673 results on '"Stationary distribution"'
Search Results
2. Dynamical analysis on stochastic two-species models.
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Wang, Guangbin, Lv, Jingliang, and Zou, Xiaoling
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STOCHASTIC analysis , *STOCHASTIC models , *GLOBAL asymptotic stability , *COMPUTER simulation - Abstract
In this paper, we study three stochastic two-species models. We construct the stochastic models corresponding to its deterministic model by introducing stochastic noise into the equations. For the first model, we show that the system has a unique global solution starting from the positive initial value. In addition, we discuss the extinction and the existence of stationary distribution under some conditions. For the second system, we explore the existence and uniqueness of the solution. Then we obtain sufficient conditions for global asymptotic stability of the equilibrium point and the positive recurrence of solution. For the last model, the existence and uniqueness of solution, the sufficient conditions for extinction and asymptotic stability and the positive recurrence of solution and weak persistence are derived. And numerical simulations are performed to support our results. [ABSTRACT FROM AUTHOR]
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- 2024
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3. THE IMPACT OF STOCHASTIC ENVIRONMENT ON PSYCHOLOGICAL HEALTH DYNAMICS.
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RAO, FENG, WANG, ANQI, and WANG, ZHANYU
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ECOLOGICAL disturbances , *INFECTIOUS disease transmission , *MENTAL health , *COMPUTER simulation , *MATHEMATICAL models , *PSYCHOLOGICAL stress - Abstract
A mathematical model has been proposed to consider two distinct forms of psychological pressure that arise due to the COVID-19 situation and their impact on individuals' lives, including their mental well-being and happiness. For a more realistic situation, the effect of stochasticity should be taken into account. Hence, our paper mainly investigates the effect of stochastically environmental variability on the transmission dynamics of psychological stress. We obtain two thresholds ℛ s 1 and ℛ s 2 . If ℛ s 1 > 1 , the psychological stress will persist and there will be a unique stationary distribution; whereas if ℛ s 2 < 1 , the extinction of psychological stress is obtained. Moreover, we display the mean first passage time from the initial value to the state of disappearance in order to examine the impact of environmental disturbances; meanwhile, we conduct numerical simulations to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]
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- 2024
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4. Stochastic virus infection model with Ornstein–Uhlenbeck perturbation: Extinction and stationary distribution analysis.
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Cao, Zhongwei, Guo, Chenguang, Shi, Zhenfeng, Song, Zhifei, and Zu, Li
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VIRUS diseases , *ORNSTEIN-Uhlenbeck process , *INVARIANT sets , *LYAPUNOV functions , *STOCHASTIC models - Abstract
In this paper, we propose a stochastic virus infection model with nonlytic immune response, where the transmission rate is realistically modeled as being subject to continuous fluctuations, represented by the Ornstein–Uhlenbeck process. Firstly, we establish the existence and uniqueness of the global solution for the stochastic model and its invariant set, ensuring the robustness and applicability of model. Next, by constructing appropriate Lyapunov functions, we derive sufficient conditions for virus extinction and the existence of a stationary distribution for the stochastic model. These conditions elucidate the key dynamic behaviors, such as extinction and persistence, within the stochastic framework. [ABSTRACT FROM AUTHOR]
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- 2024
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5. Dynamical behaviors of stochastic eco-epidemic predator-prey model with Allee effect in prey and Lévy jump.
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Xueqing He, Ming Liu, and Xiaofeng Xu
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ALLEE effect , *PREDATION , *VERTICAL jump , *JUMP processes - Abstract
In this paper, the dynamical behaviors of a stochastic eco-epidemic predator-prey model with Lévy jump and Allee effect for prey population are investigated. First, the existence and uniqueness of the global positive solution are built. Then, the long-term behaviors of the prey and predator populations are obtained. Furthermore, we demonstrate the stochastic ultimate boundedness of all species and the ergodic stationary distribution without Lévy jump. Finally, numerical examples are provided to support the theoretical analysis results. [ABSTRACT FROM AUTHOR]
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- 2024
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6. Unveiling measles transmission dynamics: Insights from a stochastic model with nonlinear incidence.
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Zhenfeng Shi and Daqing Jiang
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STOCHASTIC models , *INFECTIOUS disease transmission , *LOGNORMAL distribution , *MEASLES , *DISEASE incidence , *ECOLOGICAL disturbances - Abstract
In this paper, taking into account the inevitable impact of environmental perturbations on disease transmission, we primarily investigate a stochastic model for measles infection with nonlinear incidence. The transmission rate in this model follows a logarithmic normal distribution influenced by an Ornstein--Uhlenbeck (OU) process. To analyze the dynamic properties of the stochastic model, our first step is to establish the existence and uniqueness of a global solution for the stochastic equations. Next, by constructing appropriate Lyapunov functions and utilizing the ergodicity of the OU process, we establish sufficient conditions for the existence of a stationary distribution, indicating the prevalence of the disease. Furthermore, we provide sufficient conditions for disease elimination. These conditions are derived by considering the interplay between the model parameters and the stochastic dynamics. Finally, we validate the theoretical conclusions through numerical simulations, which allow us to assess the practical implications of the established conditions and observe the dynamics of the stochastic model in action. By combining theoretical analysis and numerical simulations, we gain a comprehensive understanding of the stochastic model's behavior, contributing to the broader understanding of measles transmission dynamics and the development of effective control strategies. [ABSTRACT FROM AUTHOR]
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- 2024
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7. Dynamics and optimal therapy of a stochastic HTLV‐1 model incorporating Ornstein–Uhlenbeck process.
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Chen, Siyu, Liu, Zhijun, Zhang, Xinan, and Wang, Lianwen
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As the prevalence of viral infection in body, human T‐cell leukemia virus type 1 (HTLV‐1) is receiving increasing attention. Research on the corresponding virus models is of great significance to tackle the challenges of understanding HTLV‐1 development and treatment. This paper focuses on the dynamic analysis for a stochastic model with nonlinear cytotoxic T lymphocyte (CTL) response, which is driven by Ornstein–Uhlenbeck (OU) process to model the progression of HTLV‐1 in vivo. Rich dynamic behaviors such as the extinction of infected CD4+ T cells (ITCs), stationary distribution (SD), probability density, and finite‐time stability (FTS) of the model are established to reveal the interaction of cell populations. The optimal therapeutic strategy based on the cost‐benefit viewpoint is further obtained. Finally, illustrative numerical simulations are represented to corroborate the effectiveness of treatment and the ambient perturbation's impact that strengthening the noise strength can lead to rapid virus clearance. [ABSTRACT FROM AUTHOR]
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- 2024
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8. Dynamical behaviors of a stochastic SIRV epidemic model with the Ornstein–Uhlenbeck process.
