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Osteoclasts are giant bone-digesting cells that harbor specialized lysosome-related organelles termed secretory lysosomes (SLs). SLs store cathepsin K and serve as a membrane precursor to the ruffled border, the osteoclast’s ‘resorptive apparatus’. Yet, the molecular composition and spatiotemporal organization of SLs remains incompletely understood. Here, using organelle-resolution proteomics, we identify member a2 of the solute carrier 37 family (Slc37a2) as a SL sugar transporter. We demonstrate in mice that Slc37a2 localizes to the SL limiting membrane and that these organelles adopt a hitherto unnoticed but dynamic tubular network in living osteoclasts that is required for bone digestion. Accordingly, mice lacking Slc37a2 accrue high bone mass owing to uncoupled bone metabolism and disturbances in SL export of monosaccharide sugars, a prerequisite for SL delivery to the bone-lining osteoclast plasma membrane. Thus, Slc37a2 is a physiological component of the osteoclast’s unique secretory organelle and a potential therapeutic target for metabolic bone diseases.

血管球瘤是一种来源于正常血管球细胞的间质性肿瘤，常发生于四肢真皮深部或皮下组织，口腔颌面部受累者较少见，而发生于上颌骨的血管球瘤罕见报道。本文报道1例发生于上颌骨、具有典型疼痛症状和特异性影像学表现的血管球瘤，分析和总结其临床病理学特征、影像学特点、治疗及预后，以期为正确诊断和治疗血管球瘤提供参考。.

Lifetime imaging methods using phosphorescence quenching by oxygen for molecular oxygen concentration measurement have been developed and used for non-invasive oxygen monitoring. This study reports photoacoustic (PA) oxygen imaging powered by polyacrylamide (PAAm) hydrogel nanoparticle (NP) which offer advantages including improved biocompatibility, reduced toxicity, and active tumor targeting. A known oxygen indicator, oxyphor G2, was conjugated with the matrix of the NPs, giving G2-PAA NPs, followed by PEGylation for biocompatibility and F3 surface modification for tumor targeting. Using two lasers providing pump and probe pulses, respectively, PA imaging was performed so as to quantitatively map the oxygen concentration in biological tissues in vivo, including cancer tumors and normal thigh muscles. Furthermore, via the imaging at the pump wavelength and two additional wavelengths, the accumulation of the G2-PAA NPs in the tumors were also determined. The successful imaging experiment accomplished on animal models renders a method for in vivo non-invasive imaging and assessment of hypoxic tumor microenvironments, which is critical for assessing cancer progression, metastasis, and treatment.

Introduction:Rheumatic heart disease is among the leading causes of acquired valvular heart disease in the developing world. However, there is no data available for rheumatic heart disease in the paediatric population of Sabah. This study collected data for acute rheumatic fever admissions among the paediatric population in Sabah over a period of 3 years.Methods:This is a retrospective cohort study. All records for admissions to paediatric wards in Sabah for acute rheumatic fever from January 2016 to December 2018 were collected. The patient records were then traced and required information were collected.Results:A total of 52 cases of acute rheumatic fever were admitted. It was observed that the incidence of acute rheumatic fever was 74.4 per 100,000 paediatric admissions. Patients from the West Coast Division made up most of the admissions (n = 24, 46.2%). Male patients (n = 35, 67.3%) of the indigenous Kadazan-Dusun ethnicity (n = 21, 40.4%) were most commonly encountered. The mean age at time of presentation was 9.58 years. Most cases admitted (n = 38, 73.1%) were categorised as Priority 1 (severe rheumatic heart disease).Conclusion:Most patients who were admitted had symptoms of heart failure and were diagnosed with severe rheumatic heart disease. Although this disease is preventable, the incidence in Sabah remains high. This study was limited as we only looked at patients who were admitted and we foresee the real incidence to be higher. Hence, there is an urgent need for a rheumatic heart disease registry in Malaysia to gather more data for prevention and early intervention.

