A Stochastic Model with Saturation Infection for Internal HIV Dynamics

2015 ◽  
Vol 713-715 ◽  
pp. 1546-1551 ◽  
Author(s):  
Jin Qiang Wang ◽  
Mao Xing Liu
Keyword(s):  
Asymptotic Behavior ◽  
Stochastic Model ◽  
Numerical Simulations ◽  
Infection Rate ◽  
Virus Dynamics ◽  
Hiv Dynamics

In this paper, a stochastic model with a saturation infection rate representing HIV internal virus dynamics is investigated. We prove that the model exists non-negative solutions. Then we analyse the asymptotic behavior of the model. Finally, numerical simulations are presented to illustrate our mathematical findings.

scholarly journals Asymptotic Behavior Analysis for a Three-Species Food Chain Stochastic Model with Regime Switching

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Junmei Liu ◽  
Yonggang Ma
Keyword(s):  
Asymptotic Behavior ◽  
Lyapunov Function ◽  
Stochastic Model ◽  
Numerical Simulations ◽  
Behavior Analysis ◽  
Food Chain ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
Stationary Distributions ◽  
Theoretical Results

This paper discusses the asymptotic behavior of a class of three-species stochastic model with regime switching. Using the Lyapunov function, we first obtain sufficient conditions for extinction and average time persistence. Then, we prove sufficient conditions for the existence of stationary distributions of populations, and they are ergodic. Numerical simulations are carried out to support our theoretical results.

scholarly journals Detectable sensation of a stochastic smoking model

2020 ◽  
Vol 18 (1) ◽  
pp. 1045-1055
Author(s):  
Abdullah Alzahrani ◽  
Anwar Zeb
Keyword(s):  
Stochastic Model ◽  
Numerical Simulations ◽  
Sufficient Conditions

Abstract This paper is related to the stochastic smoking model for the purpose of creating the effects of smoking that are not observed in deterministic form. First, formulation of the stochastic model is presented. Then the sufficient conditions for extinction and persistence are determined. Furthermore, the threshold of the proposed stochastic model is discussed, when noises are small or large. Finally, the numerical simulations are shown graphically with the software MATLAB.

Asymptotic behavior and stability of a stochastic model for AIDS transmission

2008 ◽  
Vol 204 (1) ◽  
pp. 99-108 ◽  
Author(s):  
Yongsheng Ding ◽  
Min Xu ◽  
Liangjian Hu
Keyword(s):  
Asymptotic Behavior ◽  
Stochastic Model

scholarly journals Interacting branching processes and linear file-sharing networks

2010 ◽  
Vol 42 (03) ◽  
pp. 834-854 ◽  
Author(s):  
Lasse Leskelä ◽  
Philippe Robert ◽  
Florian Simatos
Keyword(s):  
Communication Network ◽  
Asymptotic Behavior ◽  
Distributed Systems ◽  
Stochastic Model ◽  
Branching Processes ◽  
File Sharing ◽  
Independent Interest ◽  
Constant Flow

File-sharing networks are distributed systems used to disseminate files among nodes of a communication network. The general simple principle of these systems is that once a node has retrieved a file, it may become a server for this file. In this paper, the capacity of these networks is analyzed with a stochastic model when there is a constant flow of incoming requests for a given file. It is shown that the problem can be solved by analyzing the asymptotic behavior of a class of interacting branching processes. Several results of independent interest concerning these branching processes are derived and then used to study the file-sharing systems.

scholarly journals A Stochastic Model for Three Species

2018 ◽  
Vol 7 (4.10) ◽  
pp. 497
Author(s):  
Y. Suresh Kumar ◽  
N. Seshagiri Rao ◽  
B. V AppaRao
Keyword(s):  
Stochastic Process ◽  
Stochastic Model ◽  
Global Stability ◽  
Numerical Simulations ◽  
Local Stability ◽  
Equilibrium Points ◽  
Limited Resources

The present work is related to a three species ecosystem including a mutualism interaction between two species and a predator, where the predator is depending on both the mutual species. All three species in this model are considered in limited resources. The sustainability of the system (local stability) is discussed through the perturbed technique at the possible existing each equilibrium points. Using Lyapunov's technique the global stability of the system is also described. Further the nature of the system is observed by introducing the stochastic process to the species and the numerical simulations are studied to know the interaction among the species. 

Investigation of the Asymptotic Behavior of Stresses at the Tip of Wedge- and Cone-Shaped Cracks

2012 ◽  
Vol 528 ◽  
pp. 119-126
Author(s):  
T. Korepanova ◽  
V.P. Matveenko ◽  
N. Sevodina
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Conditions ◽  
Numerical Simulations ◽  
Numerical Method ◽  
Stress Singularity ◽  
Singular Solutions ◽  
Different Boundary Conditions ◽  
Crack Faces ◽  
Made In

Numerical method is proposed for construction of singular solutions for spatial crossing wedge-and cone-shaped cracks. The results of numerical simulations made in the study allowed us to estimate the stress singularity indices at the tip of wedge-shaped cracks for different boundary conditions on the crack faces and at the tip of crossing cone cracks. The stress singularity at the tips of cone-shaped cracks is investigated.

The asymptotic behavior of a stochastic multigroup SIS model

2018 ◽  
Vol 11 (03) ◽  
pp. 1850037 ◽  
Author(s):  
Chunyan Ji ◽  
Daqing Jiang
Keyword(s):  
Asymptotic Behavior ◽  
Numerical Simulations ◽  
Stationary Distribution ◽  
Endemic Equilibrium ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Sis Model ◽  
Stochastic Perturbations ◽  
Long Time ◽  
Theoretical Results

In this paper, we explore the long time behavior of a multigroup Susceptible–Infected–Susceptible (SIS) model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also show that the disease is fluctuating around the endemic equilibrium under some conditions. Moreover, there is a stationary distribution under stronger conditions. At last, some numerical simulations are applied to support our theoretical results.

scholarly journals Analysis of an algorithm catching elephants on the Internet

2008 ◽  
Vol DMTCS Proceedings vol. AI,... (Proceedings) ◽  
Author(s):  
Yousra Chabchoub ◽  
Christine Fricker ◽  
Frédéric Meunier ◽  
Danielle Tibi
Keyword(s):  
Asymptotic Behavior ◽  
Markov Chain ◽  
Stochastic Model ◽  
Limit Theorems ◽  
Bloom Filter ◽  
Simplified Model ◽  
The Internet ◽  
Huge Amount ◽  
International Audience ◽  
On Line

International audience The paper deals with the problem of catching the elephants in the Internet traffic. The aim is to investigate an algorithm proposed by Azzana based on a multistage Bloom filter, with a refreshment mechanism (called $\textit{shift}$ in the present paper), able to treat on-line a huge amount of flows with high traffic variations. An analysis of a simplified model estimates the number of false positives. Limit theorems for the Markov chain that describes the algorithm for large filters are rigorously obtained. The asymptotic behavior of the stochastic model is here deterministic. The limit has a nice formulation in terms of a $M/G/1/C$ queue, which is analytically tractable and which allows to tune the algorithm optimally.

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