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Shang, Jiaxin and Li, Wenhe
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ORNSTEIN-Uhlenbeck process , *PROBABILITY density function , *EPIDEMICS , *LOTKA-Volterra equations , *LYAPUNOV functions , *PREVENTIVE medicine - Abstract
Vaccination is an important tool in disease control to suppress disease, and vaccine-influenced diseases no longer conform to the general pattern of transmission. In this paper, by assuming that the infection rate is affected by the Ornstein–Uhlenbeck process, we obtained a stochastic SIRV model. First, we prove the existence and uniqueness of the global positive solution. Sufficient conditions for the extinction and persistence of the disease are then obtained. Next, by creating an appropriate Lyapunov function, the existence of the stationary distribution for the model is proved. Further, the explicit expression for the probability density function of the model around the quasi-equilibrium point is obtained. Finally, the analytical outcomes are examined by numerical simulations. [ABSTRACT FROM AUTHOR]
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- 2024
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9. Dynamics of a Stochastic SVEIR Epidemic Model with Nonlinear Incidence Rate.
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Wang, Xinghao, Zhang, Liang, and Zhang, Xiao-Bing
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INFECTIOUS disease transmission , *EPIDEMICS , *DISEASE outbreaks , *STOCHASTIC analysis , *NONLINEAR functions , *BASIC reproduction number - Abstract
This paper delves into the analysis of a stochastic epidemic model known as the susceptible–vaccinated–exposed–infectious–recovered (SVEIR) model, where transmission dynamics are governed by a nonlinear function. In the theoretical analysis section, by suitable stochastic Lyapunov functions, we establish that when the threshold value, denoted as R 0 s , falls below 1, the epidemic is destined for extinction. Conversely, if the reproduction number R 0 of the deterministic model surpasses 1, the model manifests an ergodic endemic stationary distribution. In the numerical simulations and data interpretation section, leveraging a graphical analysis with COVID-19 data, we illustrate that random fluctuations possess the capacity to quell disease outbreaks, underscoring the role of vaccines in curtailing the spread of diseases. This study not only contributes to the understanding of epidemic dynamics but also highlights the pivotal role of stochasticity and vaccination strategies in epidemic control and management. The inherent balance and patterns observed in epidemic spread and control strategies, reflect a symmetrical interplay between stochasticity, vaccination, and disease dynamics. [ABSTRACT FROM AUTHOR]
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- 2024
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10. Stationary distribution and near‐optimal control of a stochastic reaction–diffusion HIV model.
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Shi, Dan, Zhang, Mengqing, and Zhang, Qimin
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PONTRYAGIN'S minimum principle , *HIV , *STOCHASTIC models - Abstract
Considering stochastic perturbations and spatial diffusion in both virus‐to‐cell and cell‐to‐cell transmissions, a stochastic reaction–diffusion HIV model is developed. Firstly, the existence and uniqueness of a global positive solution and stationary distribution are demonstrated. Secondly, considering the effect of drug therapy on the disease, the control strategy is introduced into the stochastic HIV model. By employing Pontryagin's stochastic maximum principle, the sufficient and necessary conditions are obtained for near‐optimal control. Finally, numerical simulations are reported to support and supplement our theoretical results. [ABSTRACT FROM AUTHOR]
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- 2024
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11. The Threshold of a Stochastic SIRS Epidemic Model with a General Incidence.
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Lakhal, Mohammed, Guendouz, Tarik El, Taki, Regragui, and El Fatini, Mohamed
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EPIDEMICS , *LYAPUNOV functions , *COMPUTER simulation - Abstract
In this article, a SIRS epidemic model with a general incidence rate is proposed and investigated. We briefly verify the global existence of a unique positive solution for the proposed system. Moreover, and unlike other works, we were able to find the stochastic threshold R s of the proposed model which was used for the discussion of the persistence in mean and extinction of the disease. Moreover, we utilize stochastic Lyapunov functions to show under sufficient conditions the existence and uniqueness of stationary distributions of the solution. Lastly, numerical simulation is executed to conform our analytical results. [ABSTRACT FROM AUTHOR]
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- 2024
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12. A LITERATURE REVIEW ON DEVELOPMENT OF QUEUEING NETWORKS.
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Narmadha, V. and Rajendran, P.
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QUEUEING networks , *QUANTITATIVE research , *TELECOMMUNICATION network management - Abstract
This study conducts a quantitative research survey on the development of queueing networks over years. Development is a process of gradual change that takes place over many years, during which a theory slowly progress and attain a good state. Queueing theory has been through many developments which made its existence inevitable in every field. Queueing networks can be considered as a collection of nodes, where each node stands for a service facility. It has been proved to be a powerful and versatile tool for modelling facilities in manufacturing units and telecommunication networks. This paper presents the development in Queueing networks and its types over years. This paper's main objective is to give all the analysts and researchers the knowledge about the evolution that happened in Queueing networks over years. [ABSTRACT FROM AUTHOR]
- Published
- 2024
13. Dynamics of a Stochastic SEIR Epidemic Model with Vertical Transmission and Standard Incidence.
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Li, Ruichao and Guo, Xiurong
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ECOLOGICAL disturbances , *COMMUNICABLE diseases , *LYAPUNOV functions , *COMPUTER simulation - Abstract
A stochastic SEIR epidemic model with standard incidence and vertical transmission was developed in this work. The primary goal of this study was to determine whether stochastic environmental disturbances affect dynamic features of the epidemic model. The existence, uniqueness, and boundedness of global positive solutions are stated. A threshold was determined for the extinction of the infectious disease. After that, the existence and uniqueness of an ergodic stationary distribution were verified by determining the correct Lyapunov function. Ultimately, theoretical outcomes of numerical simulations are shown. [ABSTRACT FROM AUTHOR]
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- 2024
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14. Analysis of a Stochastic Within-Host Model of Dengue Infection with Immune Response and Ornstein–Uhlenbeck Process.
- Author
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Liu, Qun and Jiang, Daqing
- Abstract
In this paper, assuming the certain variable satisfies the Ornstein–Uhlenbeck process, we formulate a stochastic within-host dengue model with immune response to obtain further understanding of the transmission dynamics of dengue fever. Then we analyze the dynamical properties of the stochastic system in detail, including the existence and uniqueness of the global solution, the existence of a stationary distribution, and the extinction of infected monocytes and free viruses. In particular, it is worth revealing that we get the specific form of covariance matrix in its probability density around the quasi-endemic equilibrium of the stochastic system. Finally, numerical illustrative examples are depicted to confirm our theoretical findings. [ABSTRACT FROM AUTHOR]
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- 2024
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15. Dynamical behavior of a stochastic COVID-19 model with two Ornstein–Uhlenbeck processes and saturated incidence rates.
