Displaying publications 1 - 20 of 37 in total

  1. Farrukh Mukhamedov
    In the present paper we provide a construction of Quantum Markov chain on a Cayley tree. Moreover, we give a concrete example of such chains, which is shift invariant and has the clustering property
    Matched MeSH terms: Markov Chains
  2. Mustapha I, Mohd Ali B, Rasid MF, Sali A, Mohamad H
    Sensors (Basel), 2015;15(8):19783-818.
    PMID: 26287191 DOI: 10.3390/s150819783
    It is well-known that clustering partitions network into logical groups of nodes in order to achieve energy efficiency and to enhance dynamic channel access in cognitive radio through cooperative sensing. While the topic of energy efficiency has been well investigated in conventional wireless sensor networks, the latter has not been extensively explored. In this paper, we propose a reinforcement learning-based spectrum-aware clustering algorithm that allows a member node to learn the energy and cooperative sensing costs for neighboring clusters to achieve an optimal solution. Each member node selects an optimal cluster that satisfies pairwise constraints, minimizes network energy consumption and enhances channel sensing performance through an exploration technique. We first model the network energy consumption and then determine the optimal number of clusters for the network. The problem of selecting an optimal cluster is formulated as a Markov Decision Process (MDP) in the algorithm and the obtained simulation results show convergence, learning and adaptability of the algorithm to dynamic environment towards achieving an optimal solution. Performance comparisons of our algorithm with the Groupwise Spectrum Aware (GWSA)-based algorithm in terms of Sum of Square Error (SSE), complexity, network energy consumption and probability of detection indicate improved performance from the proposed approach. The results further reveal that an energy savings of 9% and a significant Primary User (PU) detection improvement can be achieved with the proposed approach.
    Matched MeSH terms: Markov Chains
  3. Alyousifi Y, Ibrahim K, Kang W, Zin WZW
    Environ Monit Assess, 2020 Oct 21;192(11):719.
    PMID: 33083907 DOI: 10.1007/s10661-020-08666-8
    An environmental problem which is of concern across the globe nowadays is air pollution. The extent of air pollution is often studied based on data on the observed level of air pollution. Although the analysis of air pollution data that is available in the literature is numerous, studies on the dynamics of air pollution with the allowance for spatial interaction effects through the use of the Markov chain model are very limited. Accordingly, this study aims to explore the potential impact of spatial dependence over time and space on the distribution of air pollution based on the spatial Markov chain (SMC) model using the longitudinal air pollution index (API) data. This SMC model is pertinent to be applied since the daily data of API from 2012 to 2014 that have been gathered from 37 different air quality stations in Peninsular Malaysia is found to exhibit the property of spatial autocorrelation. Based on the spatial transition probability matrices found from the SMC model, specific characteristics of air pollution are studied in the regional context. These characteristics are the long-run proportion and the mean first passage time for each state of air pollution. It is found that the probability for a particular station's state to remain good is 0.814 if its neighbors are in a good state of air pollution and 0.7082 if its neighbors are in a moderate state. For a particular station having neighbors in a good state of air pollution, the proportion of time for it to continue being in a good state is 0.6. This proportion reduces to 0.4, 0.01, and 0 for the cell of moderate, unhealthy, and very unhealthy states, respectively. In addition, there exists a significant spatial dependence of API, indicating that air pollution for a particular station is dependent on the states of the neighboring stations.
    Matched MeSH terms: Markov Chains
  4. Raouf MA, Hashim F, Liew JT, Alezabi KA
    PLoS One, 2020;15(8):e0237386.
    PMID: 32790697 DOI: 10.1371/journal.pone.0237386
    The IEEE 802.11ah standard relies on the conventional distributed coordination function (DCF) as a backoff selection method. The DCF is utilized in the contention-based period of the newly introduced medium access control (MAC) mechanism, namely restricted access window (RAW). Despite various advantages of RAW, DCF still utilizes the legacy binary exponential backoff (BEB) algorithm, which suffers from a crucial disadvantage of being prone to high probability of collisions with high number of contending stations. To mitigate this issue, this paper investigates the possibility of replacing the existing exponential sequence (i.e., as in BEB) with a better pseudorandom sequence of integers. In particular, a new backoff algorithm, namely Pseudorandom Sequence Contention Algorithm (PRSCA) is proposed to update the CW size and minimize the collision probability. In addition, the proposed PRSCA incorporates a different approach of CW freezing mechanism and backoff stage reset process. An analytical model is derived for the proposed PRSCA and presented through a discrete 2-D Markov chain model. Performance evaluation demonstrates the efficiency of the proposed PRSCA in reducing collision probability and improving saturation throughput, network throughput, and access delay performance.
