A Collocation Technique via Pell-Lucas Polynomials to Solve Fractional Differential EquationModel for HIV/AIDS with Treatment Compartment

In this study,a numerical method based on the Pell-Lucas polynomials(PLPs)is developed to solve the fractional order HIV/AIDS epidemic model with a treatment compartment.The HIV/AIDS mathematical model with a treatment compartment is divided into five classes,namely,susceptible patients(S),HIV-positive individuals(I),individuals with full-blown AIDS but not receiving ARV treatment(A),individuals being treated(T),and individuals who have changed their sexual habits sufficiently(R).According to the method,by utilizing the PLPs and the collocation points,we convert the fractional order HIV/AIDS epidemic model with a treatment compartment into a nonlinear system of the algebraic equations.Also,the error analysis is presented for the Pell-Lucas approximation method.The aim of this study is to observe the behavior of five populations after 200 days when drug treatment is applied to HIV-infectious and full-blown AIDS people.To demonstrate the usefulness of this method,the applications are made on the numerical example with the help of MATLAB.In addition,four cases of the fractional order derivative(p=1,p=0.95,p=0.9,p=0.85)are examined in the range[0,200].Owing to applications,we figured out that the outcomes have quite decent errors.Also,we understand that the errors decrease when the value of N increases.The figures in this study are created in MATLAB.The outcomes indicate that the presented method is reasonably sufficient and correct.

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。

HIV/AIDS患者肠内营养治疗喂养不耐受发生风险预测模型的构建与验证

目的调查HIV/AIDS患者肠内营养治疗喂养不耐受的影响因素,建立列线图预测模型并进行验证。方法回顾性分析2015年1月1日至2021年9月30日南宁市第四人民医院收治的HIV/AIDS住院患者临床资料,通过二分类Logistic回归模型,探索HIV/AIDS患者肠内营养治疗喂养不耐受的危险因素,构建列线图预测模型并验证评价。结果共纳入174例HIV/AIDS患者,其中76例HIV/AIDS患者发生早期肠内营养喂养不耐受(43.68%)。多因素分析显示,平均动脉压≤80 mmHg[OR=2.822,95%CI(1.267,6.287)]、急性生理学与慢性健康状况评分Ⅱ>15分[OR=5.625,95%CI(1.435,22.048)]、机械通气应用[OR=5.459,95%CI(2.046,14.564)]、高效抗反转录病毒治疗[OR=2.428,95%CI(1.118,5.275)]、肌松剂应用[OR=3.833,95%CI(1.758,8.357)]、CD4^(+)T细胞计数≤200个·μL^(-1)[OR=3.785,95%CI(1.126,12.724)]、抗生素使用数量>2种[OR=2.365,95%CI(1.039,5.384)]是HIV/AIDS患者肠内营养治疗发生喂养不耐受的影响因素。列线图预测模型AUC值为0.849[95%CI(0.794,0.905)],最大约登指数为0.555时,最佳临界值为0.331,灵敏度为88.16%,特异度为67.35%;校准曲线、决策曲线评价模型具有较好的一致性及获益性。结论本研究构建的HIV/AIDS患者肠内营养治疗喂养不耐受风险预测模型可为医护人员快速识别HIV/AIDS患者喂养不耐受发生风险、及时采取预防性护理措施提供参考依据。

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.

具有非线性免疫反应的随机HIV模型的平稳分布

针对一类具有靶细胞生长和非线性免疫反应的随机HIV模型,利用随机Lyapunov分析法以及It8公式证明其存在唯一的遍历平稳分布,得到了存在平稳分布的充分条件.证明中构造了新颖的随机Lyapunov函数,得出了当关键阈值基本再生数R_(0)^(S)>1和病毒繁殖数R_(1)^(S)>1同时成立时,随机HIV模型存在唯一的遍历平稳分布的结论.遍历平稳分布的存在意味着所有个体都可以长期共存.