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Li, Xiaoyu and Li, Zhiming
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According to the transmission characteristics of COVID-19, this paper proposes a stochastic SAIRS epidemic model with two mean reversion Ornstein–Uhlenbeck processes and saturated incidence rates. We first prove the existence and uniqueness of the global solution in the stochastic model. Using several suitable Lyapunov methods, we then derive the extinction and persistence of COVID-19 under certain conditions. Further, stationary distribution and ergodic properties are obtained. Moreover, we obtain the probability density function of the stochastic model around the equilibrium. Numerical simulations illustrate our theoretical results and the effect of essential parameters. Finally, we apply the model to investigate the latest outbreak of the COVID-19 epidemic in Guangzhou city, China. [ABSTRACT FROM AUTHOR]
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- 2024
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16. Wolbachia invasion to wild mosquito population in stochastic environment.
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Cui, Yuanping, Li, Xiaoyue, Mao, Xuerong, and Yang, Hongfu
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AEDES aegypti , *WOLBACHIA , *MOSQUITOES , *MOSQUITO control - Abstract
Releasing Wolbachia-infected mosquitoes to invade the wild mosquito population is a method of mosquito control. In this paper, a stochastic mosquito population model with Wolbachia invasion perturbed by environmental fluctuation is studied. Firstly, the well-posedness, positivity, and Markov-Feller property of the solution for this model are proved. Then a group of sharp threshold-type conditions is provided to characterize the long-term behavior of the model, which pinpoints the almost necessary and sufficient conditions for the persistence and extinction of Wolbachia-infected and uninfected mosquito populations. Our results indicate that even for a low initial Wolbachia infection frequency, a successful Wolbachia invasion into the wild mosquito population can be driven by stochastic environmental fluctuations. Finally, some numerical experiments are carried out to support our theoretical results. [ABSTRACT FROM AUTHOR]
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- 2024
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17. Vaccination effect on a stochastic epidemic model with healing and relapse.
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Abdeslami, M. M., Basri, L., El Fatini, M., Sekkak, I., and Taki, R.
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STOCHASTIC models , *HEALING , *VACCINATION , *STOCHASTIC systems , *COMMUNICABLE diseases - Abstract
In this work, we consider a stochastic epidemic model with vaccination, healing and relapse. We prove the existence and the uniqueness of the positive solution. We establish sufficient conditions for the extinction and the persistence in mean of the stochastic system. Moreover, we also establish sufficient conditions for the existence of ergodic stationary distribution to the model, which reveals that the infectious disease will persist. The graphical illustrations of the approximate solutions of the stochastic epidemic model have been performed. [ABSTRACT FROM AUTHOR]
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- 2024
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18. Role of ART and PrEP treatments in a stochastic HIV/AIDS epidemic model.
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Luo, Yantao, Huang, Jianhua, Teng, Zhidong, and Liu, Qun
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BASIC reproduction number , *AIDS , *HIV , *PRE-exposure prophylaxis , *EPIDEMICS , *STOCHASTIC models - Abstract
In this paper, a stochastic HIV/AIDS epidemic model is presented to study the synthetic effect of ART (antiretroviral therapy) and PrEP (pre-exposure prophylaxis) treatments among MSM (men who have sex with men). Firstly, we give the global stability of disease-free equilibrium and the endemic equilibrium in terms of basic reproduction number R 0 for deterministic model. And then the existence of global positive solutions and the existence of unique ergodic stationary distribution under R 0 S > 1 for stochastic model are given. Further, the long-time stochastic dynamic of the model is investigated, including the criteria on the extinction and persistence in mean for the stochastic model. Finally, we give some numerical simulations to illustrate our theoretical results, and the sensitive analysis shows that ART (antiretroviral therapy) and PrEP (pre-exposure prophylaxis) treatments can effectively control the spread of AIDS among MSM population. [ABSTRACT FROM AUTHOR]
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- 2024
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19. Dynamic properties for a stochastic SEIR model with Ornstein–Uhlenbeck process.
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Lu, Chun and Xu, Chuanlong
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ORNSTEIN-Uhlenbeck process , *STOCHASTIC models , *PROBABILITY density function , *BASIC reproduction number , *FOKKER-Planck equation - Abstract
In this article, we are committed to the study of dynamic properties for a stochastic SEIR epidemic model with infectivity in latency and home quarantine about the susceptible and Ornstein–Uhlenbeck process. Firstly, we provide a criterion for the presence of an ergodic stationary distribution of the model. Secondly, by extracting the corresponding Fokker–Planck equation, we derive the probability density function around quasi-endemic equilibrium of the stochastic model. Thirdly, we establish adequate criteria for extinction. Finally, by using the epidemic data of corresponding deterministic model, two numerical tests are presented to illustrate the effectiveness of the theoretical results. • A stochastic SEIR model with Ornstein-Uhlenbeck process is investigated. • Sufficient criteria for the existence of an ergodic stationary distribution are derived. • The probability density function of the stochastic model is obtained. • The criterion for extinction is closely related to the basic reproduction number. [ABSTRACT FROM AUTHOR]
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- 2024
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20. Dynamic analysis and optimal control of a stochastic COVID-19 model.
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Zhang, Ge, Li, Zhiming, Din, Anwarud, and Chen, Tao
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STOCHASTIC control theory , *STOCHASTIC models , *OPTIMAL control theory , *VIRAL transmission , *INFECTIOUS disease transmission - Abstract
In this paper, we construct a stochastic SAIR (Susceptible–Asymptomatic–Infected–Removed) epidemic model to study the dynamic and control strategy of COVID-19. The existence and uniqueness of the global positive solution are obtained by using the Lyapunov method. We prove the necessary conditions for the existence of extinction and ergodic stationary distribution by defining two new thresholds, respectively. Through the stochastic control theory, the optimal control strategy is obtained. Numerical simulations show the validity of stationary distribution and optimal control. The parameters of the model are estimated by a set of real COVID-19 data. And, the sensitivity of all parameters shows that decreasing physical interaction and screening the asymptomatic as swiftly as possible can prevent the wide spread of the virus in communities. Finally, we also display the trend of the epidemic without control strategies. [ABSTRACT FROM AUTHOR]
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- 2024
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21. Analysis of MAP/G/1 queue with inventory as the model of the node of wireless sensor network with energy harvesting.
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Dudin, Alexander and Klimenok, Valentina
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WIRELESS sensor nodes , *WIRELESS sensor networks , *ENERGY harvesting , *TAXI service , *CONTROLLED atmosphere packaging , *MARKOV processes , *INVENTORIES - Abstract
Queueing systems where certain inventory items are required to provide service to a customer have become popular in the literature from early 1990th. Such systems are similar to those models analysed in the literature models with paired customers, assembly-like queues, passenger–taxi models, etc. During the last few years they are considered in the context of modelling operation of the nodes of a wireless sensor network with energy harvesting. Distinguishing feature of the model considered in this paper, besides the suggestion that arrival flow of customers is described by the Markovian arrival process, is the assumption about a general distribution of the service time while only exponential or phase-type distribution was previously assumed in the existing literature. We apply the well-known technique of M/G/1 type Markov chains and semi-regenerative processes to obtain the ergodicity criterion in a transparent form, stationary distribution of the system under study and the Laplace–Stieltjes transform of the sojourn time distribution. This creates an opportunity to formulate and solve various optimization problems. A number of numerical examples illustrate the computational tractability of the theoretical results and illustrate the behavior of the system performance measures depending on its parameters. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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22. A stochastic predator–prey model with two competitive preys and Ornstein–Uhlenbeck process.