Vitamin C deficiency has been a historical disease rarely seen nowadays. We illustrate a case of a boy with autism presenting with severe pulmonary hypertension and refusal to walk secondary to vitamin C deficiency. Initiating treatment with high-dose vitamin C reversed his symptoms and he regained full power of his lower limbs with total normalisation of his pulmonary pressures.

On the 18th of March 2020, the Malaysia government declared a movement control order (MCO) due to the unprecedented COVID-19 pandemic. Although the majority of patients presented with respiratory-related symptoms, COVID-19 patients may present atypically with neurological manifestations and may even have an increased risk of stroke. The Malaysia Stroke Council is concerned regarding the level of care given to stroke patients during this pandemic. During the recent National Stroke Workflow Steering Committee meeting, a guide was made based on the currently available evidences to assist Malaysian physicians providing acute stroke care in the hospital setting in order to provide the best stroke care while maintaining their own safety. The guide comprises of prehospital stroke awareness, hyperacute stroke care, stroke care unit and intensive care unit admission, post-stroke rehabilitation and secondary prevention practice. We urge continuous initiative to provide the best stroke care possible and ensure adequate safety for both patients and the stroke care team.

Recently, Eil et al. showed that tumors with necrotic cores had elevated K+ concentrations due to the release of K+ by necrosis, which acts to suppress T-cell function by high extracellular K+ concentration. These findings demonstrate the importance of developing a tool for imaging K+ distributions. Here, we demonstrate K+ nanosensor-enabled photoacoustic imaging for measuring K+ levels in vivo. The nanosensor is an in-house synthesized optical contrast agent that is sensitive to K+ levels within biological ranges. The use of this K+ nanosensor, combined with multi-spectral photoacoustic imaging, allowed measurement of K+ levels in vivo.

Cold spray is an emerging additive manufacturing technique with potential applications in surface functionalization, bulk component production and restoration/repair. During the cold spray process, metallic powders are accelerated to supersonic velocities by the carrier gas of high pressure and temperature and impact on the substrate to form layers of coating through deformation-induced bonding. However, the coating fabricated by this process suffers from low cohesive strength and weak interfacial bonding. Therefore, process optimization through numerical simulation is much needed. Here we employ finite element simulation with Johnson-Cook plasticity and dynamic failure model to numerically predict the temperature distribution within single particle, and they show good agreement with experimental observation using SEM. This provides a validated description of microscopic phenomena using numerical simulation, hence it can be employed further to study the bonding strength of the metal cold spray coating. Through microstructural analysis, we propose a semi-empirical relationship between the nodal temperature profile and local bonding strength, hence identified that the increase of the localized bonding area in a single splat is the determining factor for the increase of the bonding strength.

The accumulation of potassium (K+) in the tumor microenvironment (TME) has been recently shown to inhibit immune cell efficacy, and thus immunotherapy. Despite the abundance of K+ in the body, few ways exist to measure it in vivo. To address this technology gap, we combine an optical K+ nanosensor with photoacoustic (PA) imaging. Using multi-wavelength deconvolution, we are able to quantitatively evaluate the TME K+ concentration in vivo, and its distribution. Significantly elevated K+ levels were found in the TME, with an average concentration of approximately 29 mM, compared to 19 mM found in muscle. These PA measurements were confirmed by extraction of the tumor interstitial fluid and subsequent measurement via inductively coupled plasma mass spectrometry.

We describe how 4-dimensional in vivo biochemical analysis can be performed using photoacoustic contrast nanoagents that have been designed to probe both structural and chemical information in vivo, enabling noninvasive, real time, spatially resolved chemical imaging. Early chemical imaging of a patient’s tumor can inform the decision of effective treatment, regarding choices of chemotherapy, radiation, or immunotherapy.

