Quasi-stationary and ratio of expectations distributions: A comparative study

A Scheduling Mechanism Based on Optimization Using IoT-Tasks Orchestration for Efficient Patient Health Monitoring

Over the past years, numerous Internet of Things (IoT)-based healthcare systems have been developed to monitor patient health conditions, but these traditional systems do not adapt to constraints imposed by revolutionized IoT technology. IoT-based healthcare systems are considered mission-critical applications whose missing deadlines cause critical situations. For example, in patients with chronic diseases or other fatal diseases, a missed task could lead to fatalities. This study presents a smart patient health monitoring system (PHMS) based on an optimized scheduling mechanism using IoT-tasks orchestration architecture to monitor vital signs data of remote patients. The proposed smart PHMS consists of two core modules: a healthcare task scheduling based on optimization and optimization of healthcare services using a real-time IoT-based task orchestration architecture. First, an optimized time-constraint-aware scheduling mechanism using a real-time IoT-based task orchestration architecture is developed to generate autonomous healthcare tasks and effectively handle the deployment of emergent healthcare tasks. Second, an optimization module is developed to optimize the services of the e-Health industry based on objective functions. Furthermore, our study uses Libelium e-Health toolkit to monitors the physiological data of remote patients continuously. The experimental results reveal that an optimized scheduling mechanism reduces the tasks starvation by 14% and tasks failure by 17% compared to a conventional fair emergency first (FEF) scheduling mechanism. The performance analysis results demonstrate the effectiveness of the proposed system, and it suggests that the proposed solution can be an effective and sustainable solution towards monitoring patient's vital signs data in the IoT-based e-Health domain.

Quasi-stationary probability distribution for the SIR epidemic model

In this paper, we propose two new approximations to the joint quasi-stationary distribution (QSD) of the number susceptible and infected individuals in the Susceptible-Infected-Recovered (SIR) stochastic epidemic model and we derive the marginal QSD of the infected individuals. These two approximations depend on the basic reproduction number [Formula: see text] and give a positive probability of the QSD to all the transient states. Numerical comparisons are presented to check the accuracy of these approximations.

Hamiltonian Analysis of Subcritical Stochastic Epidemic Dynamics

We extend a technique of approximation of the long-term behavior of a supercritical stochastic epidemic model, using the WKB approximation and a Hamiltonian phase space, to the subcritical case. The limiting behavior of the model and approximation are qualitatively different in the subcritical case, requiring a novel analysis of the limiting behavior of the Hamiltonian system away from its deterministic subsystem. This yields a novel, general technique of approximation of the quasistationary distribution of stochastic epidemic and birth-death models and may lead to techniques for analysis of these models beyond the quasistationary distribution. For a classic SIS model, the approximation found for the quasistationary distribution is very similar to published approximations but not identical. For a birth-death process without depletion of susceptibles, the approximation is exact. Dynamics on the phase plane similar to those predicted by the Hamiltonian analysis are demonstrated in cross-sectional data from trachoma treatment trials in Ethiopia, in which declining prevalences are consistent with subcritical epidemic dynamics.

On the Markovian approach for modeling the dynamics of nosocomial infections

We analyze the dynamics of nosocomial infections in intensive care units (ICUs) by using a Markov chain model. Since population size in the ICU is small, in contrast to previous studies, we concentrate on the analytical solution rather than using simulation. We investigate how changes in the system parameters affect to some important behavioral indicators of the spread of the pathogen. We also present an exact measure of the number of secondary cases of infection produced by one colonized patient.

Experimental demonstration of a two-phase population extinction hazard

Population extinction is a fundamental biological process with applications to ecology, epidemiology, immunology, conservation biology and genetics. Although a monotonic relationship between initial population size and mean extinction time is predicted by virtually all theoretical models, attempts at empirical demonstration have been equivocal. We suggest that this anomaly is best explained with reference to the transient properties of ensembles of populations. Specifically, we submit that under experimental conditions, many populations escape their initially vulnerable state to reach quasi-stationarity, where effects of initial conditions are erased. Thus, extinction of populations initialized far from quasi-stationarity may be exposed to a two-phase extinction hazard. An empirical prediction of this theory is that the fit Cox proportional hazards regression model for the observed survival time distribution of a group of populations will be shown to violate the proportional hazards assumption early in the experiment, but not at later times. We report results of two experiments with the cladoceran zooplankton Daphnia magna designed to exhibit this phenomenon. In one experiment, habitat size was also varied. Statistical analysis showed that in one of these experiments a transformation occurred so that very early in the experiment there existed a transient phase during which the extinction hazard was primarily owing to the initial population size, and that this was gradually replaced by a more stable quasi-stationary phase. In the second experiment, only habitat size unambiguously displayed an effect. Analysis of data pooled from both experiments suggests that the overall extinction time distribution in this system results from the mixture of extinctions during the initial rapid phase, during which the effects of initial population size can be considerable, and a longer quasi-stationary phase, during which only habitat size has an effect. These are the first results, to our knowledge, of a two-phase population extinction process.