    Matched MeSH terms: Markov Chains
  5. Ravi Kumar, P., Alex Goh, K.L., Ashutosh, K.S.
    Link analysis algorithms for Web search engines determine the importance and relevance of Web pages. Among the link analysis algorithms, PageRank is the state of the art ranking mechanism that is used in Google search engine today. The PageRank algorithm is modeled as the behavior of a randomized Web surfer; this model can be seen as Markov chain to predict the behavior of a system that travels from one state to another state considering only the current condition. However, this model has the dangling node or hanging node problem because these nodes cannot be presented in a Markov chain model. This paper focuses on the application of Markov chain on PageRank algorithm and discussed a few methods to handle the dangling node problem. The Experiment is done running on WEBSPAM-UK2007 to show the rank results of the dangling nodes.
    Matched MeSH terms: Markov Chains
  6. Teh Sin Yin, Ong Ker Hsin, Soh Keng Lin, Khoo Michael Boon Chong, Teoh Wei Li
    Sains Malaysiana, 2015;44:1067-1075.
    The existing optimal design of the fixed sampling interval S2-EWMA control chart to monitor the sample variance of a process is based on the average run length (ARL) criterion. Since the shape of the run length distribution changes with the magnitude of the shift in the variance, the median run length (MRL) gives a more meaningful explanation about the in-control and out-of-control performances of a control chart. This paper proposes the optimal design of the S2-EWMA chart, based on the MRL. The Markov chain technique is employed to compute the MRLs. The performances of the S2-EWMA chart, double sampling (DS) S2 chart and S chart are evaluated and compared. The MRL results indicated that the S2-EWMA chart gives better performance for detecting small and moderate variance shifts, while maintaining almost the same sensitivity as the DS S2 and S charts toward large variance shifts, especially when the sample size increases.
    Matched MeSH terms: Markov Chains
  7. Annazirin Eli, Mardhiyyah Shaffie, Wan Zawiah W
    Sains Malaysiana, 2012;41:1403-1410.
    Statistical modeling of extreme rainfall is essential since the results can often facilitate civil engineers and planners to estimate the ability of building structures to survive under the utmost extreme conditions. Data comprising of annual maximum series (AMS) of extreme rainfall in Alor Setar were fitted to Generalized Extreme Value (GEV) distribution using method of maximum likelihood (ML) and Bayesian Markov Chain Monte Carlo (MCMC) simulations. The weakness of ML method in handling small sample is hoped to be tackled by means of Bayesian MCMC simulations in this study. In order to obtain the posterior densities, non-informative and independent priors were employed. Performances of parameter estimations were verified by conducting several goodness-of-fit tests. The results showed that Bayesian MCMC method was slightly better than ML method in estimating GEV parameters.
    Matched MeSH terms: Markov Chains
  8. Apenteng OO, Ismail NA
    PLoS One, 2015;10(7):e0131950.
    PMID: 26147199 DOI: 10.1371/journal.pone.0131950
    The spread of human immunodeficiency virus (HIV) infection and the resulting acquired immune deficiency syndrome (AIDS) is a major health concern in many parts of the world, and mathematical models are commonly applied to understand the spread of the HIV epidemic. To understand the spread of HIV and AIDS cases and their parameters in a given population, it is necessary to develop a theoretical framework that takes into account realistic factors. The current study used this framework to assess the interaction between individuals who developed AIDS after HIV infection and individuals who did not develop AIDS after HIV infection (pre-AIDS). We first investigated how probabilistic parameters affect the model in terms of the HIV and AIDS population over a period of time. We observed that there is a critical threshold parameter, R0, which determines the behavior of the model. If R0 ≤ 1, there is a unique disease-free equilibrium; if R0 < 1, the disease dies out; and if R0 > 1, the disease-free equilibrium is unstable. We also show how a Markov chain Monte Carlo (MCMC) approach could be used as a supplement to forecast the numbers of reported HIV and AIDS cases. An approach using a Monte Carlo analysis is illustrated to understand the impact of model-based predictions in light of uncertain parameters on the spread of HIV. Finally, to examine this framework and demonstrate how it works, a case study was performed of reported HIV and AIDS cases from an annual data set in Malaysia, and then we compared how these approaches complement each other. We conclude that HIV disease in Malaysia shows epidemic behavior, especially in the context of understanding and predicting emerging cases of HIV and AIDS.