With the capability of presenting endogenous tissue contrast or exogenous contrast agents in deep biological samples at high spatial resolution, photoacoustic (PA) imaging has shown significant potential for many preclinical and clinical applications. However, due to strong background signals from various intrinsic chromophores in biological tissue, such as hemoglobin, achieving highly sensitive PA imaging of targeting probes labeled by contrast agents has remained a challenge. In this study, we introduce a novel technique called transient triplet differential (TTD) imaging which allows for substantial reduction of tissue background signals. TTD imaging detects directly the triplet state absorption, which is a special characteristic of phosphorescence capable dyes not normally present among intrinsic chromophores of biological tissue. Thus, these triplet state absorption PA images can facilitate “true” background free molecular imaging. We prepared a known phosphorescent dye probe, methylene blue conjugated polyacrylamide nanoparticles, with peak absorption at 660 nm and peak lowest triplet state absorption at 840 nm. We find, through studies on phantoms and on an in vivo tumor model, that TTD imaging can generate a superior contrast-to-noise ratio, compared to other image enhancement techniques, through the removal of noise generated by strongly absorbing intrinsic chromophores, regardless of their identity.

In vivo photoacoustic (PA) imaging with high spatial resolution and depth penetration has remained a challenge due to the high background signal from chromophores in biological tissue. In this study, we introduce a novel imaging technique called triplet differential (TD) imaging which allows for the substantial reduction of background signals from tissue. TD imaging uses the ability of molecules to enter a triplet state via intersystem crossing from an excited singlet state. Molecules in the triplet state exhibit a spectral shift in their optical absorption spectra, creating two separate absorption peaks for each molecule’s singlet and triplet states. Since the PA signal is proportional to optical absorption, a differential signal can be obtained by comparing the PA signal for molecules raised to the triplet state to those in the singlet state. We worked with methylene blue conjugated polyacrylamide nanoparticles with a polyethylene glycol dimethacrylate cross-linker (MBNP) which has a singlet peak absorption at 660nm and triplet peak absorption at 840nm. Since only certain molecules such as methylene blue can enter the triplet state efficiently, the difference in the PA signal before and after excitation of the MBNP to the triplet state is largely independent of the background noise and mainly contributed by the MBNP in the triplet state. Preliminary results have shown that up to an 8-fold increase in the PA signal of the MBNP in the triplet state can be achieved.

Ultrasound Computer Tomography (USCT) is a promising new imaging system for breast cancer diagnosis. An essential step before further processing is to remove the water background from the reconstructed images. In this paper we present a fully-automated image segmentation method based on three-dimensional active contours. The active contour method is extended by applying gradient vector flow and encoding the USCT aperture characteristics as additional weighting terms. A surface detection algorithm based on a ray model is developed to initialize the active contour, which is iteratively deformed to capture the breast outline in USCT reflection images. The evaluation with synthetic data showed that the method is able to cope with noisy images, and is not influenced by the position of the breast and the presence of scattering objects within the breast. The proposed method was applied to 14 in-vivo images resulting in an average surface deviation from a manual segmentation of 2.7 mm. We conclude that automated segmentation of USCT reflection images is feasible and produces results comparable to a manual segmentation. By applying the proposed method, reproducible segmentation results can be obtained without manual interaction by an expert.

Electrical performance of a 3D planar solid oxide fuel cell, with ammonia internal decomposition as fuel and yttrium-stabled zirconia as electrolyte, has been simulated numerically, incorporated with the software Comsol Multiphysics. With the help of the software, gas concentration distribution in an anode/cathode channel as well as current density distribution was demonstrated. The poor gas concentration distribution in the cathode channel is mainly responsible for the poor current density distribution. Furthermore, the effect of current density on the solid oxide fuel cell ohmic and activation overpotential was analyzed. The simulation results conform to the data in the experimental literature well.

