scholarly journals How successful are mutants in multiplayer games with fluctuating environments? Sojourn times, fixation and optimal switching

2018 ◽  
Vol 5 (3) ◽  
pp. 172176
Author(s):  
Joseph W. Baron ◽  
Tobias Galla
Keyword(s):  
Stochastic Model ◽  
Optimal Switching ◽  
Multiplayer Games ◽  
Sojourn Times ◽  
Switching Dynamics ◽  
Fluctuating Environments ◽  
Probability Of Fixation ◽  
Birth Death

Using a stochastic model, we investigate the probability of fixation, and the average time taken to achieve fixation, of a mutant in a population of wild-types. We do this in a context where the environment in which the competition takes place is subject to stochastic change. Our model takes into account interactions which can involve multiple participants. That is, the participants take part in multiplayer games. We find that under certain circumstances, there are environmental switching dynamics which minimize the time that it takes for the mutants to fixate. To analyse the dynamics more closely, we develop a method by which to calculate the sojourn times for general birth–death processes in fluctuating environments.

scholarly journals An approximate stochastic model for phage reproduction in a bacterium

1962 ◽  
Vol 2 (4) ◽  
pp. 478-483 ◽  
Author(s):  
J. Gani
Keyword(s):  
Stochastic Model ◽  
Recent Article ◽  
Deterministic Model ◽  
Approximate Model ◽  
Death Process ◽  
Reproductive Process ◽  
Previous Note ◽  
The Subject ◽  
Birth Death

The stochastic birth-death process considered in this paper provides an approximate model for phage reproduction in a bacterium. In a recent paper, Hershey [1] has discussed reproduction and recombination in phage crosses, and a deterministic model for the reproductive process has been the subject of a previous note by the author [2]. A very readable account of the process is given by Sanders [3] in his recent article, “The life of viruses”.

scholarly journals Switching dynamics of border ownership: A stochastic model for bi-stable perception

2011 ◽  
Vol 51 (18) ◽  
pp. 2085-2098 ◽  
Author(s):  
Naoki Kogo ◽  
Alessandra Galli ◽  
Johan Wagemans
Keyword(s):  
Stochastic Model ◽  
Switching Dynamics

scholarly journals Threshold behaviour of emerging epidemics featuring contact tracing

2011 ◽  
Vol 43 (04) ◽  
pp. 1048-1065 ◽  
Author(s):  
Frank G. Ball ◽  
Edward S. Knock ◽  
Philip D. O'Neill
Keyword(s):  
Stochastic Model ◽  
Contact Tracing ◽  
Death Process ◽  
Infectious Period ◽  
Threshold Parameter ◽  
Threshold Behaviour ◽  
Numerical Studies ◽  
Period Distribution ◽  
Extinction Probabilities ◽  
Birth Death

This paper is concerned with a stochastic model for the spread of an epidemic with a contact tracing scheme, in which diagnosed individuals may name some of their infectious contacts, who are then removed if they have not been already. Traced individuals may or may not also be asked to name their own contacts. The epidemic is studied by considering an approximating, modified birth-death process with intersibling dependencies, for which a threshold parameter and expressions from which extinction probabilities may be calculated are derived. When all individuals can name their contacts, it is shown that this threshold parameter depends on the infectious period distribution only through its mean. Numerical studies show that the infectious period distribution choice can have a material effect on the threshold behaviour of an epidemic, while the dependencies help reduce spread.

scholarly journals Threshold behaviour of emerging epidemics featuring contact tracing

2011 ◽  
Vol 43 (4) ◽  
pp. 1048-1065 ◽  
Author(s):  
Frank G. Ball ◽  
Edward S. Knock ◽  
Philip D. O'Neill
Keyword(s):  
Stochastic Model ◽  
Contact Tracing ◽  
Death Process ◽  
Infectious Period ◽  
Threshold Parameter ◽  
Threshold Behaviour ◽  
Numerical Studies ◽  
Period Distribution ◽  
Extinction Probabilities ◽  
Birth Death

This paper is concerned with a stochastic model for the spread of an epidemic with a contact tracing scheme, in which diagnosed individuals may name some of their infectious contacts, who are then removed if they have not been already. Traced individuals may or may not also be asked to name their own contacts. The epidemic is studied by considering an approximating, modified birth-death process with intersibling dependencies, for which a threshold parameter and expressions from which extinction probabilities may be calculated are derived. When all individuals can name their contacts, it is shown that this threshold parameter depends on the infectious period distribution only through its mean. Numerical studies show that the infectious period distribution choice can have a material effect on the threshold behaviour of an epidemic, while the dependencies help reduce spread.

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