具有两种感染模式和免疫反应的多时滞HIV模型的动力学分析

研究了基于游离病毒和细胞–细胞两种传播机制和适应性免疫的多时滞HIV动力学模型,计算出模型存在五个平衡点和五个基本再生数。通过构造适当的Lyapunov函数,得到了模型的五个平衡点全局渐近稳定的充分条件。发现将一个时滞τ_(3)作为分支参数,可引起两个平衡点E_(2)和E_(4)失稳,并产生Hopf分支。结果说明τ_(3)可导致病毒载量出现周期振荡和免疫反应可降低感染风险。最后利用数值模拟验证所得结论,并对比了不同时滞参数对E_(2)和E_(4)的稳定性影响。

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.

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.

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.

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.

Association between Macroscopic-factors and Identified HIV/AIDS Cases among Injecting Drug Users: An Analysis Using Geographically Weighted Regression Model

Drug use （DU）, particularly injecting drug use （IDU） has been the main route of transmission and spread of Human Immunodeficiency Virus （HIV）/Acquired Immune Deficiency Syndrome （AIDSJ among injecting drug users （IDUs）[1]. Previous studies have proven that needles or cottons sharing during drug injection were major risk factors for HIV/AIDS transmission at the personal level[z4]. Being a social behavioral issue, HIV/AIDS related risk factors should be far beyond the personal level. Therefore, studies on HIV/AIDS related risk factors should focus not only on the individual factors, but also on the association between HIV/AIDS cases and macroscopic-factors, such as economic status, transportation, health care services, etc[1]. The impact of the macroscopic-factors on HIV/AIDS status might be either positive or negative, which are potentially reflected in promoting, delaying or detecting HIV/AIDS epidemics.

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.

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.

Mammalian cell cultures as models for Mycobacterium tuberculosis-human immunodeficiency virus(HIV) interaction studies:A review

Mycobacterium tuberculosis(MTB) and human immunodeficiency virus(HIV) co-infections have remained a major public health concern worldwide,particularly in Southern Africa.Yet our understanding of the molecular interactions between the pathogens has remained poor,primarily due to lack of suitable preclinical models for such studies.We reviewed the use,this far,of mammalian cell culture models in HIV-MTB interaction studies.Studies have described the use of primary human cell cultures,including monocyte-derived macrophage(MDM) fractions of peripheral blood mononuclear cell(PBMC),alveolar macrophages(AM),cell lines such as the monocyte-derived macrophage cell line(U937),T lymphocyte cell lines(CEMx174,ESAT-6-specific CD4+ T-cells) and an alveolar epithelial cell line(A549) and special models such as stem cells,three dimensional(3D) or organoid cell models [including a blood-brain barrier(BBB) cell model] in HIV-MTB interaction studies.The use of cell cultures from other mammals,including:mouse cell lines [macrophage cell lines RAW 264.7 and J774.2,fibroblast cell lines(NIH 3T3,C3 H clones),embryonic fibroblast cell lines and T-lymphoma cell lines(S1A.TB,TIMI.4 and R1.1)]; rat(T cells:Rat2,RGE,XC and HH16,and alveolar cells:NR8383) and primary guinea pigs derived AMs,in HIV-MTB studies is also described.Given the spectrum of the models available,cell cultures offer great potential for host-HIV-MTB interactions studies.

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.

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.

Providing a Therapeutic Scheduling for HIV Infected Individuals with Genetic Algorithms Using a Cellular Automata Model of HIV Infection in the Peripheral Blood Stream

The aim of this study is to develop two-dimensional cellular automata model of HIV infection that depicts the dynamics involved in the interactions between acquired immune system and HIV infection in the peripheral blood stream. The appropriate biological rules of cellular automata model have been extracted from expert knowledge and the model has been simulated with determined initial conditions. Obtained results have been validated through comparing with the accepted AIDS reference curve. The new rules and states were added to the proposed model to show the effects of applying combined antiretroviral therapy. Our results showed that by applying RTI and PI drugs with maximum drug effectiveness, comparing with cases in which no treatment was applied, the steady state concentrations of healthy (infected) CD4+T cells were increased (decreased) 53% (41%). Also, the use of cART with maximum drug effectiveness led to a 69% reduction in the steady state level of viral load. At this time, obtained results have been validated through comparing with available clinical data. Our results showed good agreement with both reference curve and the clinical data. In the second phase of this study, by applying genetic algorithms, a therapeutic schedule has been provided that its use, while maintaining the quality of the treatment, leads to a 47% reduction in both drug dosage and the side effects of antiretroviral drugs.