Ultrasound (US) backscatter from bones depends on the mechanical properties and the microstructure of the interrogated bone. On the other hand, photoacoustics (PA) is sensitive to optical properties of tissue and can detect composition variation. Therefore, PA can provide complementary information about bone health and integrity. In this work, a comparative study of US backscattering and PA back-propagating signals from animal trabecular bones was performed. Both methods were applied using a linear frequency modulation chirp and matched filtering. A 2.2 MHz ultrasonic transducer was employed to detect both signals. The use of the frequency domain facilitates spectral analysis. The variation of signals shows that in addition to sensitivity to mineral changes, PA exhibits sensitivity to changes in the organic part of the bone. It is, therefore, concluded that the combination of both modalities can provide complementary detailed information on bone health than either method separately. In addition, comparison of PA and US depthwise images shows the higher penetration of US. Surface scan images exhibit very weak correlation between US and PA which could be caused by the different signal generation origins in mechanical versus optical properties, respectively.

Human enteroviruses (HEVs) have been recognized to cause a significant number of respiratory tract infections in many regions. Previous studies conducted to analyse enteroviral respiratory tract infections focused on outbreaks. Data in the Southeast Asian region is still rather limited to date.We conducted a prospective analysis to understand the epidemiological characteristics of enteroviral lower respiratory tract infections (LRTIs) among paediatric patients admitted to Hospital Ampang, a tertiary hospital in Malaysia.Nasopharyngeal aspirates for common respiratory viruses and throat swabs for enteroviruses were obtained for rtPCR analyses. All positive enteroviral results were then cultured for species identification.Of the total 211 recruited patients, enteroviral LRTIs made up 8%. The clinical features of enteroviral infections are mostly clinically indistinguishable from that of respiratory syncytial virus (RSV) infections. However, RSV appears to be more lymphocytosis causing than enteroviruses (EV). We found a higher asthma incidence within the enteroviral group compared to RSV group. Enteroviral infections continue to play an important role in LRTIs in children beyond infancy and up to school age. Among the enteroviral strains, EV71 contributes a major role in enteroviral LRTIs in our center. Routine testing for enterovirus would certainly help identify a significant proportion of unexplained viral LRTIs among paediatric patients. However, further cost analyses studies would be helpful to determine if incorporating testing for enteroviruses into routine respiratory viruses panel tests is economically feasible.

The performance of a H2S solid oxide fuel cell with proton conductor electrolyte, which is constructed by Co-Mo metal sulfide as an anode electro-catalyst, was tested at different Co/Mo ratios. The results indicate that the maximum power output, 6.0 mW · cm−2, was obtained at Co:Mo = 2:3, the next is 5.2 mW · cm−2 at Co:Mo = 1:1, and the minimal is 4.5 mW · cm−2 at Co:Mo = 2:1. However, the obtained power output value is not consistent with the sequence of conductivity of anode materials, which results from the fact that the performance of solid oxide fuel cells are greatly affected by anode electro-catalytic activity. The electro-catalyst tests by the cyclic voltammetry method were designed to conform it. The electrical energy obtained from H2S solid oxide fuel cell is dependent on the Co/Mo metal sulfide as an anode at different atom ratios.

Clofazimine (CFZ) is a broad spectrum antimycobacterial agent recommended by the World Health Organization as a first line treatment for leprosy and second line treatment for multidrug resistant tuberculosis. Oral administration of CFZ leads to a red skin pigmentation side effect. Since CFZ is a weakly basic, red phenazine dye, the skin pigmentation side effect results from lipophilic partitioning of the circulating, free base (neutral) form of CFZ into the skin. Here, we developed a stable and biocompatible formulation of CFZ-HCl microcrystals that mimics the predominant form of the drug that bioaccumulates in macrophages, following long term oral CFZ administration. In mice, intravenous injection of these biomimetic CFZ-HCl microcrystals led to visible drug accumulation in macrophages of the reticuloendothelial system with minimal skin accumulation or pigmentation. In fact, no skin pigmentation was observed when the total amount of CFZ-HCl administered was equivalent to the total oral dose leading to maximal skin pigmentation. Thus, parenteral (injected or inhaled) biomimetic formulations of CFZ-HCl could be instrumental to avoid the pigmentation side effect of oral CFZ therapy.