    Matched MeSH terms: Markov Chains*
  9. Alyousifi Y, Othman M, Husin A, Rathnayake U
    Ecotoxicol Environ Saf, 2021 Dec 20;227:112875.
    PMID: 34717219 DOI: 10.1016/j.ecoenv.2021.112875
    Fuzzy time series (FTS) forecasting models show a great performance in predicting time series, such as air pollution time series. However, they have caused major issues by utilizing random partitioning of the universe of discourse and ignoring repeated fuzzy sets. In this study, a novel hybrid forecasting model by integrating fuzzy time series to Markov chain and C-Means clustering techniques with an optimal number of clusters is presented. This hybridization contributes to generating effective lengths of intervals and thus, improving the model accuracy. The proposed model was verified and validated with real time series data sets, which are the benchmark data of actual trading of Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and PM10 concentration data from Melaka, Malaysia. In addition, a comparison was made with some existing fuzzy time series models. Furthermore, the mean absolute percentage error, mean squared error and Theil's U statistic were calculated as evaluation criteria to illustrate the performance of the proposed model. The empirical analysis shows that the proposed model handles the time series data sets more efficiently and provides better overall forecasting results than existing FTS models. The results prove that the proposed model has greatly improved the prediction accuracy, for which it outperforms several fuzzy time series models. Therefore, it can be concluded that the proposed model is a better option for forecasting air pollution parameters and any kind of random parameters.
    Matched MeSH terms: Markov Chains
  10. Tay BA
    PMID: 25215723
    We study a series of N oscillators, each coupled to its nearest neighbors, and linearly to a phonon field through the oscillator's number operator. We show that the Hamiltonian of a pair of adjacent oscillators, or a dimer, within the series of oscillators can be transformed into a form in which they are collectively coupled to the phonon field as a composite unit. In the weak coupling and rotating-wave approximation, the system behaves effectively as the trilinear boson model in the one excitation subspace of the dimer subsystem. The reduced dynamics of the one excitation subspace of the dimer subsystem coupled weakly to a phonon bath is similar to that of a two-level system, with a metastable state against the vacuum. The decay constant of the subsystem is proportional to the dephasing rate of the individual oscillator in a phonon bath, attenuated by a factor that depends on site asymmetry, intersite coupling, and the resonance frequency between the transformed oscillator modes, or excitons. As a result of the collective effect, the excitation relaxation lifetime is prolonged over the dephasing lifetime of an individual oscillator coupled to the same bath.
    Matched MeSH terms: Markov Chains
  11. Khalid R, Nawawi MK, Kawsar LA, Ghani NA, Kamil AA, Mustafa A
    PLoS One, 2013;8(4):e58402.
    PMID: 23560037 DOI: 10.1371/journal.pone.0058402
    M/G/C/C state dependent queuing networks consider service rates as a function of the number of residing entities (e.g., pedestrians, vehicles, and products). However, modeling such dynamic rates is not supported in modern Discrete Simulation System (DES) software. We designed an approach to cater this limitation and used it to construct the M/G/C/C state-dependent queuing model in Arena software. Using the model, we have evaluated and analyzed the impacts of various arrival rates to the throughput, the blocking probability, the expected service time and the expected number of entities in a complex network topology. Results indicated that there is a range of arrival rates for each network where the simulation results fluctuate drastically across replications and this causes the simulation results and analytical results exhibit discrepancies. Detail results that show how tally the simulation results and the analytical results in both abstract and graphical forms and some scientific justifications for these have been documented and discussed.
    Matched MeSH terms: Markov Chains
  12. Aziz F, Arof H, Mokhtar N, Shah NM, Khairuddin ASM, Hanafi E, et al.
    PLoS One, 2018;13(8):e0202092.
    PMID: 30157219 DOI: 10.1371/journal.pone.0202092
    In this paper, an image-based waste collection scheduling involving a node with three waste bins is considered. First, the system locates the three bins and determines the waste level of each bin using four Laws Masks and a set of Support Vector Machine (SVM) classifiers. Next, a Hidden Markov Model (HMM) is used to decide on the number of days remaining before waste is collected from the node. This decision is based on the HMM's previous state and current observations. The HMM waste collection scheduling seeks to maximize the number of days between collection visits while preventing waste contamination due to late collection. The proposed system was trained using 100 training images and then tested on 100 test images. Each test image contains three bins that might be shifted, rotated, occluded or toppled over. The upright bins could be empty, partially full or full of garbage of various shapes and sizes. The method achieves bin detection, waste level classification and collection day scheduling rates of 100%, 99.8% and 100% respectively.
