Continuous-time stochastic models of a multigrade population

1978 ◽  
Vol 15 (1) ◽  
pp. 26-37 ◽  
Author(s):  
Sally I. McClean
Keyword(s):  
Markov Model ◽  
Exponential Distribution ◽  
Stochastic Models ◽  
Continuous Time ◽  
Time Dependent ◽  
Poisson Arrival ◽  
Mixed Exponential Distribution ◽  
Previous Assumption

The continuous-time Markov model of a multigrade organization is extended in several ways. Firstly the internal transitions and the leaving process are generalized to a semi-Markov formulation which allows for the inclusion of well-authenticated leaving distributions such as the mixed exponential distribution. The previous assumption of Poisson recruitment is then generalized to allow for a time-dependent Poisson arrival distribution in which the instantaneous probability of an arrival is a mixture of exponential terms. Finally we extend the capital-related manpower model to describe a multigrade organization.

Continuous-time stochastic models of a multigrade population

1978 ◽  
Vol 15 (01) ◽  
pp. 26-37 ◽  
Author(s):  
Sally I. McClean
Keyword(s):  
Markov Model ◽  
Exponential Distribution ◽  
Stochastic Models ◽  
Continuous Time ◽  
Time Dependent ◽  
Poisson Arrival ◽  
Mixed Exponential Distribution ◽  
Previous Assumption

The continuous-time Markov model of a multigrade organization is extended in several ways. Firstly the internal transitions and the leaving process are generalized to a semi-Markov formulation which allows for the inclusion of well-authenticated leaving distributions such as the mixed exponential distribution. The previous assumption of Poisson recruitment is then generalized to allow for a time-dependent Poisson arrival distribution in which the instantaneous probability of an arrival is a mixture of exponential terms. Finally we extend the capital-related manpower model to describe a multigrade organization.

Ehrenfest urn models

1965 ◽  
Vol 2 (02) ◽  
pp. 352-376 ◽  
Author(s):  
Samuel Karlin ◽  
James McGregor
Keyword(s):  
Exponential Distribution ◽  
Continuous Time ◽  
Random Variables ◽  
Independent Random Variables ◽  
Urn Models ◽  
Time Intervals ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Random Times

In the Ehrenfest model with continuous time one considers two urns and N balls distributed in the urns. The system is said to be in stateiif there areiballs in urn I, N −iballs in urn II. Events occur at random times and the time intervals T between successive events are independent random variables all with the same negative exponential distributionWhen an event occurs a ball is chosen at random (each of theNballs has probability 1/Nto be chosen), removed from its urn, and then placed in urn I with probabilityp, in urn II with probabilityq= 1 −p, (0 <p< 1).

scholarly journals Computing Optimal Properties of Drugs Using Mathematical Models of Single Channel Dynamics

2018 ◽  
Vol 6 (1) ◽  
pp. 41-64 ◽  
Author(s):  
Aslak Tveito ◽  
Mary M. Maleckar ◽  
Glenn T. Lines
Keyword(s):  
Differential Equations ◽  
Markov Model ◽  
Stochastic Models ◽  
Markov Models ◽  
Single Channel ◽  
Probability Density Functions ◽  
Density Functions ◽  
Mathematical Framework ◽  
Wild Type ◽  
Channel Dynamics

AbstractSingle channel dynamics can be modeled using stochastic differential equations, and the dynamics of the state of the channel (e.g. open, closed, inactivated) can be represented using Markov models. Such models can also be used to represent the effect of mutations as well as the effect of drugs used to alleviate deleterious effects of mutations. Based on the Markov model and the stochastic models of the single channel, it is possible to derive deterministic partial differential equations (PDEs) giving the probability density functions (PDFs) of the states of the Markov model. In this study, we have analyzed PDEs modeling wild type (WT) channels, mutant channels (MT) and mutant channels for which a drug has been applied (MTD). Our aim is to show that it is possible to optimize the parameters of a given drug such that the solution of theMTD model is very close to that of the WT: the mutation’s effect is, theoretically, reduced significantly.We will present the mathematical framework underpinning this methodology and apply it to several examples. In particular, we will show that it is possible to use the method to, theoretically, improve the properties of some well-known existing drugs.

scholarly journals A Numerical Approach for Evaluating the Time-Dependent Distribution of a Quasi Birth-Death Process

2021 ◽  
Author(s):  
Michel Mandjes ◽  
Birgit Sollie
Keyword(s):  
Continuous Time ◽  
Real Life ◽  
Numerical Approach ◽  
Time Dependent ◽  
Death Process ◽  
Continuous Time Markov Chain ◽  
Likelihood Estimator ◽  
Real Life Data ◽  
The Matrix ◽  
Birth Death

AbstractThis paper considers a continuous-time quasi birth-death (qbd) process, which informally can be seen as a birth-death process of which the parameters are modulated by an external continuous-time Markov chain. The aim is to numerically approximate the time-dependent distribution of the resulting bivariate Markov process in an accurate and efficient way. An approach based on the Erlangization principle is proposed and formally justified. Its performance is investigated and compared with two existing approaches: one based on numerical evaluation of the matrix exponential underlying the qbd process, and one based on the uniformization technique. It is shown that in many settings the approach based on Erlangization is faster than the other approaches, while still being highly accurate. In the last part of the paper, we demonstrate the use of the developed technique in the context of the evaluation of the likelihood pertaining to a time series, which can then be optimized over its parameters to obtain the maximum likelihood estimator. More specifically, through a series of examples with simulated and real-life data, we show how it can be deployed in model selection problems that involve the choice between a qbd and its non-modulated counterpart.

scholarly journals A geographical location prediction method based on continuous time series Markov model

PLoS ONE ◽  
2018 ◽  
Vol 13 (11) ◽  
pp. e0207063 ◽  
Author(s):  
Yongping Du ◽  
Chencheng Wang ◽  
Yanlei Qiao ◽  
Dongyue Zhao ◽  
Wenyang Guo
Keyword(s):  
Time Series ◽  
Markov Model ◽  
Continuous Time ◽  
Geographical Location ◽  
Prediction Method ◽  
Location Prediction

STOCHASTIC MODELING OF PHYTOPLANKTON–ZOOPLANKTON INTERACTIONS WITH TOXIN PRODUCING PHYTOPLANKTON

2018 ◽  
Vol 26 (01) ◽  
pp. 87-106 ◽  
Author(s):  
T. MIHIRI M. DE SILVA ◽  
SOPHIA R.-J. JANG
Keyword(s):  
Markov Chain ◽  
Stochastic Modeling ◽  
Stochastic Models ◽  
Continuous Time ◽  
Toxin Production ◽  
Mutual Interference ◽  
Deterministic System ◽  
Continuous Time Markov Chain ◽  
Deterministic Systems ◽  
Population Interactions

We construct models of continuous-time Markov chain (CTMC) and Itô stochastic differential equations of population interactions based on a deterministic system of two phytoplankton and one zooplankton populations. The mechanisms of mutual interference among the predator zooplankton and the avoidance of toxin-producing phytoplankton (TPP) by zooplankton are incorporated. Sudden population extinctions occur in the stochastic models that cannot be captured in the deterministic systems. In addition, the effect of periodic toxin production by TPP is lessened when the birth and death of the populations are modeled randomly.

Sign in / Sign up

Export Citation Format

Share Document