Homogeneous Semi-Markov Research Articles

An Application of Homogenous Semi-Markov Model for Assessing HIV/AIDS Progression to ART Patients in Namibia

Background: The progression of HIV infection to AIDS and then to death can be considered a stochastic process. Disease progression can be broken down into a finite number of intermediate states, based on CD4 counts. The five states of the Markov process of HIV/AIDS progression are commonly defined as: S1: CD4 count > 500 cells/microliter; S2: 350 < CD4 count ≤ 500 cells/microliter; S3: 200 < CD4 count ≤ 350 cells/microliter; S4: CD4 count ≤ 200 cells/microliter; and D: Death.
 Objectives: The objective of this study was to model the progression of HIV/AIDS disease of patients under ART follow-up in Namibia using homogenous semi-Markov processes, using the data obtained from Ministry of Health and Social Services.
 Methods: A retrospective study design was used to obtain data on 2422 patients who were observed 11028 times. The semi-Markov model was employed to estimate the transition probabilities and transition intensity rate. Time Homogeneous Semi-Markov model was fitted to assess effectiveness of ART by comparing the forward transition and reverse transitions.
 Results: As expected the probabilities of transiting from good states to worse states increased with time (from state 1 to state 3 and 4 after 6 months is 0.023 and 0.004, after 12 months is 0.059 and 0.010 respectively). As time increase the probabilities of remaining in the same state is decreasing (probabilities of remaining in state 1 after 6, 12 and 18 months is 0.804, 0.698 and 0.633). As expected the intensity indicates that the rate of transiting from good states to worst states is decreasing (the intensity of transiting from state 1 to 3 and 4 is p<0.001).
 The strongest predictor of transition from state 1 to 2 is TDF/3TC/EFV, which has a hazard ratio of 1.338 (with p value of 0.002). Patients who were prescribed TDF/3TC/EFV, are over 1.338 times more likely to transit from state 1 to state 2 than patients who did not receive TDF/3TC/EFV. A hazard ratio of 0.678 for the predictor variable female shows that female were less likely to transit from state 2 to 3 than their male counterparts. The hazard ratios of females from a bad state to a better state are more than 1, which is an indication that females are less likely to respond to treatment compared to males.
 Conclusions: HIV can progress to AIDS without delay if there is no intervention. Early ART initiation is crucial to reduce the probabilities of transiting from good states to worse states.

Sequential Interval Reliability for Discrete-Time Homogeneous Semi-Markov Repairable Systems

In this paper, a new reliability measure, named sequential interval reliability, is introduced for homogeneous semi-Markov repairable systems in discrete time. This measure is the probability that the system is working in a given sequence of non-overlapping time intervals. Many reliability measures are particular cases of this new reliability measure that we propose; this is the case for the interval reliability, the reliability function and the availability function. A recurrent-type formula is established for the calculation in the transient case and an asymptotic result determines its limiting behaviour. The results are illustrated by means of a numerical example which illustrates the possible application of the measure to real systems.

Semi-Markov model for vehicular green transmission

To integrate the Fifth Generation (5G) Vehicular ad hoc network (VANET) based clustering in cellular networks is useful for improving the throughput, saving scarce spectrum resources and preventing network congestion, as well as reducing the packet loss. However, it is a challenging problem to find an optimized clustering algorithm that has efficient stability adapting to dynamic VANETs. Considering the advantages of software-defined networking (SDN), an the 5G VANET system is employed with an SDN-enabled social-aware adaptive clustering algorithm (SESAC) which exploits a social pattern (i.e., future route) of every vehicle to optimize the stability of each cluster. To design the homogeneous Semi-Markov model for discrete time, which is based on the movement of each vehicle. The state transition probability and exact time probability dissemination are inputs while social patterns of each vehicle’s are output. The anticipated social patterns are generally used to make groups(cluster); where the vehicles are in a similar cluster, the cluster head (CH) will share a similar way (similar route). The cluster heads (CHs) are selected by some specific metrics such as inter vehicle distance, relative speed, and attributes of vehicle. Finally the SESAC algorithm is analyzed and compared with the conventional clustering algorithm.

HAART Alan HIV/AIDS Hastalarının Risk Faktörlerinin ve Hastalık Progresyonunun Tanımlanması İçin Cox PH Regresyonu ve Homojen Semi-Markov Modelleri

HAART Alan HIV/AIDS Hastalarının Risk Faktörlerinin ve Hastalık Progresyonunun Tanımlanması İçin Cox PH Regresyonu ve Homojen Semi-Markov Modelleri

Statistical Analysis of Adult HIV/AIDS Patients and Modelling of AIDS Disease Progression

This study has been intended to apply the cox proportional hazard model to review the determinant factors of survival time and discrete time homogeneous semi markov model to predict the clinical progression of AIDS disease by secondary data obtained from the antiretroviral therapy unit of Dilla and Hawassa University Referral Hospitals. Patients were followed for a median of 34 months. Of total sample, 517 (68.4%) were female and 239 (31.6%) were male. In the followed up period, 110 (14.5%) patients died and 646 (85.5%) patients were censored. The cox regression result indicated that the survival time of the HIV patient was significantly connected with adherence level, age, alcohol use, CD4, condom use, functional status, marital status and WHO stage. The outcome of homogenous semi-markov model showed that the survival probability of a patient increased when CD4 count increased. The study is suggested that the above significant variables should be viewed as significant component of the routine clinical care for patients on ART and patients require checking CD4 count in the suitable day as physician arrange to know their disease stage.