- Author
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Liu, Qun
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ORNSTEIN-Uhlenbeck process , *STOCHASTIC models , *STOCHASTIC systems , *DENSITY matrices , *POPULATION dynamics - Abstract
In this paper, a stochastic predator–prey model with two competitive preys and Ornstein–Uhlenbeck process is formulated and analysed, which is used to obtain a better understanding of the population dynamics. At first, we validate that the stochastic system has a unique global solution with any initial value. Then we analyse the stochastic dynamics of the model in detail, including pth moment boundedness, asymptotic pathwise estimation in turn. After that, we obtain sufficient conditions for the existence of a stationary distribution of the system by adopting stochastic Lyapunov function methods. In addition, under some mild conditions, we derive the specific form of covariance matrix in the probability density near the quasi-positive equilibrium of the stochastic system. Finally, numerical illustrative examples are depicted to confirm our theoretical findings. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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23. Stationary distribution and global stability of stochastic predator-prey model with disease in prey population.
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Gokila, C., Sambath, M., Balachandran, K., and Ma, Yong-Ki
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STOCHASTIC models , *BIOTIC communities , *PREDATION , *BIOLOGICAL models , *LYAPUNOV functions , *COMPUTER simulation - Abstract
In this paper, a new stochastic four-species predator-prey model with disease in the first prey is proposed and studied. First, we present the stochastic model with some biological assumptions and establish the existence of globally positive solutions. Moreover, a condition for species to be permanent and extinction is provided. The above properties can help to save the dangered population in the ecosystem. Through Lyapunov functions, we discuss the asymptotic stability of a positive equilibrium solution for our model. Furthermore, it is also shown that the system has a stationary distribution and indicating the existence of a stable biotic community. Finally, our results of the proposed model have revealed the effect of random fluctuations on the four species ecosystem when adding the alternative food sources for the predator population. To illustrate our theoretical findings, some numerical simulations are presented. [ABSTRACT FROM AUTHOR]
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- 2023
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24. On the Telegraph Process Driven by Geometric Counting Process with Poisson-Based Resetting.
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Di Crescenzo, Antonio, Iuliano, Antonella, Mustaro, Verdiana, and Verasani, Gabriella
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TELEGRAPH & telegraphy , *ASYMPTOTIC distribution , *COUNTING , *VELOCITY , *COINCIDENCE - Abstract
We investigate the effects of the resetting mechanism to the origin for a random motion on the real line characterized by two alternating velocities v 1 and v 2 . We assume that the sequences of random times concerning the motions along each velocity follow two independent geometric counting processes of intensity λ , and that the resetting times are Poissonian with rate ξ > 0 . Under these assumptions we obtain the probability laws of the modified telegraph process describing the position and the velocity of the running particle. Our approach is based on the Markov property of the resetting times and on the knowledge of the distribution of the intertimes between consecutive velocity changes. We obtain also the asymptotic distribution of the particle position when (i) λ tends to infinity, and (ii) the time goes to infinity. In the latter case the asymptotic distribution arises properly as an effect of the resetting mechanism. A quite different behavior is observed in the two cases when v 2 < 0 < v 1 and 0 < v 2 < v 1 . Furthermore, we focus on the determination of the moment-generating function and on the main moments of the process describing the particle position under reset. Finally, we analyse the mean-square distance between the process subject to resets and the same process in absence of resets. Quite surprisingly, the lowest mean-square distance can be found for ξ = 0 , for a positive ξ , or for ξ → + ∞ depending on the choice of the other parameters. [ABSTRACT FROM AUTHOR]
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- 2023
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25. Dynamics of a stochastic phytoplankton–zooplankton system with defensive and offensive effects.
- Author
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Wang, Yi, Guo, Qing, Zhao, Min, Dai, Chuanjun, and Liu, He
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STOCHASTIC systems , *PLANKTON populations , *WHITE noise , *POPULATION dynamics , *PHYTOPLANKTON - Abstract
In this paper, we propose a stochastic phytoplankton–zooplankton system considering phytoplankton defensive and zooplankton offensive effects. The aim of this paper is to study the effects of environmental fluctuations on plankton population dynamics. We prove the existence, uniqueness and stochastically ultimately boundedness of global positive solutions, and the extinction and persistence in the mean of plankton populations. When the system is persistent in the mean, there exists a unique stationary distribution. To further investigate the dynamics of the stochastic plankton system, we perform some numerical simulations and find that the white noise can directly affect the survival of plankton populations. The phytoplankton defense can strengthen the capability of phytoplankton protection that will benefit the plankton survival and weaken the impact of environmental fluctuations, but it has a negative effect on zooplankton population. Our findings reveal that zooplankton offense is beneficial to the survival of phytoplankton but may threaten the persistence of zooplankton population. An appropriate increase of phytoplankton defense or decrease of zooplankton offense can potentially change the survival state of the plankton system. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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26. Dynamic properties of deterministic and stochastic SIIIRS models with multiple viruses and saturation incidences.
- Author
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Li, Xiaoyu, Li, Zhiming, and Ding, Shuzhen
- Abstract
Abstract The classical compartment model is often used to study the spread of an epidemic with one virus. However, there are few types of research on epidemic models with multiple viruses. The article aims to propose two new deterministic and stochastic SIIIRS models with multiple viruses and saturation incidences. We obtain asymptotic properties of disease-free and several endemic equilibria for the deterministic model. In the stochastic case, we prove the existence and uniqueness of positive global solutions. The extinction and persistence of diseases are obtained under different threshold conditions. We analyze the existence of stationary distribution through a suitable Lyapunov function. The results indicate that the extinction or persistence of the two viruses is closely related to the intensity of white noise interference. Specifically, considerable white noise is beneficial for the extinction of diseases, while slight one can lead to long-term epidemics of diseases. Finally, numerical simulations illustrate our theoretical results and the effect of essential parameters. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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27. Dynamics of a stochastic multi-stage sheep brucellosis model with incomplete immunity.