    Matched MeSH terms: Markov Chains
  13. Yap KL, Chong YW, Liu W
    PLoS One, 2020;15(1):e0227982.
    PMID: 31978101 DOI: 10.1371/journal.pone.0227982
    The rapid increase in the usage of the mobile internet has led to a great expansion of cellular data networks in order to provide better quality of service. However, the cost to expand the cellular network is high. One of the solutions to provide affordable wireless connectivity is the deployment of a WiFi access point to offload users' data usage. Nevertheless, the frequent and inefficient handover process between the WiFi AP and cellular network, especially when the mobile device is on the go, may degrade the network performance. Mobile devices do not have the intelligence to select the optimal network to enhance the quality of service (QoS). This paper presents an enhanced handover mechanism using mobility prediction (eHMP) to assist mobile devices in the handover process so that users can experience seamless connectivity. eHMP is tested in two wireless architectures, homogeneous and heterogeneous networks. The network performance significantly improved when eHMP is used in a homogeneous network, where the network throughput increases by 106% and the rate of retransmission decreases by 85%. When eHMP is used in a heterogeneous network, the network throughput increases by 55% and the retransmission rate decreases by 75%. The findings presented in this paper reveal that mobility prediction coupled with the multipath protocol can improve the QoS for mobile devices. These results will contribute to a better understanding of how the network service provider can offload traffic to the WiFi network without experiencing performance degradation.
    Matched MeSH terms: Markov Chains
  14. Camara M, Jamil NR, Abdullah AFB, Hashim RB, Aliyu AG
    Sci Total Environ, 2020 May 30;737:139800.
    PMID: 32526579 DOI: 10.1016/j.scitotenv.2020.139800
    The evaluation of the importance of having accurate and representative stations in a network for river water quality monitoring is always a matter of concern. The minimal budget and time demands of water quality monitoring programme may appear very attractive, especially when dealing with large-scale river watersheds. This article proposes an improved methodology for optimising water quality monitoring network for present and forthcoming monitoring of water quality under a case study of the Selangor River watershed in Malaysia, where different monitoring networks are being used by water management authorities. Knowing that the lack of financial resources in developing countries like Malaysia is one of the reasons for inadequate monitoring network density, to identify an optimised network for cost-efficiency benefits in this study, a geo-statistical technique coupled Kendall's W was first applied to analyse the performance of each monitoring station in the existing networks under the monitored water quality parameters. Second, the present and future changes in non-point pollution sources were simulated using the integrated Cellular Automata and Markov chain model (CA-Markov). Third, Station Potential Pollution Score (SPPS) determined based on Analytic Hierarchy Process (AHP) was used to weight each station under the changes of non-point pollution sources for 2015, 2024, and 2033 prior to prioritisation. Finally, according to the Kendall's W test on kriging results, the weights of non-point sources from the AHP evaluation and fuzzy membership functions, six most efficient sampling stations were identified to build a robust network for the present and future monitoring of water quality status in the Selangor River watershed. This study proposes a useful approach to the pertinent agencies and management authority concerned to establish appropriate methods for developing an efficient water quality monitoring network for tropical rivers.
    Matched MeSH terms: Markov Chains
  15. Chong SY, Tiňo P, He J, Yao X
    Evol Comput, 2019;27(2):195-228.
    PMID: 29155606 DOI: 10.1162/evco_a_00218
    Studying coevolutionary systems in the context of simplified models (i.e., games with pairwise interactions between coevolving solutions modeled as self plays) remains an open challenge since the rich underlying structures associated with pairwise-comparison-based fitness measures are often not taken fully into account. Although cyclic dynamics have been demonstrated in several contexts (such as intransitivity in coevolutionary problems), there is no complete characterization of cycle structures and their effects on coevolutionary search. We develop a new framework to address this issue. At the core of our approach is the directed graph (digraph) representation of coevolutionary problems that fully captures structures in the relations between candidate solutions. Coevolutionary processes are modeled as a specific type of Markov chains-random walks on digraphs. Using this framework, we show that coevolutionary problems admit a qualitative characterization: a coevolutionary problem is either solvable (there is a subset of solutions that dominates the remaining candidate solutions) or not. This has an implication on coevolutionary search. We further develop our framework that provides the means to construct quantitative tools for analysis of coevolutionary processes and demonstrate their applications through case studies. We show that coevolution of solvable problems corresponds to an absorbing Markov chain for which we can compute the expected hitting time of the absorbing class. Otherwise, coevolution will cycle indefinitely and the quantity of interest will be the limiting invariant distribution of the Markov chain. We also provide an index for characterizing complexity in coevolutionary problems and show how they can be generated in a controlled manner.