The mechanisms by which erythemal UVB irradiation modulates systemic immune responses to antigens applied to non-irradiated sites are poorly understood. In this study, regulatory CD4+ T cells were identified in the skin-draining lymph nodes (SDLNs) of UVB-irradiated, but otherwise naive mice. A transgenic mouse strain (DO11.10) was utilized in which the majority of CD4+ T cells expressed the ovalbumin (OVA(323-339)) T-cell receptor. Thus, T-cell responses could be examined following erythemal UVB irradiation without further antigen sensitization. CD4+ T cells from the SDLNs of UVB-irradiated mice had significantly reduced capacity to respond to presentation of the OVA(323-339) peptide in vitro. Transfer of CD4+ T cells from the SDLNs of UVB-irradiated antigen-naive mice significantly reduced both OVA sensitization and contact hypersensitivity responses to an experimental hapten in the recipient mice. Depletion of CD4+CD25+ cells abrogated this UVB-suppressive effect in the in vitro proliferation assay. There was also a significant increase in the proportion of CD4+CD25+Foxp3+ cells in the SDLNs of UVB-irradiated mice. The potential of these regulatory cells poised to regulate responses to incoming antigens at distant non-irradiated sites broadens the biological impact of UVB irradiation of skin on immunity.

A robust test for linear contrast using modified maximum likelihood estimators based on symmetrically censored samples proposed by Tiku (1973, 1982a) is studied in this paper from the Bayesian point of view. The effects of asymmetric censoring on this testing procedure is investigated and a good approximation to its posterior distribution in this case is worked out. We also present an example which illustrates the method of obtaining the highest posterior density interval for the linear combination of the unknown location parameters.

Calcium/calmodulin-dependent protein kinase (CaMK) is a major down stream mediator of Ca(2+) signaling in a wide range of cellular functions, including ion channel and cell cycle regulation and neurotransmitter synthesis and release. Here we have investigated the role of the CaMK signaling pathway in osteoclast differentiation and bone resorption. We observed that the CaMKI, CaMKII gamma isoforms were present in both bone-marrow derived macrophages and RAW264.7 murine macrophage cell line, and that expression persisted during osteoclast differentiation in the presence of receptor activator of nuclear factor kappa B (NF-kappaB) ligand (RANKL). RANKL-induced differentiation was accompanied by increased cyclic AMP response element transcriptional activity, and ERK phosphorylation, which are both downstream targets of CaMK. Two selective inhibitors of CaMKs, KN-93 and KN-62, inhibited osteoclastogenesis in a time and concentration-dependent manner. This was accompanied by suppression of cathepsin K expression and osteoclastic bone resorption, which are markers for differentiated osteoclast function. KN-93 and KN-62 both inhibited RANKL-induced ERK phosphorylation and CREB transcriptional activity. These findings imply a role for CaMK in osteoclast differentiation and bone resorption.

This study examines the sensitivity and specificity of backscattered ultrasound (US) and backscattering photoacoustic (PA) signals for bone composition variation assessment. The conventional approach in the evaluation of bone health relies on measurement of bone mineral density (BMD). Although, a crucial and probably the most important parameter, BMD is not the only factor defining the bone health. New trends in osteoporosis research, also pursue the changes in collagen content and cross-links with bone diseases and aging. Therefore, any non-invasive method that can assess any of these parameters can improve the diagnostic tools and also can help with the biomedical studies on the diseases themselves. Our previous studies show that both US and PA are responsive to changes in the BMD, PA is, in addition, sensitive to changes in the collagen content of the bone. Measurements were performed on bone samples before and after mild demineralization and decollagenization at the exact same points. Results show that combining both modalities can enhance the sensitivity and specificity of diagnostic tool.

In this paper, I have shown that under some mild conditions, the number of initiated cells in an extended two-stage model of carcinogenesis can be approximated by a diffusion process. By using this approximation, I have derived the probability distribution for the number of initiated cells in terms of Laguerre polynomials under normal prevention conditions. This follows from the fact that many of the dietary components are antioxidants which would neutralize the hydroxyl free radicals and hence, reduce the proliferation rates of initiated cells to interrupt or slow down the promotion stage in carcinogenesis.