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Wang, Wenxuan and Abdurahman, Xamxinur
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BASIC reproduction number , *BRUCELLOSIS , *WHITE noise , *SHEEP , *IMMUNITY , *LYAPUNOV functions - Abstract
This paper considered a multi-stage sheep brucellosis model with incomplete immunity. First, we established a deterministic model, calculated the basic reproduction number ℛ 0 , set out the conditions for the global stability of the disease-free equilibrium and endemic equilibrium. Second, considering the influence of environmental white noise on brucellosis infection, we further established the stochastic version of the model. By constructing a suitable Lyapunov function, we proved the existence and uniqueness of the global positive solution. Further, we got the sufficient conditions for disease extinction and the existence of ergodic stationary distribution. Finally, we carried out some numerical simulations to verify the theoretical results. [ABSTRACT FROM AUTHOR]
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- 2023
- Full Text
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28. LONG-TIME LIMIT OF NONLINEARLY COUPLED MEASURE-VALUED EQUATIONS THAT MODEL MANY-SERVER QUEUES WITH RENEGING.
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ATAR, RAMI, WEINING KANG, KASPI, HAYA, and RAMANAN, KAVITA
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INVARIANT measures , *TRANSPORT equation , *HAZARD function (Statistics) , *EQUATIONS , *LYAPUNOV functions - Abstract
The large-time behavior of a nonlinearly coupled pair of measure-valued transport equations with discontinuous boundary conditions, parameterized by a positive real-valued parameter λ, is considered. These equations describe the hydrodynamic or fluid limit of many-server queues with reneging (with traffic intensity λ), which model phenomena in diverse disciplines, including biology and operations research. For a broad class of reneging distributions with finite mean, and service distributions with finite mean and hazard rate function that is either nonincreasing or bounded away from zero and infinity, it is shown that if the fluid equations have a unique invariant state, then the Dirac measure at this invariant state is the unique invariant distribution of the fluid equations. In particular, this implies that the stationary distributions of scaled N-server systems converge to the unique invariant state of the corresponding fluid equations. Moreover, when the mean arrival rate is not equal to the mean service rate, that is, when \lambda \not= 1, it is shown that the solution to the fluid equation starting from any initial condition converges to this unique invariant state in the large-time limit. The proof techniques are different under the two sets of assumptions on the service distribution, as well as under the two regimes λ < 1 and λ > 1. When the hazard rate function is nonincreasing, a reformulation of the dynamics in terms of a certain renewal equation is used, in conjunction with recursive asymptotic estimates. When the hazard rate function is bounded away from zero and infinity, the proof uses an extended relative entropy functional as a Lyapunov function. Analogous large-time convergence results are also established for a system of coupled measure-valued equations modeling a multiclass queue. [ABSTRACT FROM AUTHOR]
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- 2023
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29. Dynamic Behavior of a Stochastic Avian Influenza Model with Two Strains of Zoonotic Virus.
- Author
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Kong, Lili, Li, Luping, Kang, Shugui, and Chen, Fu
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AVIAN influenza , *AVIAN influenza A virus , *POULTRY farms , *WHITE noise , *PATHOGENIC viruses , *RANDOM noise theory , *INFECTIOUS disease transmission - Abstract
In this paper, a stochastic avian influenza model with two different pathogenic human–avian viruses is studied. The model analyzes the spread of the avian influenza virus from poultry populations to human populations in a random environment. The dynamic behavior of the stochastic avian influenza model is analyzed. Firstly, the existence and uniqueness of a global positive solution are obtained. Secondly, under the condition of high pathogenic virus extinction, the persistence in the mean and extinction of the infected avian population with a low pathogenic virus is analyzed. Thirdly, the sufficient conditions for the existence and uniqueness of the ergodic stationary distribution in the stochastic avian influenza model are derived. We find the threshold of the stochastic model to determine whether the disease spreads when the white noise is small. The analysis results show that random white noise is effective for disease control. Finally, the theoretical results are verified by numerical simulation, and the numerical simulation analysis is carried out for the cases that cannot be theoretically deduced. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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30. Dynamics of a Stochastic SVEIR Epidemic Model Incorporating General Incidence Rate and Ornstein–Uhlenbeck Process.
- Author
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Zhang, Xinhong, Su, Tan, and Jiang, Daqing
- Abstract
In this paper, considering the inevitable effects of environmental perturbations on disease transmission, we mainly study a stochastic SVEIR epidemic model in which the transmission rate satisfies the log-normal Ornstein–Uhlenbeck process and the incidence rate is general. To analyze the dynamic properties of the stochastic model, we firstly verify that there is a unique positive global solution. By constructing several suitable Lyapunov functions and using the ergodicity of the Ornstein–Uhlenbeck process, we establish sufficient conditions for the existence of stationary distribution, which means the disease will prevail. The sufficient condition for disease extinction is also given. Next, as a special case, we investigate the asymptotic stability of equilibria for the deterministic model and establish the exact expression of the probability density function of stationary distribution for the stochastic model. Finally, we calculate the mean first passage time from the initial value to the stationary state or extinction state to study the influence of environmental perturbations; meanwhile, some numerical simulations are carried out to demonstrate theoretical conclusions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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31. Temporal network modeling with online and hidden vertices based on the birth and death process.
- Author
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Zeng, Ziyan, Feng, Minyu, and Kurths, Jürgen
- Subjects
- *
TIME-varying networks , *DISTRIBUTION (Probability theory) , *PHASE transitions , *MARKOV processes , *SOCIAL interaction - Abstract
• We propose a temporal network model considering the stochastic phase transition of vertices. • Theoretical analysis is derived based on the continuous Markov chain method and confirmed by simulations. • Application in fitting the real network is discussed. Complex networks have played an important role in describing real complex systems since the end of the last century. Recently, research on real-world data sets reports intermittent interaction among social individuals. In this paper, we pay attention to this typical phenomenon of intermittent interaction by considering the state transition of network vertices between online and hidden based on the birth and death process. By continuous-time Markov theory, we show that both the number of each vertex's online neighbors and the online network size are stable and follow the homogeneous probability distribution in a similar form, inducing similar statistics as well. In addition, all propositions are verified via simulations. Moreover, we also present the degree distributions based on small-world and scale-free networks and find some regular patterns by simulations. The application in fitting real networks is discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
32. Stochastic Reaction Networks Within Interacting Compartments.
- Author
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Anderson, David F. and Howells, Aidan S.
