Development of Personalized Sleep Induction System based on Mental States

Sleep is an essential behavior to prevent the decrement of cognitive, motor, and emotional performance and various diseases. However, it is not easy to fall asleep when people want to sleep. There are various sleep-disturbing factors such as the COVID-19 situation, noise from outside, and light during the night. We aim to develop a personalized sleep induction system based on mental states using electroencephalogram and auditory stimulation. Our system analyzes users' mental states using an electroencephalogram and results of the Pittsburgh sleep quality index and Brunel mood scale. According to mental states, the system plays sleep induction sound among five auditory stimulation: white noise, repetitive beep sounds, rainy sound, binaural beat, and sham sound. Finally, the sleep-inducing system classified the sleep stage of participants with 94.7% and stop auditory stimulation if participants showed non-rapid eye movement sleep. Our system makes 18 participants fall asleep among 20 participants. © 2023 IEEE.

Global asymptotic stability, extinction and ergodic stationary distribution in a stochastic model for dual variants of SARS-CoV-2

Several mathematical models have been developed to investigate the dynamics SARS-CoV-2 and its different variants. Most of the multi-strain SARS-CoV-2 models do not capture an important and more realistic feature of such models known as randomness. As the dynamical behavior of most epidemics, especially SARS-CoV-2, is unarguably influenced by several random factors, it is appropriate to consider a stochastic vaccination co-infection model for two strains of SARS-CoV-2. In this work, a new stochastic model for two variants of SARS-CoV-2 is presented. The conditions of existence and the uniqueness of a unique global solution of the stochastic model are derived. Constructing an appropriate Lyapunov function, the conditions for the stochastic system to fluctuate around endemic equilibrium of the deterministic system are derived. Stationary distribution and ergodicity for the new co-infection model are also studied. Numerical simulations are carried out to validate theoretical results. It is observed that when the white noise intensities are larger than certain thresholds and the associated stochastic reproduction numbers are less than unity, both strains die out and go into extinction with unit probability. More-over, it is observed that, for weak white noise intensities, the solution of the stochastic system fluctuates around the endemic equilibrium (EE) of the deterministic model. Frequency distributions are also studied to show random fluctuations due to stochastic white noise intensities. The results presented herein also reveal the impact of vaccination in reducing the co-circulation of SARS-CoV-2 variants within a given population. © 2022 International Association for Mathematics and Computers in Simulation (IMACS)

Stochastic compartmental models of the COVID-19 pandemic must have temporally correlated uncertainties

Compartmental models are an important quantitative tool in epidemiology, enabling us to forecast the course of a communicable disease. However, the model parameters, such as the infectivity rate of the disease, are riddled with uncertainties, which has motivated the development and use of stochastic compartmental models. Here, we first show that a common stochastic model, which treats the uncertainties as white noise, is fundamentally flawed since it erroneously implies that greater parameter uncertainties will lead to the eradication of the disease. Then, we present a principled modelling of the uncertainties based on reasonable assumptions on the contacts of each individual. Using the central limit theorem and Doob's theorem on Gaussian Markov processes, we prove that the correlated Ornstein-Uhlenbeck (OU) process is the appropriate tool for modelling uncertainties in the infectivity rate. We demonstrate our results using a compartmental model of the COVID-19 pandemic and the available US data from the Johns Hopkins University COVID-19 database. In particular, we show that the white noise stochastic model systematically underestimates the severity of the Omicron variant of COVID-19, whereas the OU model correctly forecasts the course of this variant. Moreover, using an SIS model of sexually transmitted disease, we derive an exact closed-form solution for the final distribution of infected individuals. This analytical result shows that the white noise model underestimates the severity of the pandemic because of unrealistic noise-induced transitions. Our results strongly support the need for temporal correlations in modelling of uncertainties in compartmental models of infectious disease. © 2023 The Authors.

Transfer Function Model for COVID-19 Deaths in USA Using Case Counts as Input Series.

This paper presents a transfer function time series forecast model for COVID-19 deaths using reported COVID-19 case positivity counts as the input series. We have used deaths and case counts data reported by the Center for Disease Control for the USA from July 24 to December 31, 2021. To demonstrate the effectiveness of the proposed transfer function methodology, we have compared some summary results of forecast errors of the fitted transfer function model to those of an adequate autoregressive integrated moving average model and observed that the transfer function model achieved better forecast results than the autoregressive integrated moving average model. Additionally, separate autoregressive integrated moving average models for COVID-19 cases and deaths are also reported.

Prediction of novel coronavirus pneumonia epidemic trend based on ARIMA model

In order to improve the speed and efficiency of the Department of epidemic prevention and control, this paper uses ARIMA model to train and fit the number of confirmed cases on the basis of the historical epidemic diagnosis information of Guangdong Province. By dealing with the stability of time series, determining the parameters of ARIMA model and testing residual white noise, the ARIMA model is established to predict the number of confirmed epidemic cases, and the number of confirmed epidemic cases in March may 2021 in Guangdong Province is accurately predicted, so as to help the epidemic prevention and control departments improve the accuracy and effectiveness of epidemic control. © 2022 SPIE.

Nonlinear Stochastic SIS Epidemic Model Incorporating Lévy Process

In this work, we study a stochastic SIS epidemic model with Lévy jumps and nonlinear incidence rates. Firstly, we present our proposed model and its parameters. We establish sufficient conditions for the extinction and persistence of the disease in the population using some stochastic analysis background. We illustrate our theoretical results by numerical simulations. We conclude that the white noise and Lévy jump influence the transmission of the epidemic.