UVB irradiation of the shaved dorsal skin of mice can cause both local and systemic suppression of contact hypersensitivity responses; the former demonstrated by administration of the sensitizing Ag/hapten to the irradiated site and the latter by its administration at least 72 h later to distal unirradiated sites. The immunological basis of systemic immunomodulation is not clear. When haptens (trinitrochlorobenzene, FITC) were administered to the shaved ventral skin 4 days after irradiation (8 kJ/m2) to the shaved dorsum of BALB/c mice, CD11c+/FITC+ cells in the skin-draining lymph nodes from control and irradiated mice produced on a per cell basis similar levels of IL-12 and PGE2 were phenotypically mature and efficient at presenting FITC to lymphocytes from FITC-sensitized mice. Ag presentation by FACS-sorted CD11c+ lymph node cells isolated 4 days after UVB irradiation was as efficient as were cells from unirradiated mice at presentation in vitro of an OVA peptide (OVA323–339) to CD4+ cells from OVA-TCR-transgenic DO11.10 mice. Further, IFN-γ levels were increased in the cultures containing CD11c+ cells from UVB-irradiated mice, suggesting that inflammation may precede downstream immunosuppression. These results suggest that the primary cause of reduced contact hypersensitivity responses in mice in which UV irradiation and the sensitizing Ag are applied to different sites several days apart must originate from cells other than CD11c+ APCs that directly or by production of soluble mediators (IL-12, PGE2) affect cellular responses in the nodes of UVB-irradiated mice.

In this paper we have developed a state space model for carcinogenesis. By using this state space model we have also developed statistical procedures to estimate the unknown parameters via multi-level Gibbs sampling method. We have applied this model and the methods to the British physician data on lung cancer with smoking. Our results indicate that the tobacco nicotine is an initiator. If $t > 60$ years old, then the tobacco nicotine is also a promoter.

Bronchial carcinoids are uncommon pulmonary tumours, and the gold standard management is surgical resection. Their management is often complicated by their proximal location and propensity to bleed when manipulated. A 22-year-old man was found to have typical carcinoid tumour involving the carina and surgical resection was considered not feasible. We report our experience with a multimodality approach involving arterial embolisation, with subsequent endobronchial resection and ablation. Residual disease was found and managed with definitive carinal resection.

We used ultrasound (US) and photoacoustic (PA) imaging modalities to characterize cattle trabecular bones. The PA signals were generated with an 805-nm continuous wave laser used for optimally deep optical penetration depth. The detector for both modalities was a 2.25-MHz US transducer with a lateral resolution of ~1 mm at its focal point. Using a lateral pixel size much larger than the size of the trabeculae, raster scanning generated PA images related to the averaged values of the optical and thermoelastic properties, as well as density measurements in the focal volume. US backscatter yielded images related to mechanical properties and density in the focal volume. The depth of interest was selected by time-gating the signals for both modalities. The raster scanned PA and US images were compared with microcomputed tomography (μCT) images averaged over the same volume to generate similar spatial resolution as US and PA. The comparison revealed correlations between PA and US modalities with the mineral volume fraction of the bone tissue. Various features and properties of these modalities such as detectable depth, resolution, and sensitivity are discussed.

In this paper, we have developed some state space models for carcinogenesis involving multievent models and multiple pathways models. In these state space models, the stochastic system models are stochastic models of carcinogenesis expressed in terms of stochastic differential equations, whereas the observation models are statistical models based on the observed number of detectable preneoplastic lesions per individual over time and the observed number of detectable cancer tumors per individual over time. In this paper, we have applied some of the theories to some animal papillomas data from some initiation-promotion experiments on skin cancer in mice to estimate some unknown parameters. For this data set we have obtained excellent fit by a model with three piece-wise intervals.