- Abstract
Stochastic reaction networks, which are usually modeled as continuous-time Markov chains on Z ≥ 0 d , and simulated via a version of the “Gillespie algorithm,” have proven to be a useful tool for the understanding of processes, chemical and otherwise, in homogeneous environments. There are multiple avenues for generalizing away from the assumption that the environment is homogeneous, with the proper modeling choice dependent upon the context of the problem being considered. One such generalization was recently introduced in Duso and Zechner (Proc Nat Acad Sci 117(37):22674–22683 , Duso and Zechner (2020)), where the proposed model includes a varying number of interacting compartments, or cells, each of which contains an evolving copy of the stochastic reaction system. The novelty of the model is that these compartments also interact via the merging of two compartments (including their contents), the splitting of one compartment into two, and the appearance and destruction of compartments. In this paper we begin a systematic exploration of the mathematical properties of this model. We (i) obtain basic/foundational results pertaining to explosivity, transience, recurrence, and positive recurrence of the model, (ii) explore a number of examples demonstrating some possible non-intuitive behaviors of the model, and (iii) identify the limiting distribution of the model in a special case that generalizes three formulas from an example in Duso and Zechner (Proc Nat Acad Sci 117(37):22674–22683 , Duso and Zechner (2020)). [ABSTRACT FROM AUTHOR]
- Published
- 2023
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33. Limit theorem for stationary distribution of a critical controlled branching process with immigration.
- Author
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Vinokurov, Vladimir I.
- Subjects
- *
BRANCHING processes , *LIMIT theorems , *GAMMA distributions , *EMIGRATION & immigration , *PARAMETERS (Statistics) - Abstract
We consider the sequence {ξn,t}t≥1 of controlled critical branching processes with immigration, where n = 1, 2, ... is an integer parameter limiting the population size. It is shown that for n → ∞ the stationary distributions of considered branching processes normalized by n converge to the distribution of a random variable whose square has a gamma distribution. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
34. Stationary distribution and probability density function of a stochastic waterborne pathogen model with saturated direct and indirect transmissions.
- Author
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Liu, Yue
- Subjects
- *
PROBABILITY density function , *BASIC reproduction number , *WATERBORNE infection , *STABILITY criterion , *STOCHASTIC systems - Abstract
We investigate the dynamical behavior of deterministic and stochastic waterborne pathogen models with saturated incidence rates. In particular, the indirect transmission via person–water–person contact is half‐saturated and the direct transmission by person–person contact takes the saturated form. Possible equilibrium points of the model are investigated, and their stability criterion is discussed. Basic reproduction number R0$$ {\mathcal{R}}_0 $$ of the model is obtained through the next‐generation matrix method. It has been shown that the disease‐free equilibrium is locally stable when R0<1$$ {\mathcal{R}}_0<1 $$ and unstable for R0>1$$ {\mathcal{R}}_0>1 $$. Furthermore, a stochastic Lyapunov method is adopted to establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the proposed stochastic model, which reveals that the infection will persist if R0s>1$$ {\mathcal{R}}_0^s>1 $$. We also obtain an exact expression of the probability density function near the quasi‐endemic equilibrium of stochastic system. Finally, numerical simulations are carried out to support our analytical findings. Results suggest that saturation constants in both direct and indirect transmissions play a positive role in controlling disease. Our results may provide some new insights for the elimination of waterborne disease. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
35. Pathwise methods for the integration of a stochastic SVIR model.
- Author
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Muñoz, Mario, de la Cruz, Hugo, and Mora, Carlos
- Abstract
We propose an approach for the precise numerical integration of a stochastic SVIR model defined by a stochastic differential equation (SDE) with non‐globally Lipschitz continuous coefficients and multiplicative noise. This equation, based on a compartmental epidemic model, describes a continuous vaccination strategy with environmental noise effects. By means of an appropriate invertible continuous transformation, we link the solution to the stochastic SVIR model to the solution of an auxiliary random differential equation (RDE) that has an Ornstein–Uhlenbeck process as the only input parameter of the system. In this way, based on this explicit conjugacy between both equations, new pathwise numerical schemes are constructed for the SVIR model. In particular, we propose an exponential method that outperforms other integrators in the literature and is able to approximate, with high stability, meaningful probabilistic features of the continuous system, including its stationary distribution and ergodicity. A simulation study is presented to illustrate the practical performance of the introduced methods, and a comparative analysis with other integrators commonly used for the simulation of epidemiological models is performed. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
36. Stochastic Dynamics Analysis of Epidemic Models Considering Negative Feedback of Information.
- Author
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Wu, Wanqin, Luo, Wenhui, Chen, Hui, and Zhao, Yun
- Subjects
- *
STOCHASTIC analysis , *EPIDEMICS , *LYAPUNOV functions , *COMMUNICABLE diseases , *MEDICAL model - Abstract
In this article, we mainly consider the dynamic analysis of a stochastic infectious disease model with negative feedback, a symmetric and compatible distribution family. Based on the sir epidemic model taking into account the isolation (y) and the death (v), we consider adding a new variable (w) to control the information of non-drug interventions, which measures transformations in isolation performance that determine the epidemic, and establish a new model. We have demonstrated various properties of the model solution using Lyapunov functions for this model. To begin with, we demonstrate the existence and uniqueness of the global positive solution. After that, we obtained the conditions that need to be met for the extinction of the disease and verified the correctness of the conclusion by simulating numerical values. Afterwards, we prove the stochastic boundedness and stationary distribution of the model solution. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
37. Analysis of an avian influenza model with Allee effect and stochasticity.
- Author
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Geng, Jing, Wang, Yao, Liu, Yu, Yang, Ling, and Yan, Jie
- Subjects
- *
ALLEE effect , *AVIAN influenza , *STOCHASTIC systems , *LYAPUNOV functions , *STOCHASTIC models , *VIRAL transmission - Abstract
In this paper, we investigate a two-dimensional avian influenza model with Allee effect and stochasticity. We first show that a unique global positive solution always exists to the stochastic system for any positive initial value. Then, under certain conditions, this solution is proved to be stochastically ultimately bounded. Furthermore, by constructing a suitable Lyapunov function, we obtain sufficient conditions for the existence of stationary distribution with ergodicity. The conditions for the extinction of infected avian population are also analytically studied. These theoretical results are conformed by computational simulations. We numerically show that the environmental noise can bring different dynamical outcomes to the stochastic model. By scanning different noise intensities, we observe that large noise can cause extinction of infected avian population, which suggests the repression of noise on the spread of avian virus. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
38. Global dynamics of a stochastic reaction–diffusion predator–prey system with space-time white noise.
- Author
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Qi, Haokun and Meng, Xinzhu
- Subjects
- *
WHITE noise , *PREDATION , *STOCHASTIC partial differential equations , *ECOLOGICAL disturbances , *SPACETIME - Abstract
This paper proposes a stochastic reaction–diffusion predator–prey system with fear under the interference of space-time white noise by using the related theories of stochastic partial differential equations. The motivation of this paper is twofold: (i) mathematically, to try to investigate the effects of environmental noise and diffusion on population dynamics; (ii) biologically, to study how environmental noise affects the permanence of species. First, we analyse the well-posedness of solutions. Then sufficient conditions for extinction and permanence of prey and predator populations are derived. Moreover, we present the existence and uniqueness of stationary distribution of this system. Finally, based on numerical simulations and theoretical analysis, it is revealed that (i) high-intensity white noise can lead to the extinction of predator populations; (ii) low-intensity white noise may prolong the period of periodic solutions. This study provides new theoretical guidance for exploring ecological issues in the face of environmental disturbance and spatial diffusion. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
39. Lost sales obsolescence inventory systems with positive lead time: a system-point level-crossing approach.
- Author
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Preethi, K., Shophia Lawrence, A., and Sivakumar, B.
