The Classification of States for Markov Chain in Random Environments and m-irreducible

First of all, we introduces the concept of m-irreducible of Markov chain in random environment. Then under the condition of m-irreducible, the relationship of recurrent and positive recurrent between two states is studied. We also give several conditions that can imply a state is recurrent and positive recurrent. And then the period of a state is discussed and we obtained that under the condition of m-irreducible, for any two states in x, they have the same period.

The relationship between SARS-COV-2 RNA positive duration and the risk of recurrent positive

Background:The management of discharge COVID-19 patients with recurrent positive SARS-CoV-2 RNA is challenging.However,there are fewer scientific dissertations about the risk of recurrent positive.The aim of this study was to explore the relationship between SARS-COV-2 RNA positive duration(SPD)and the risk of recurrent positive.

Distributional Chaos Occurring on the Set of Proper Positive Upper Banach Density Recurrent Points of One-sided Symbolic Systems

The purpose of this paper is to show that for one-sided symbolic systems,there exists an uncountable distributionally scrambled set contained in the set of proper positive upper Banach density recurrent points.

Extinction and Persistent of a Stochastic Multi-group SIR Epidemic Model

We establish a stochastic differential equation epidemic model of multi-group SIR type based on the deterministic multi-group SIR mode. Then, we define the basic reproduction number R0^S and show that it is a sharp threshold for the dynamic of the stochastic multi-group SIR model. More specially, if R0^S 〈 1, then the disease-free equilibrium will be asymptotically stable which means the disease will die out, if R0^S 〉 1, the disease-free equilibrium will unstable, and our model will positively recurrence to a positive domain which implies the persistence of our model. Numerical simulation examples are carried out to substantiate the analytical results.

THE MATCHED QUEUEING SYSTEM GI。PH/PH/1

We study the matched queueing system GIoPH/PH/1, where the type-I input is a renewal process, the type-II input is a PH renewal process, and the service times are i. i. d. random variables with PH-distributions. First, a condition is given for the stationarity of the system. Then the distributions of the number of type-I customers at the arrival epoches of type-I customers and the number of type-I customers at an arbitrary epoch are derived. We also discuss the occupation time and the waiting time. Their L. S. transforms are derived. Finally, we discuss some problems in numerical computation.

Ergodicity of one-dimensional regime-switching diffusion processes

In this work,for a one-dimensional regime-switching diffusion process,we show that when it is positive recurrent,then there exists a stationary distribution,and when it is null recurrent,then there exists an invariant measure. We also provide the explicit representation of the stationary distribution and invariant measure based on the hitting times of the process.

Dynamics of stochastic predator-prey models with distributed delay and stage structure for prey

In this paper,we analyze two stochastic predator-prey models with distributed delay and stage structure for prey.For the nonautonomous periodic case of the model,by using Khasminskii’s theory of periodic solution,we show that the system has at least one positive T-periodic solution.For the model which is disturbed by both white and telegraph noises,we obtain sufficient criteria for positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching.The positive recurrence implies that both prey and predator populations will be persistent in the long term.

Demand for longer quarantine period among common and uncommon COVID-19 infections: a scoping review

Background:As one of the non-pharmacological interventions to control the transmission of COVID-19,determining the quarantine duration is mainly based on the accurate estimates of the incubation period.However,patients with coarse information of the exposure date,as well as infections other than the symptomatic,were not taken into account in previously published studies.Thus,by using the statistical method dealing with the interval-censored data,we assessed the quarantine duration for both common and uncommon infections.The latter type includes the presymptomatic,the asymptomatic and the recurrent test positive patients.Methods:As of 10 December 2020,information on cases have been collected from the English and Chinese databases,including Pubmed,Google scholar,CNKI(China National Knowledge Infrastructure)and Wanfang.Official websites and medias were also searched as data sources.All data were transformed into doubly interval-censored and the accelerated failure time model was applied.By estimating the incubation period and the time-to-event distribution of worldwide COVID-19 patients,we obtain the large percentiles for determining and suggesting the quarantine policies.For symptomatic and presymptomatic COVID-19 patients,the incubation time is the duration from exposure to symptom onset.For the asymptomatic,we substitute the date of first positive result of nucleic acid testing for that of symptom onset.Furthermore,the time from hospital discharge or getting negative test result to the positive recurrence has been calculated for recurrent positive patients.Results:A total of 1920 laboratory confirmed COVID-19 cases were included.Among all uncommon infections,34.1%(n=55)of them developed symptoms or were identified beyond fourteen days.Based on all collected cases,the 95th and 99th percentiles were estimated to be 16.2 days(95%Cl 15.5-17.0)and 22.9 days(21.7-24.3)respectively.Besides,we got similar estimates based on merely symptomatic and presymptomatic infections as 15.1 days(14.4-15.7)and 21.1 days(20.0-22.2).Conclusions:There are a certain number of infected people who require longer quarantine duration.Our findings well support the current practice of the extended active monitoring.To further prevent possible transmissions induced and facilitated by such infectious outliers after the 14-days quarantine,properly prolonging the quarantine duration could be prudent for high-risk scenarios and in regions with insufficient test resources.

Explicit Stationary Distribution of the(L,1)-reflecting Random Walk on the Half Line

In this paper,we consider the（L,1） state-dependent reflecting random walk（RW） on the half line,which is an RW allowing jumps to the left at a maximal size L.For this model,we provide an explicit criterion for（positive） recurrence and an explicit expression for the stationary distribution.As an application,we prove the geometric tail asymptotic behavior of the stationary distribution under certain conditions.The main tool employed in the paper is the intrinsic branching structure within the（L,1）-random walk.

STABILITY OF GENERALIZED JACKSON NETWORKS WITH INFINITE SUPPLY OF WORK

A general Jackson network （GJN） with infinite supply of work is considered. By fluid limit model, the author finds that the Markov process describing the dynamics of the GJN with infinite supply of work is positive Harris recurrent if the corresponding fluid model is stable. Furthermore, the author proves that the fluid model is stable if the usual traffic condition holds.