To assess impacts of changing environment, in this paper we propose a multiple branching model of carcinogenesis and use the model to demonstrate how the changing environment would affect the incidence and the survival function of cancer tumors. It is shown through some computer simulation that if there are initiation and promotion on the two-stage pathway, then the effects of changing environment seem to be negligible.

By surveying recent studies by molecular biologists and cancer geneticists, in this paper we have proposed some stochastic models of carcinogenesis and provided some biological evidences for these models. Because most of these models are quite complicated far beyond the scope of the MVK two-stage model, the traditional Markov theory approach becomes too complicated to be of much use. In this paper, we thus propose an alternative approach through stochastic differential equations. For validating the model and for estimating unknown parameters, we further use these stochastic differential equations to develop state space models (Kalman filter models) for carcinogenesis. In this paper, we have used the multievent model as an example to illustrate our modeling approach and some basic theories. These theories will be used by these authors to analyze data from experiments by scientists at BPNNL (Battelle Pacific Northwest National Laboratory) in Richland, WA.

This is a follow-up paper of Tan and Zhu [1] in which we have considered a large population consisting of single males, single females, married couples, and prostitutes. For assessing effects of risk factors on the HIV epidemic by heterosexual transmission and the role of prostitutes in this paper, we have developed chain multinomial models for the HIV epidemic in these populations. Through Monte Carlo studies, we have shown that prostitutes form a stepping stone for the HIV epidemic by heterosexual transmission. Among the risk factors affecting HIV prevalence, our numerical results have indicated that the frequency of condom use is the most important factor followed by the number of sexual partners per unit time. Thus, promoting condom use among prostitutes may serve as a major avenue to control the spread of HIV through heterosexual transmission.

To assess effects of risk factors on the HIV epidemic by heterosexual transmission and the role of prostitutes, in this paper we consider four populations and derive the probabilities of HIV infection in these populations. The four populations considered are the single males, the single females, the married couples, and the prostitutes. It is shown that prostitutes form a stepping stone for the HIV epidemic by heterosexual transmission. Thus, in a society in which homosexual transmission and IV drug use are not frequent, the HIV epidemic can hardly be maintained without prostitutes.

In this paper, we derive a stochastic model for the HIV epidemic in homosexual populations involving age and race. To account for effects of different mixing patterns, a low risk selection rule is introduced. The model is then formulated in terms of chain multinomial distributions by means of which the means are derived. Some simulation studies by computer indicate clearly that age and race have a significant impact on the HIV epidemic.

Assuming some general models for the HIV epidemic, in this paper this paper I derive the HIV incubation distributions under AZT treatment. It is shown that under some conditions, these probability distributions are mixtures of some generalized Gamma distributions and products of generalized Gamma distributions

The paper presents a two‐dimensional unsteady‐flow model, RBFVM‐2D, based on the finite‐volume method with a combination of unstructured triangular and quadrilateral grids in a river‐basin system. The attractive feature of this model is that it calculate of the mass and momentum flux across each side of elements as a Riemann problem, which is solved using the Osher scheme. This feature enables this model to deal with the wetting and drying processes for flood‐plain and wetland studies, dam breaking phenomena involving discontinuous flows, subcritical and supercritical flows, and other cases. The computations of tributary inflows and regulated flows through gates, weirs, and culverts or bridges are also included. Sample applications of this model to two dam‐break problems showed fairly satisfactory results. Also, this model was applied to a portion of the Kissimmee River Basin in Florida for flow simulations and the results agreed well with the field and laboratory data in a physical‐model study of this ri...

In this paper, I derive some first passage probability distributions for some continuous time Markov chains. By using these results, I then derive some exact HIV incubation distributions under treatment by anti-viral drugs such as AZT under some general conditions. It is shown that under some special conditions, these distributions are mixtures of generalized Gamma distributions.

In this paper, we develop a general Markov model for the HIV epidemic involving both sexual contact and IV drug use. For this model, we derive the probability generating function of the HIV epidemic and derive equations for the means, the variances and the covariances of the numbers of susceptible people, latent people, infective people and AIDS cases. By using these equations, we generate some simulation studies to illustrate effects of some risk factors on the mean HIV behavior and on the variances and the covariances of the numbers of latent people, infective people and AIDS cases.

