Convergence to the structured coalescent process

2016 ◽  
Vol 53 (2) ◽  
pp. 502-517 ◽  
Author(s):  
Ryouta Kozakai ◽  
Akinobu Shimizu ◽  
Morihiro Notohara
Keyword(s):  
Markov Chain ◽  
Weak Convergence ◽  
Continuous Time ◽  
Markov Chain Model ◽  
Random Mating ◽  
Chain Model ◽  
Continuous Time Markov Chain ◽  
Genealogical Relationship ◽  
Strict Condition ◽  
Structured Coalescent

Abstract The coalescent was introduced by Kingman (1982a), (1982b) and Tajima (1983) as a continuous-time Markov chain model describing the genealogical relationship among sampled genes from a panmictic population of a species. The random mating in a population is a strict condition and the genealogical structure of the population has a strong influence on the genetic variability and the evolution of the species. In this paper, starting from a discrete-time Markov chain model, we show the weak convergence to a continuous-time Markov chain, called the structured coalescent model, describing the genealogy of the sampled genes from whole population by means of passing the limit of the population size. Herbots (1997) proved the weak convergence to the structured coalescent on the condition of conservative migration and Wright–Fisher-type reproduction. We will give the proof on the condition of general migration rates and exchangeable reproduction.

A new stochastic model of microsatellite evolution

1999 ◽  
Vol 36 (3) ◽  
pp. 621-631 ◽  
Author(s):  
Richard Durrett ◽  
Semyon Kruglyak
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Markov Chain Model ◽  
Chain Model ◽  
Continuous Time Markov Chain ◽  
Base Pairs ◽  
Microsatellite Evolution ◽  
Experimental Findings ◽  
Best Fit ◽  
Simple Sequence

We introduce a continuous-time Markov chain model for the evolution of microsatellites, simple sequence repeats in DNA. We prove the existence of a unique stationary distribution for our model, and fit the model to data from approximately 106 base pairs of DNA from fruit flies, mice, and humans. The slippage rates from the best fit for our model are consistent with experimental findings.

scholarly journals Using a stochastic continuous-time Markov chain model to examine alternative timing and duration of the COVID-19 lockdown in Kuwait: what can be done now?

2022 ◽  
Vol 80 (1) ◽  
Author(s):  
Mustafa Al-Zoughool ◽  
Tamer Oraby ◽  
Harri Vainio ◽  
Janvier Gasana ◽  
Joseph Longenecker ◽  
...  
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Disease Transmission ◽  
Markov Chain Model ◽  
Substantial Reduction ◽  
Control Measures ◽  
Optimal Timing ◽  
Chain Model ◽  
Continuous Time Markov Chain ◽  
Epidemic Curve

Abstract Background Kuwait had its first COVID-19 in late February, and until October 6, 2020 it recorded 108,268 cases and 632 deaths. Despite implementing one of the strictest control measures-including a three-week complete lockdown, there was no sign of a declining epidemic curve. The objective of the current analyses is to determine, hypothetically, the optimal timing and duration of a full lockdown in Kuwait that would result in controlling new infections and lead to a substantial reduction in case hospitalizations. Methods The analysis was conducted using a stochastic Continuous-Time Markov Chain (CTMC), eight state model that depicts the disease transmission and spread of SARS-CoV 2. Transmission of infection occurs between individuals through social contacts at home, in schools, at work, and during other communal activities. Results The model shows that a lockdown 10 days before the epidemic peak for 90 days is optimal but a more realistic duration of 45 days can achieve about a 45% reduction in both new infections and case hospitalizations. Conclusions In the view of the forthcoming waves of the COVID19 pandemic anticipated in Kuwait using a correctly-timed and sufficiently long lockdown represents a workable management strategy that encompasses the most stringent form of social distancing with the ability to significantly reduce transmissions and hospitalizations.

A three-state continuous time Markov chain model for HIV disease burden

2018 ◽  
Vol 46 (9) ◽  
pp. 1671-1688 ◽  
Author(s):  
Hrishikesh Chakraborty ◽  
Akhtar Hossain ◽  
Mahbub A.H.M. Latif
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Disease Burden ◽  
Markov Chain Model ◽  
Chain Model ◽  
Hiv Disease ◽  
Continuous Time Markov Chain

scholarly journals A joint logistic regression and covariate-adjusted continuous-time Markov chain model

2017 ◽  
Vol 36 (28) ◽  
pp. 4570-4582 ◽  
Author(s):  
Maria Laura Rubin ◽  
Wenyaw Chan ◽  
Jose-Miguel Yamal ◽  
Claudia Sue Robertson
Keyword(s):  
Logistic Regression ◽  
Markov Chain ◽  
Continuous Time ◽  
Markov Chain Model ◽  
Chain Model ◽  
Continuous Time Markov Chain

scholarly journals Using a Stochastic Continuous-Time Markov Chain Model to Examine Alternative Timing and Duration of the COVID-19 Lockdown in Kuwait: What Can be Done Now?

2021 ◽  
Author(s):  
Mustafa Al-Zoughool ◽  
Tamer Oraby ◽  
Harri Vainio ◽  
Janvier Gasana ◽  
Joseph Longnecker ◽  
...  
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Disease Transmission ◽  
Markov Chain Model ◽  
Substantial Reduction ◽  
Control Measures ◽  
Optimal Timing ◽  
Chain Model ◽  
Continuous Time Markov Chain ◽  
Epidemic Curve

Abstract Background: Kuwait had its first COVID-19 in late February, and until October 6, 2020 it recorded 108,268 cases and 632 deaths. Despite implementing one of the strictest control measures-including a three-week complete lockdown, there was no sign of a declining epidemic curve. The objective of the current analyses is to determine, hypothetically, the optimal timing and duration of a full lockdown in Kuwait that would result in controlling new infections and lead to a substantial reduction in case hospitalizations. Methods: The analysis was conducted using a stochastic Continuous-Time Markov Chain (CTMC), eight state model that depicts the disease transmission and spread of SARS-CoV 2. Transmission of infection occurs between individuals through social contacts at home, in schools, at work, and during other communal activities. Results: The model shows that a lockdown 10 days before the epidemic peak for 90 days is optimal but a more realistic duration of 45 days can achieve about a 45% reduction in both new infections and case hospitalizations.Conclusions: In the view of the forthcoming waves of the COVID19 pandemic anticipated in Kuwait using a correctly-timed and sufficiently long lockdown represents a workable management strategy that encompasses the most stringent form of social distancing with the ability to significantly reduce transmissions and hospitalizations.

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