- Theory for Motor Proteins: Discrete-State Stochastic Models

2015 ◽  
pp. 148-173
Keyword(s):  
Stochastic Models ◽  
Motor Proteins ◽  
Discrete State

scholarly journals Distributed State Space Generation of Discrete-State Stochastic Models

1998 ◽  
Vol 10 (1) ◽  
pp. 82-93 ◽  
Author(s):  
Gianfranco Ciardo ◽  
Joshua Gluckman ◽  
David Nicol
Keyword(s):  
State Space ◽  
Stochastic Models ◽  
Discrete State ◽  
State Space Generation

Two remarks on insensitive stochastic models

1986 ◽  
Vol 18 (03) ◽  
pp. 791-814 ◽  
Author(s):  
R. Schassberger
Keyword(s):  
Markov Chains ◽  
Stochastic Models ◽  
Detailed Account ◽  
List Type ◽  
Type Number ◽  
Discrete State ◽  
Close Relationship

This paper contains two contributions to the insensitivity theory for generalized semi-Markov schemes, namely (1) a detailed account of a close relationship between insensitive schemes and partially balanced discrete-state Markov chains, and (2) an extension of the notion of an insensitive scheme in order to incorporate insensitivity phenomena not previously covered.

scholarly journals A Stochastic Model for Malaria Transmission Dynamics

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Rachel Waema Mbogo ◽  
Livingstone S. Luboobi ◽  
John W. Odhiambo
Keyword(s):  
Infectious Diseases ◽  
Stochastic Model ◽  
Malaria Transmission ◽  
Stochastic Models ◽  
Continuous Time ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Infected Mosquito ◽  
Deterministic Models ◽  
Discrete State

Malaria is one of the three most dangerous infectious diseases worldwide (along with HIV/AIDS and tuberculosis). In this paper we compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in malaria transmission dynamics. Relationships between the basic reproduction number for malaria transmission dynamics between humans and mosquitoes and the extinction thresholds of corresponding continuous-time Markov chain models are derived under certain assumptions. The stochastic model is formulated using the continuous-time discrete state Galton-Watson branching process (CTDSGWbp). The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction from stochastic models contribute crucial knowledge on disease control and elimination and mitigation of infectious diseases. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that malaria outbreak is more likely if the disease is introduced by infected mosquitoes as opposed to infected humans. These insights demonstrate the importance of a policy or intervention focusing on controlling the infected mosquito population if the control of malaria is to be realized.

Relationships between Models of Genetic Regulatory Networks with Emphasis on Discrete State Stochastic Models

2016 ◽  
pp. 52-79 ◽  
Author(s):  
Randip Pal
Keyword(s):  
Stochastic Models ◽  
Regulatory Networks ◽  
Regulation Of Gene Expression ◽  
Boolean Networks ◽  
Genetic Regulatory Networks ◽  
Discrete State ◽  
Detailed Model ◽  
Stochastic Master Equation ◽  
Differential Equation Models ◽  
Effective Integration

Genetic Regulatory Networks (GRNs) represent the interconnections between genomic entities that govern the regulation of gene expression. GRNs have been represented by various types of mathematical models that capture different aspects of the biological system. This chapter discusses the relationships among the most commonly used GRN models that can enable effective integration of diverse types of sub-models. A detailed model in the form of stochastic master equation is described, followed by it coarse-scale and deterministic approximations in the form of Probabilistic Boolean Networks and Ordinary Differential Equation models respectively.

Relationships between Models of Genetic Regulatory Networks with Emphasis on Discrete State Stochastic Models

2020 ◽  
pp. 226-248
Author(s):  
Randip Pal
Keyword(s):  
Stochastic Models ◽  
Regulatory Networks ◽  
Regulation Of Gene Expression ◽  
Boolean Networks ◽  
Genetic Regulatory Networks ◽  
Discrete State ◽  
Detailed Model ◽  
Stochastic Master Equation ◽  
Differential Equation Models ◽  
Effective Integration

Genetic Regulatory Networks (GRNs) represent the interconnections between genomic entities that govern the regulation of gene expression. GRNs have been represented by various types of mathematical models that capture different aspects of the biological system. This chapter discusses the relationships among the most commonly used GRN models that can enable effective integration of diverse types of sub-models. A detailed model in the form of stochastic master equation is described, followed by it coarse-scale and deterministic approximations in the form of Probabilistic Boolean Networks and Ordinary Differential Equation models respectively.

Two remarks on insensitive stochastic models

1986 ◽  
Vol 18 (3) ◽  
pp. 791-814 ◽  
Author(s):  
R. Schassberger
Keyword(s):  
Markov Chains ◽  
Stochastic Models ◽  
Detailed Account ◽  
List Type ◽  
Type Number ◽  
Discrete State ◽  
Close Relationship

This paper contains two contributions to the insensitivity theory for generalized semi-Markov schemes, namely (1)a detailed account of a close relationship between insensitive schemes and partially balanced discrete-state Markov chains, and(2)an extension of the notion of an insensitive scheme in order to incorporate insensitivity phenomena not previously covered.

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