In this paper, we propose a general class of stochastic models for the HIV epidemic in homosexual populations. This class of models are referred to as chain multinomial models. We illustrate this class of models by assuming some stochastic models of the HIV epidemic in homosexual populations in Sections 2-4 and derive the means, the variances and the covariances; we also derive results for the mean behaviors of these models. It is shown that under proportional mixing, the mean behaviors and the trend of these models are quite similar to one another; yet the variances and covariances of the infective people and AIDS cases of these models are very different over different models. These results suggest that the infection duration of infective people and sexual activity levels have significant impact on the projection of HIV epidemic.

In this paper we develop a stochastic model for the HIV epidemic involving both sexual contact and IV drug use by taking into account the dynamic of the HIV epidemic. The model is formulated in terms of the chain multi-nomial model which provides a mechanism by means of which one may derive the moments of the numbers of S people, L people, I people and A people. By using the model we show by Monte Carlo studies that the randomness of the number of different partners per unit time seem to have little effects on the HIV epidemic if the expected number of different partners per unit time is not very small (say >= 0.5). However, the numerical results indicate clearly that in almost all the cases the results of the deterministic model provide poor approximation to the corresponding expected numbers of the stochastic model.

By assuming the Longini et al. staging system in this paper, we derive the probability distributions of times to pre-AIDS symptoms, to clinical AIDS and to death from AIDS under various conditions. Specific conditions involve random test for HIV antibodies, left censoring for HIV transmission and central interval censoring for seroconversion. Using these distribution results, we then derive the means and the variances of times to pre-AIDS symptoms, to clinical AIDS and to death from AIDS as well as the average incubation periods under various conditions. Some numerical results show clearly that these distributions were affected significantly by the transition parameters, the random test, and the censoring.

To describe the dynamics of the AIDS epidemic, the purpose of this paper is to develop a stochastic model for the AIDS epidemic in complex situations. To take into account different risk groups, social factors and levels of sexual activities, in this paper we consider l risk populations with each risk population being further classified into n subpopulations. To take into account some important biological aspects of AIDS epidemic, in each population we postulate an L person and divide the infectious persons (I persons) into @k stages and the AIDS cases (A persons) into m stages. Given these specifications, the probability generating function (PGF) of the numbers of L persons, infectious persons and AIDS cases is then derived under some general conditions. By using this PGF, it is shown that the expected values, the variances and the covariances of the latent persons, infective persons and AIDS cases satisfy some ordinary differential equations. These equations have been solved numerically to assess effects of various factors on the AIDS epidemic.

Extending my previous work [1-3], in this paper I proceed to develop a stochastic model for HIV epidemic in a homosexual population under general conditions. Through computer generated data, I assess various deterministic models as compared with the expected numbers of the stochastic models. It is shown that different mixing patterns have significant impacts on the HIV epidemic except possibly restricted mixing. Thus, in populations with preferred mixing (mixing proportion less than 1) and with proportional mixing, the numbers of S people, L people, I people and A people differ significantly from the corresponding expected numbers of the stochastic models. For the L people, I people and A people, the numbers of the deterministic models first appear to be smaller and later appear to be larger than the corresponding mean numbers of the stochastic models, indicating that while in the short run the deterministic models would underestimate the true numbers, in the long run the deterministic models would overestimate the true numbers.

To assess the effects of random test and various factors on AIDS epidemic, in this paper we consider the situation in which AIDS transmission is developed by blood transfusion and then proceed to develop a stochastic model involving latency of AIDS viruses. Using computed simulation, we then compute and compare the probabilities of developing AIDS for both tested and not tested individuals. The effects of various factors are also being assessed by computer simulation results. It is demonstrated that even within the Weibull family, different probability distributions of latency and incubation insert very different effects on the time to AIDS symptoms and the effects of intervention by random test and treatment.