- Subjects
- *
LEAD time (Supply chain management) , *POSITIVE systems , *DISTRIBUTION (Probability theory) , *INVENTORIES , *OBSOLESCENCE - Abstract
In this article, we provide a comprehensive analyses of two continuous review lost sales inventory system based on different replenishment policies, namely $(s,S)$ and $(s,Q)$. We assume that the arrival times of demands form a Poisson process and that the demand sizes have i.i.d. exponential distribution. We assume that the items in stock may obsolete after an exponential time. The lead time for replenishment is exponential. We also assume that the excess demands and the demands that occurred during stock out periods are lost. Using the system point method of level crossing and integral equation method, we derive the steady-state probability distribution of inventory level explicitly. After deriving some system performance measures, we computed the total expected cost rate. We also provide numerical examples of sensitivity analyses involving different parameters and costs. As a result of our numerical analysis, we provide several insights on the optimal $(s,S)$ and $(s,Q)$ policies for inventory systems of obsolescence items with positive lead times. The better policy for maintaining inventory can be quantified numerically. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
40. Study on Dynamic Behavior of a Stochastic Predator–Prey System with Beddington–DeAngelis Functional Response and Regime Switching.
- Author
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Wang, Quan, Zu, Li, Jiang, Daqing, and O'Regan, Donal
- Subjects
- *
STOCHASTIC systems , *PREDATION , *LYAPUNOV functions , *STOCHASTIC models , *WHITE noise , *COMPUTER simulation , *TELEGRAPH & telegraphy - Abstract
In this paper, by introducing environmental white noise and telegraph noise, we proposed a stochastic predator–prey model with the Beddington–DeAngelis type functional response and investigated its dynamical behavior. Persistence and extinction are two core contents of population model research, so we analyzed these two properties. The sufficient conditions of the strong persistence in the mean and extinction were established and the threshold between them was obtained. Moreover, we took stability into account and, by means of structuring a suitable Lyapunov function with regime switching, we proved that the stochastic system has a unique stationary distribution. Finally, numerical simulations were used to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
41. DYNAMICAL BEHAVIOR OF A STOCHASTIC FOOD CHAIN CHEMOSTAT MODEL WITH VARIABLE YIELDS.
- Author
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LIU, XIAOJUAN and SUN, SHULIN
- Subjects
- *
FOOD chains , *CHEMOSTAT , *LYAPUNOV functions , *STOCHASTIC models , *COMPUTER simulation - Abstract
In this paper, we consider a stochastic food chain chemostat model with variable yields. First, we prove the stochastic model has a unique global positive solution. Second, by employing suitable Lyapunov functions, Itô ′ s formula and some other important inequalities, the existence of a unique ergodic stationary distribution of a stochastic food chain chemostat model is researched, which can help us better understand the statistical characteristics of stochastic food chain chemostat models. Second, we investigate the extinction of the microorganism and the bacteria. Moreover, the case of extinction for bacteria but persistence for microbial species is considered. Finally, some numerical simulations are carried out to illustrate our theoretical results and the influence of the variable yields on the microorganism and the bacteria. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
42. Asymptotic behaviour of critical decomposable 2-type Galton–Watson processes with immigration.
- Author
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Barczy, Mátyás, Bezdány, Dániel, and Pap, Gyula
- Subjects
- *
EMIGRATION & immigration , *STOCHASTIC processes - Abstract
In this paper the asymptotic behaviour of a critical 2-type Galton–Watson process with immigration is described when its offspring mean matrix is reducible, in other words, when the process is decomposable. It is proved that, under second or fourth order moment assumptions on the offspring and immigration distributions, a sequence of appropriately scaled random step processes formed from a critical decomposable 2-type Galton–Watson process with immigration converges weakly. The limit process can be described using one or two independent squared Bessel processes and possibly the unique stationary distribution of an appropriate single-type subcritical Galton–Watson process with immigration. Our results complete and extend the results of Foster and Ney (1978) for some strongly critical decomposable 2-type Galton–Watson processes with immigration. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
43. Analysis and simulation of a stochastic COVID-19 model with large-scale nucleic acid detection and isolation measures: A case study of the outbreak in Urumqi, China in August 2022.
- Author
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Ting Zeng, Zhidong Teng, Rifhat, Ramziya, Xiaodong Wang, Lei Wang, and Kai Wang
- Subjects
- *
STOCHASTIC analysis , *COVID-19 pandemic , *COMPUTER simulation , *DISEASE outbreaks , *NUCLEIC acid analysis - Abstract
In this paper, a stochastic COVID-19 model with large-scale nucleic acid detection and isolation measures is proposed. Firstly, the existence and uniqueness of the global positive solution is obtained. Secondly, threshold criteria for the stochastic extinction and persistence in the mean with probability one are established. Moreover, a sufficient condition for the existence of unique ergodic stationary distribution for any positive solution is also established. Finally, numerical simulations are carried out in combination with real COVID-19 data from Urumqi, China and the theoretical results are verified. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
44. An Alleviation of Cloud Congestion Analysis of Fluid Retrial User on Matrix Analytic Method in IoT-based Application.
- Author
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Nandhini, K. and Vidhya, V.
- Subjects
- *
CLOUD computing , *INTERNET of things , *SOCIAL networks , *COMMUNICATION , *BIG data - Abstract
Cloud Computing (CC) and Internet of Things (IoT) are upgrowing human intervention to enhance the daily lifestyle. Currently, the heavy loaded traffic congestion is a very big challenge over IoT-based applications. For that purpose, the researchers approached various ways to overcome the congestion mechanism in recent years. Even though, they have futile to acheive the best resource storage accessing capacity expectation other than, Cloud Computing. Data sharing is a key impediment of Cloud Computing as well as Internet of Things. These are the constituent that give rise to the combination of the IoT and cloud computing paradigm as IoT Cloud. Though, preserving the missed data during the execution time is a key factor to indulge the Retrial Queueing Theory (RQT), who is facing issue upon accessing Cloud Service Provider (CSP) enter into virtual pool to preserve the data for reuse. The paper imposes Markov Fluid analysis with Matrix Analytic Method (MAM) allows the data as continuous length of data rather than individual data to avoid the congestion. The virtual orbit queue follow constant retrial rate discipline, that is, head of the orbital users makes attempt to occupy the server are assumed to be independent and identically distributed (i.i.d). Steady-state expression presented to study the behaviour of congestion. An illustrative analysis is produced to gain deep perception into the system model. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
45. Dynamic Properties for a Second-Order Stochastic SEIR Model with Infectivity in Incubation Period and Homestead-Isolation of the Susceptible Population.