    Matched MeSH terms: Markov Chains
  16. Aziz F, Arof H, Mokhtar N, Mubin M
    J Neural Eng, 2014 Oct;11(5):056018.
    PMID: 25188730 DOI: 10.1088/1741-2560/11/5/056018
    This paper presents a wheelchair navigation system based on a hidden Markov model (HMM), which we developed to assist those with restricted mobility. The semi-autonomous system is equipped with obstacle/collision avoidance sensors and it takes the electrooculography (EOG) signal traces from the user as commands to maneuver the wheelchair. The EOG traces originate from eyeball and eyelid movements and they are embedded in EEG signals collected from the scalp of the user at three different locations. Features extracted from the EOG traces are used to determine whether the eyes are open or closed, and whether the eyes are gazing to the right, center, or left. These features are utilized as inputs to a few support vector machine (SVM) classifiers, whose outputs are regarded as observations to an HMM. The HMM determines the state of the system and generates commands for navigating the wheelchair accordingly. The use of simple features and the implementation of a sliding window that captures important signatures in the EOG traces result in a fast execution time and high classification rates. The wheelchair is equipped with a proximity sensor and it can move forward and backward in three directions. The asynchronous system achieved an average classification rate of 98% when tested with online data while its average execution time was less than 1 s. It was also tested in a navigation experiment where all of the participants managed to complete the tasks successfully without collisions.
    Matched MeSH terms: Markov Chains*
  17. Yen FY, Chong KM, Ha LM
    PLoS One, 2013;8(6):e65440.
    PMID: 23755231 DOI: 10.1371/journal.pone.0065440
    This paper proposes three synthetic-type control charts to monitor the mean time-between-events of a homogenous Poisson process. The first proposed chart combines an Erlang (cumulative time between events, Tr ) chart and a conforming run length (CRL) chart, denoted as Synth-Tr chart. The second proposed chart combines an exponential (or T) chart and a group conforming run length (GCRL) chart, denoted as GR-T chart. The third proposed chart combines an Erlang chart and a GCRL chart, denoted as GR-Tr chart. By using a Markov chain approach, the zero- and steady-state average number of observations to signal (ANOS) of the proposed charts are obtained, in order to evaluate the performance of the three charts. The optimal design of the proposed charts is shown in this paper. The proposed charts are superior to the existing T chart, Tr chart, and Synth-T chart. As compared to the EWMA-T chart, the GR-T chart performs better in detecting large shifts, in terms of the zero- and steady-state performances. The zero-state Synth-T4 and GR-Tr (r = 3 or 4) charts outperform the EWMA-T chart for all shifts, whereas the Synth-Tr (r = 2 or 3) and GR-T 2 charts perform better for moderate to large shifts. For the steady-state process, the Synth-Tr and GR-Tr charts are more efficient than the EWMA-T chart in detecting small to moderate shifts.
    Matched MeSH terms: Markov Chains*
  18. Wu DB, Hussain S, Mak V, Lee KK
    Value Health, 2014 Nov;17(7):A382.
    PMID: 27200852 DOI: 10.1016/j.jval.2014.08.2625
    OBJECTIVES. Osteoporotic fractures are common in older adults and are often associated with high morbidity and mortality. As the incidence increases with age, it is natural that osteoporotic fractures have become a major health problem worldwide. Increasing number of patients with osteoporotic fracture will have a serious economic impact on the patient themselves and the society. The objective of this study is to study the cost-effectiveness of strontium ranelate compared to alendronate for patients with post-menopausal osteoporotic fractures in Malaysia.
    METHODS. A Markov model was developed to project clinical and economic benefits of strontium in a hypothetical cohort of patients (N=1,000) over a 5-year time horizon. This study was conducted from a payer perspective. Model parameters including transition probabilities and costs of treating fracture at various sites were Malaysia-specific. Drug costs were obtained from a public teaching hospital in Kuala Lumpur. Utilities were derived from previous literatures and efficacy data were derived from two pivotal trials, i. e. SOTI and TROPOS trials. Outcomes were presented as cost per quality-adjusted life year (QALY) gained. A discount rate of 3% was applied. Both 1-way and multivariate probabilistic sensitivity analyses were undertaken to evaluate robustness of results.