Determinants of Non-Adherence to Antiretroviral Therapy and Modeling Progression of Adherence Level: At Yirgalem Regional Hospital, Ethiopia; January, 2012

Non-adherence is a global problem and has been seen in all diseases. According to WHO, adherence to long-term therapies in chronic illnesses averages 50% in developed countries? Adherence to HAART is challenging, because patients need almost perfect adherence of at least 95 percent to keep viral load at undetectable levels as long as possible and maintain the functionality of the immune system. Poor adherence to antiretroviral therapy increases the risk of incomplete viral suppression, disease progression and death. The purpose of this study was to assess the level and factors associated with non-adherence to antiretroviral therapy. A random sample of 368 patients were taken from the ART clinic at Yirgalem Regional Hospital from September 2006 to July 2011.Adherence levels were measured using methods pill count, pill identification test, and self-report. Descriptive statistics and both Bivariate and multivariate Logistic Regression were used to analyzed the data. Homogeneous Semi-Markov Stochastic Model was used to reveal the conditional probability of staying in non-adherence. The Multivariate Logistic Regression Method showed that the gender (sex), family size, social support available to the patients, ART knowledge of the patients, time on ART in month, and baseline CD4 counts/mm3 were significant factors associated with non-adherence to ART medications. The conditional probability of staying in non-adherence, until a given time in month was higher than staying in adherence. Thus, it is suggested that health-care providers need to be watchful about adherence levels of patients. Specifically males, who have been on ART for several months, living in large family members, lack of social support, having high baseline CD4 counts/mm3, and having poor knowledge of ART.

Exotic Properties of Non Homogeneous Markov and Semi-Markov Systems

In this article we study what we chose to call exotic properties of NHMS and NHSMS. The interplay between stochastic theory of NHMS and NHSMS and other branches of probability, stochastic processes and mathematics, we believe is a fascinating one apart from being important. In many cases the information needed for the evolution of a NHMS is a larger set than the history of the multidimensional process NHMS. In our world where an overflow of information exists almost in all problems, it is almost surely that this will be available. Here, we extend the definition of the NHMS in order to accomodate this case. In this respect we arrive at the defnition of the 𝒢-non homogeneous Markov system. We study the problem of change of measure in a 𝒢-non homogeneousMarkov system. It is proved that under certain conditions the NHMS retains the Markov property, while as expected the basic sequences of transition probabilities change and it is established how they do so. We also find the expected population structure of the NHMS under the new measure in close analytic form. We also define the 𝒢-non homogeneous semi-Markov system and we study the problem of change of measure in a 𝒢-non homogeneous semi-Markov system. It is proved that under certain conditions the NHSMS retains the semi-Markov property while as expected the basic sequences of transition probabilities change and it is established how they do so. We prove that if the input process of memberships is a non homogeneous Poisson process, then asymtotically and under certain easily met in practice conditions, the compensated population structure of the 𝒢-NHMS is a martingale. Finally we prove that the space of all random population structures, under easily met in practice conditions, is a Hilbert space.

Numerical Approach for Assessing System Dynamic Availability Via Continuous Time Homogeneous Semi-Markov Processes

Continuous-time homogeneous semi-Markov processes (CTHSMP) are important stochastic tools to model reliability measures for systems whose future behavior is dependent on the current and next states occupied by the process as well as on sojourn times in these states. A method to solve the interval transition probabilities of CTHSMP consists of directly applying any general quadrature method to the N2 coupled integral equations which describe the future behavior of a CTHSMP, where N is the number of states. However, the major drawback of this approach is its considerable computational effort. In this work, it is proposed a new more efficient numerical approach for CTHSMPs described through either transition probabilities or transition rates. Rather than N2 coupled integral equations, the approach consists of solving only N coupled integral equations and N straightforward integrations. Two examples in the context of availability assessment are presented in order to validate the effectiveness of this method against the comparison with the results provided by the classical and Monte Carlo approaches. From these examples, it is shown that the proposed approach is significantly less time-consuming and has accuracy comparable to the method of N2 computational effort.

Parametric and Non Homogeneous Semi-Markov Process for HIV Control

In AIDS control, physicians have a growing need to use pragmatically useful and interpretable tools in their daily medical taking care of patients. Semi-Markov process seems to be well adapted to model the evolution of HIV-1 infected patients. In this study, we introduce and define a non homogeneous semi-Markov (NHSM) model in continuous time. Then the problem of finding the equations that describe the biological evolution of patient is studied and the interval transition probabilities are computed. A parametric approach is used and the maximum likelihood estimators of the process are given. A Monte Carlo algorithm is presented for realizing non homogeneous semi-Markov trajectories. As results, interval transition probabilities are computed for distinct times and follow-up has an impact on the evolution of patients.

Numerical Treatment of Homogeneous Semi-Markov Processes in Transient Case–a Straightforward Approach

This paper presents the numerical solution of the process evolution equation of a homogeneous semi-Markov process (HSMP) with a general quadrature method. Furthermore, results that justify this approach proving that the numerical solution tends to the evolution equation of the continuous time HSMP are given. The results obtained generalize classical results on integral equation numerical solutions applying them to particular kinds of integral equation systems. A method for obtaining the discrete time HSMP is shown by applying a very particular quadrature formula for the discretization. Following that, the problem of obtaining the continuous time HSMP from the discrete one is considered. In addition, the discrete time HSMP in matrix form is presented and the fact that the solution of the evolution equation of this process always exists is proved. Afterwards, an algorithm for solving the discrete time HSMP is given. Finally, a simple application of the HSMP is given for a real data social security example.