability Analysis of a Delayed HIV/AIDS Epidemic Model with Treatment and Vertical Transmission

A delayed HIV/AIDS epidemic model with treatment and vertical transmission is investigated. The model allows some infected individuals to move from the symptomatic phase to the asymptomatic phase;next generation of infected individuals may be infected and it will take them some time to get maturity and infect others. Mathematical analysis shows that the global dynamics of the spread of the HIV/AIDS are completely determined by the basic reproduction number R0 for our model. If R0 R0 > 1.

Modelling the Impact of Stages of HIV Progression on Estimates

HIV/AIDS is a public health problem especially in sub-Saharan Africa where majority of infections and deaths occur. Despite the large number of studies and efforts made in covering the data gap using mathematical models, little is known on how model estimates are confounded by the transmission variabilities that exist in stages of HIV progression. This work investigates the impact of including stages of HIV transmission in HIV/AIDS models. A deterministic HIV/AIDS model is developed and extended to include stages of HIV progression of infected individuals. Theoretical investigation of the models and numerical analyses indicate that the two models produce different estimates, with the model without stages producing lower estimates than the staged model. These results call for a careful consideration in evaluating the efficiency of HIV/AIDS models that are used to estimate and project the burden of HIV/AIDS disease.

Animal models to study Mycobacterium tuberculosis and HIV co-infection

Mycobacterium tuberculosis(M.tb) and human immunodeficiency virus(HIV) co-infection has become a public health issue worldwide. Up to now, there have been many unresolved issues either in the clinical diagnosis and treatment of M.tb/HIV coinfection or in the basic understanding of the mechanisms for the impairments to the immune system by interactions of these two pathogens. One important reason for these unsolved issues is the lack of appropriate animal models for the study of M.tb/HIV coinfection. This paper reviews the recent development of research on the animal models of M.tb/HIV co-infection, with a focus on the non-human primate models.

Global and Bifurcation Analysis of an HIV Pathogenesis Model with Saturated Reverse Function

In this paper,an HIV dynamics model with the proliferation of CD4 T cells is proposed.The authors consider nonnegativity,boundedness,global asymptotic stability of the solutions and bifurcation properties of the steady states.It is proved that the virus is cleared from the host under some conditions if the basic reproduction number R0 is less than unity.Meanwhile,the model exhibits the phenomenon of backward bifurcation.We also obtain one equilibrium is semi-stable by using center manifold theory.It is proved that the endemic equilibrium is globally asymptotically stable under some conditions if R0 is greater than unity.It also is proved that the model undergoes Hopf bifurcation from the endemic equilibrium under some conditions.It is novelty that the model exhibits two famous bifurcations,backward bifurcation and Hopf bifurcation.The model is extended to incorporate the specific Cytotoxic T Lymphocytes(CTLs)immune response.Stabilities of equilibria and Hopf bifurcation are considered accordingly.In addition,some numerical simulations for justifying the theoretical analysis results are also given in paper.

一类具有Dirichlet边界条件的年龄-空间结构HIV/AIDS传染病模型的动力学分析

为了探讨个体扩散、感染年龄和Dirichlet边界环境对HIV/AIDS时空传播动力学的影响,该文构建了一类具有齐次Dirichlet边界条件的年龄空间结构HIV/AIDS传染病动力学模型.首先,应用特征线方法,作者将模型转化为一个积分反应扩散方程模型.其次,作者给出模型基本再生数R_(0)的泛函表达式,并研究了以R_(0)为阈值的模型解的动力学行为.具体地,当R_(0)<1时,HIV/AIDS在人群中可以被消除;而当R_(0)>1时,HIV感染在人群中会持续存在.最后,在二维空间区域中作者通过数值模拟验证了文中理论结果.

Building the Pharmacophore Model of HIV-1 Integrase Strand Transfer Inhibitors and Studying Their Inhibition Mechanism

The replication of HIV-1 requires the integration of its cyclic DNA into host DNA by HIV-1 integrase （IN）, which includes two important reactions, 3＇-processing and strand transfer, both catalyzed by HIV-1 IN. Disrupting either of the reactions will fulfill the purpose of inhibiting the replication of HIV-1. In this paper, pharmacophore modeling and molecular docking are employed to investigate the inhibition mechanism of the HIV-1 IN strand transfer inhibitors （INSTIs）. Based on the results, we suggest that the inhibition mechanism of INSTIs involves the inhibitor chelating the cofactors Mg2＋ and its forming hydrogen bonds with some crucial residues adjacent to the DDE active center.

Modelling two different therapy strategies for drug T-20 on HIV-1 patients

A mathematical model describing the antiretroviral therapy of Enfuvirtide on HIV-1 patients is developed. The effect of Enfuvirtide （formerly called T-20） by impulsive differential equations is modeled by two different drug elimination kinetics, the first-order elimination kinetics and the Michaelis-Menten elimination kinetics. The model is a non-autonomous system of differential equations. For a time-dependent system, the disease-free equilibrium is mainly studied. Its stability, when the therapy is taken with perfect adherence, is obtained. To ensure the disease-free equilibrium remains stable, the analytical thresholds for dosage and dosing intervals are determined. The effects of super- vised treatment interruption are also explored. It is shown that the supervised treatment interruption can be worse than no therapy at all.