    RESULTS. Compared to alendronate, strontium could prevent 328 wrist, 192 hip, 7 vertebra and 115 multiple fractures respectively over 5 years, which was translated into 27.9 QALYs gained. Using strontium can lead to cost reduction of MYR1,416,595 (USD442,685), MYR478,257 (USD149,455), MYR22,784 (USD7,120) and MYR61,883 (USD113,088) due to reduced episodes of fractures at wrist/hip/vertebra/multiple sites respectively. The total reduction of direct medical costs of MYR2,279,519 (USD712,349) was larger than the extra drug cost, hence making strontium a cost-saving therapy.
    CONCLUSIONS. It was shown that strontium appeared to be more cost-effective compared to alendronate and hence should be recommended in the public sector in Malaysia.
    Matched MeSH terms: Markov Chains
  19. Dawood F, Loo CK
    PLoS One, 2016;11(3):e0152003.
    PMID: 26998923 DOI: 10.1371/journal.pone.0152003
    Mirror neurons are visuo-motor neurons found in primates and thought to be significant for imitation learning. The proposition that mirror neurons result from associative learning while the neonate observes his own actions has received noteworthy empirical support. Self-exploration is regarded as a procedure by which infants become perceptually observant to their own body and engage in a perceptual communication with themselves. We assume that crude sense of self is the prerequisite for social interaction. However, the contribution of mirror neurons in encoding the perspective from which the motor acts of others are seen have not been addressed in relation to humanoid robots. In this paper we present a computational model for development of mirror neuron system for humanoid based on the hypothesis that infants acquire MNS by sensorimotor associative learning through self-exploration capable of sustaining early imitation skills. The purpose of our proposed model is to take into account the view-dependency of neurons as a probable outcome of the associative connectivity between motor and visual information. In our experiment, a humanoid robot stands in front of a mirror (represented through self-image using camera) in order to obtain the associative relationship between his own motor generated actions and his own visual body-image. In the learning process the network first forms mapping from each motor representation onto visual representation from the self-exploratory perspective. Afterwards, the representation of the motor commands is learned to be associated with all possible visual perspectives. The complete architecture was evaluated by simulation experiments performed on DARwIn-OP humanoid robot.
    Matched MeSH terms: Markov Chains
  20. Cheong HT, Ng KT, Ong LY, Chook JB, Chan KG, Takebe Y, et al.
    PLoS One, 2014;9(10):e111236.
    PMID: 25340817 DOI: 10.1371/journal.pone.0111236
    A novel HIV-1 recombinant clade (CRF51_01B) was recently identified among men who have sex with men (MSM) in Singapore. As cases of sexually transmitted HIV-1 infection increase concurrently in two socioeconomically intimate countries such as Malaysia and Singapore, cross transmission of HIV-1 between said countries is highly probable. In order to investigate the timeline for the emergence of HIV-1 CRF51_01B in Singapore and its possible introduction into Malaysia, 595 HIV-positive subjects recruited in Kuala Lumpur from 2008 to 2012 were screened. Phylogenetic relationship of 485 amplified polymerase gene sequences was determined through neighbour-joining method. Next, near-full length sequences were amplified for genomic sequences inferred to be CRF51_01B and subjected to further analysis implemented through Bayesian Markov chain Monte Carlo (MCMC) sampling and maximum likelihood methods. Based on the near full length genomes, two isolates formed a phylogenetic cluster with CRF51_01B sequences of Singapore origin, sharing identical recombination structure. Spatial and temporal information from Bayesian MCMC coalescent and maximum likelihood analysis of the protease, gp120 and gp41 genes suggest that Singapore is probably the country of origin of CRF51_01B (as early as in the mid-1990s) and featured a Malaysian who acquired the infection through heterosexual contact as host for its ancestral lineages. CRF51_01B then spread rapidly among the MSM in Singapore and Malaysia. Although the importation of CRF51_01B from Singapore to Malaysia is supported by coalescence analysis, the narrow timeframe of the transmission event indicates a closely linked epidemic. Discrepancies in the estimated divergence times suggest that CRF51_01B may have arisen through multiple recombination events from more than one parental lineage. We report the cross transmission of a novel CRF51_01B lineage between countries that involved different sexual risk groups. Understanding the cross-border transmission of HIV-1 involving sexual networks is crucial for effective intervention strategies in the region.
    Matched MeSH terms: Markov Chains
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