- Author
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Lu, Chun, Liu, Honghui, and Zhou, Junhua
- Subjects
- *
STOCHASTIC models , *VIRAL transmission , *PROBABILITY density function , *COVID-19 pandemic - Abstract
In this article, we analyze a second-order stochastic SEIR epidemic model with latent infectious and susceptible populations isolated at home. Firstly, by putting forward a novel inequality, we provide a criterion for the presence of an ergodic stationary distribution of the model. Secondly, we establish sufficient conditions for extinction. Thirdly, by solving the corresponding Fokker–Plank equation, we derive the probability density function around the quasi-endemic equilibrium of the stochastic model. Finally, by using the epidemic data of the corresponding deterministic model, two numerical tests are presented to illustrate the validity of the theoretical results. Our conclusions demonstrate that nations should persevere in their quarantine policies to curb viral transmission when the COVID-19 pandemic proceeds to spread internationally. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
46. COMPUTATIONAL TRANSLATION FRAMEWORK IDENTIFIES BIOCHEMICAL REACTION NETWORKS WITH SPECIAL TOPOLOGIES AND THEIR LONG-TERM DYNAMICS.
- Author
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HYUKPYO HONG, HERNANDEZ, BRYAN S., JINSU KIM, and JAE KYOUNG KIM
- Subjects
- *
NUMBERS of species , *STOCHASTIC models , *LINEAR systems , *TOPOLOGY - Abstract
Long-term behaviors of biochemical systems are described by steady states in deterministic models and stationary distributions in stochastic models. Obtaining their analytic solutions can be done for limited cases, such as linear or finite-state systems, as it generally requires solving many coupled equations. Interestingly, analytic solutions can be easily obtained when underlying networks have special topologies, called weak reversibility (WR) and zero deficiency (ZD), and the kinetic law follows a generalized form of mass-action kinetics. However, such desired topological conditions do not hold for the majority of cases. Thus, translating networks to have WR and ZD while preserving the original dynamics was proposed. Yet, this approach is limited because manually obtaining the desired network translation among the large number of candidates is challenging. Here, we prove necessary conditions for having WR and ZD after translation, and based on these conditions, we develop a user-friendly computational package, TOWARDZ, that automatically and efficiently identifies translated networks with WR and ZD. This allows us to quantitatively examine how likely it is to obtain WR and ZD after translation depending on the number of species and reactions. Importantly, we also describe how our package can be used to analytically derive steady states of deterministic models and stationary distributions of stochastic models. TOWARDZ provides an effective tool to analyze biochemical systems. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
47. Threshold Dynamics and Probability Density Function of a Stochastic Avian Influenza Epidemic Model with Nonlinear Incidence Rate and Psychological Effect.
- Author
-
Zhou, Baoquan, Jiang, Daqing, Dai, Yucong, and Hayat, Tasawar
- Abstract
In this paper, we examine a stochastic avian influenza model with a nonlinear incidence rate within avian populations and the psychological effect within the human population, where susceptible humans reduce their contact with infected avians as the number of infected humans increases. For the deterministic model, the basic reproduction number R 0 , possible equilibria, and related asymptotic stability are first studied. Then, for the stochastic model, we obtain a critical value R 0 S , which can determine the persistence and extinction of avian influenza. It is theoretically proved that the stochastic model has a unique stationary distribution ϖ (·) if R 0 S > 1 , but the disease will go to extinction when R 0 S < 1 . Taking stochasticity into account, a quasi-endemic equilibrium T ¯ ∗ related to the endemic equilibrium of the deterministic model is defined. We develop an important lemma for solving the special Fokker–Planck equation and derive the explicit expression of the density function of the distribution ϖ (·) around the equilibrium T ¯ ∗ . Numerical simulations verify our theoretical results, and we study the impact of noise and the psychological effect on the transmission dynamics of avian influenza. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
48. Analysis of a Stochastic HBV Infection Model with DNA-Containing Capsids and Virions.
- Author
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Liu, Qun and Shi, Zhenfeng
- Subjects
- *
STOCHASTIC analysis , *HEPATITIS B , *STOCHASTIC differential equations , *CAPSIDS , *STOCHASTIC systems - Abstract
In this paper, we propose a stochastic differential equation model which is used to explore how the environmental noise affects the spread of hepatitis B virus. Firstly, we show that there exists a unique global positive solution of the stochastic system with any positive initial value. Then, we adopt a stochastic Lyapunov function method to establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the proposed stochastic model. Especially, under the same conditions as the existence of a stationary distribution, it is worth noting that we obtain the specific form of probability density around the quasi-infected steady state of the stochastic system. Thirdly, we obtain sufficient criteria for extinction of the infected hepatocytes. Finally, numerical simulations are introduced to validate the theoretical findings. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
49. COST OPTIMIZATION OF QUEUEING SYSTEMS WITH VACATIONS.
- Author
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AFANASYEV, G. A.
- Subjects
- *
MATHEMATICAL optimization , *VACATIONS , *QUEUEING networks , *QUEUING theory , *PROBLEM solving , *COST - Abstract
We consider a queueing system M|G|1 with possible vacations in server operations for principal customers (for example, if a server is leased). A cost optimization problem is solved. As control parameters, we use the probability a of the vacation and its duration. Under fairly general assumptions about the system behavior during vacations, we show that the optimal value of the probability a is either 0 or 1. We also give necessary and sufficient conditions for a vacation to be carried out, i.e., a = 1. With constant vacation durations, we find conditions such that a = 1, and the vacation duration is optimal. Two examples are considered. In the first example, the revenue from the vacation is a linear function of its duration, and, in the second example, the revenue is a quadratic function. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
50. Threshold Analysis of a Stochastic SIRS Epidemic Model with Logistic Birth and Nonlinear Incidence.
- Author
-
Wang, Huyi, Zhang, Ge, Chen, Tao, and Li, Zhiming
- Subjects
- *
STOCHASTIC analysis , *BASIC reproduction number , *STOCHASTIC differential equations , *EPIDEMICS , *DISEASE outbreaks - Abstract
The paper mainly investigates a stochastic SIRS epidemic model with Logistic birth and nonlinear incidence. We obtain a new threshold value ( R 0 m ) through the Stratonovich stochastic differential equation, different from the usual basic reproduction number. If R 0 m < 1 , the disease-free equilibrium of the illness is globally asymptotically stable in probability one. If R 0 m > 1 , the disease is permanent in the mean with probability one and has an endemic stationary distribution. Numerical simulations are given to illustrate the theoretical results. Interestingly, we discovered that random fluctuations can suppress outbreaks and control the disease. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
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