Dynamics of a Stochastic Epidemic Model with Vaccination and Multiple Time-Delays for COVID-19 in the UAE

In this paper, we study the dynamics of COVID-19 in the UAE with an extended SEIR epidemic model with vaccination, time-delays, and random noise. The stationary ergodic distribution of positive solutions is examined, in which the solution fluctuates around the equilibrium of the deterministic case, causing the disease to persist stochastically. It is possible to attain infection-free status (extinction) in some situations, in which diseases die out exponentially and with a probability of one. The numerical simulations and fit to real observations prove the effectiveness of the theoretical results. Combining stochastic perturbations with time-delays enhances the dynamics of the model, and white noise intensity is an important part of the treatment of infectious diseases.

Dynamic Crowd Accident-Risk Assessment Based on Internal Energy and Information Entropy for Large-Scale Crowd Flow Considering COVID-19 Epidemic

With the increase in inevitable large-scale crowd aggregation, disastrous pedestrian stampedes occurred with increasing frequency over the past decade. To prevent these tragedies, it is significant to assess crowd accident-risk (CAR) and identify high-risk areas to control crowd flow dynamically. The cost function of a conventional fluid dynamics model is improved with new items of Gaussian white noise and protection factor, considering both the abnormal pedestrian movements and social distance control due to epidemic, thereby to establish an improved crowd flow model comprehensively. Different from conventional density-based pedestrian aggregation-risk models, this study proposes a hybrid crowd accident-risk assessment (HCRA) model based on internal energy and information entropy. Using the HCRA model, we can consider not only crowd density but also the modulus and direction of a crowd velocity vector simultaneously. Then this study designs a framework to realize crowd accident risk assessment based on the improved crowd-flow model and HCRA model. To validate the proposed models, case studies of CAR assessment in the large-scale waiting hall of the Shanghai Hongqiao railway station are conducted. The pedestrian social control distance-range of 1.0 m-2.0 m under the COVID-19 epidemic situation is verified numerically. Moreover, a valuable result is that this social control distance-range can be shortened to 1.0 m-1.9 m without increase of crow accident-risk. Subsequently, the down-limit of accommodation-capacity of this large waiting hall can be enhanced to 10.54%under this epidemic. IEEE

Single- and Multi-carrier Systems Affected by Impulsive Noise: Covid-19 View

In this work we present a fully stochastic model of performance analysis of single- and multi-carrier modulations (SCM and MCM) in communication systems affected by impulsive noise. The key performance parameter of the model is the symbol error rate (SER), which is fully determined as a function of the system parameters, including the frame length, symbol power, white noise power, impulsive noise power, and the probability of the impulse events. We derive closed-form analytical expressions for the systems and compare them with simulation results, showing very good agreement for all the impulsive noise scenarios. Specifically, we show under which conditions a MCM system performs better than a SCM system, and vice versa, which can be used to apply an optimal control policy that minimizes SER. The developed model for SCM and MCM systems is conceptually applied to the Covid-19 phenomenology, and consequently the results obtained for SCM and MCM scenarios, are interpreted as decision and management of social distancing (lock/roam) policies. Specifically, we also show under which conditions the "roam" strategy performs better than the "lock" strategy, and vice versa, which can be used to develop an optimal control policy that minimizes the mortality rate (MR). However, the proposed analytical model for the Covid-19 scenario, obtained assuming the similarity with the SCM/MCM systems, could not be tested in full due to the lack of relevant data. Therefore, any management decision cannot be based (only) on the presented model adapted to Covid-19, and necessarily requests the integration of experts opinions. Author

Stochastic differential equation model of Covid-19: Case study of Pakistan.

In recent years, the world lived a horrible nightmare named the Covid-19 pandemic. It's changing lifestyle caused the closure of critical establishments like schools, sports halls, companies, etc., as well as causing damage and menace for humanity. Mathematical models are helpful tools for modeling and analysing the infectious disease transmission This article presents a stochastic model of the Covid-19 epidemic for a population with five compartments. We give a numerical analysis of the proposed stochastic model. Also, we compare it with results of the corresponding deterministic model.

Research on dynamic coalition stability of mask production under COVID-19 epidemic

Based on evolutionary game and catastrophe theory, the stability of dynamic coalition of mask production is explored. This research introduces the Gaussian White noise and a Itô stochastic differential equation to develop dynamical equation. Then, probability density function is introduced to build the catastrophe model. Finally, some numerical simulations are given to explore the influence of excess return, default cost and initial cooperation probability. The results show: 1) Catastrophic change occurs suddenly when parameters cross the borderline of bifurcation aggregation;2) The catastrophic change occurs due to external disturbance when parameters are inside the bifurcation aggregation which is easy to recover;3) The excess return affects negatively, and the default cost and the initial cooperation probability affect positively on the stability of dynamic coalition. This research integrates evolutionary game and catastrophe theory and provide a new idea for dynamic coalition research;supports the establishment of mask production dynamic coalition and implementation for unconventional control measures under the COVID-19 epidemic. © 2021, Editorial Board of Journal of Systems Engineering Society of China. All right reserved.

Mathematical analysis and simulation of a stochastic COVID-19 Lévy jump model with isolation strategy.

This paper investigates the dynamics of a COVID-19 stochastic model with isolation strategy. The white noise as well as the Lévy jump perturbations are incorporated in all compartments of the suggested model. First, the existence and uniqueness of a global positive solution are proven. Next, the stochastic dynamic properties of the stochastic solution around the deterministic model equilibria are investigated. Finally, the theoretical results are reinforced by some numerical simulations.

Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching.

In this paper, we analyze a stochastic coronavirus (COVID-19) epidemic model which is perturbed by both white noise and telegraph noise incorporating general incidence rate. Firstly, we investigate the existence and uniqueness of a global positive solution. Then, we establish the stochastic threshold for the extinction and the persistence of the disease. The data from Indian states, are used to confirm the results established along this paper.