| 1. |
- Bartoszek, Krzysztof, 1984-, et al.
(författare)
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Critical case stochastic phylogenetic tree model via the Laplace transform
- 2014
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Ingår i: Demonstratio Matematicae. - : De Gruyter. - 0420-1213 .- 2391-4661. ; 47:2, s. 474-481
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Tidskriftsartikel (refereegranskat)abstract
- Birth-and-death models are now a common mathematical tool to describe branching patterns observed in real-world phylogenetic trees. Liggett and Schinazi (2009) is one such example. The authors propose a simple birth-and-death model that is compatible with phylogenetic trees of both in uenza and HIV, depending on the birth rate parameter. An interesting special case of this model is the critical case where the birth rate equals the death rate. This is a non-trivial situation and to study its asymptotic behaviour we employed the Laplace transform. With this we correct the proof of Liggett and Schinazi (2009) in the critical case.
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| 2. |
- Bartoszek, Krzysztof, et al.
(författare)
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Simple SIR models with Markovian control
- 2021
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Ingår i: Japanese Journal of Statistics and Data Science. - : Springer Nature. - 2520-8756 .- 2520-8764. ; 4:1, s. 731-762
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Tidskriftsartikel (refereegranskat)abstract
- We consider a random dynamical system, where the deterministic dynamics are driven by a finite-state space Markov chain. We provide a comprehensive introduction to the required mathematical apparatus and then turn to a special focus on the susceptible-infected-recovered epidemiological model with random steering. Through simulations we visualize the behaviour of the system and the effect of the high-frequency limit of the driving Markov chain. We formulate some questions and conjectures of a purely theoretical nature.
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| 3. |
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| 4. |
- Bartoszek, Krzysztof, 1984-, et al.
(författare)
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Survival time prognosis under a Markov model of cancer development
- 2010
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Ingår i: Proceedings of the XVI National Conference on Applications of Mathematics in Biology and Medicine. ; , s. 6-11
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Konferensbidrag (refereegranskat)abstract
- In this study we look at a breast cancer data set of women from the Pomerania region collected in the year 1987- 1992 in the Medical University of Gdansk.We analyze the clinical risk factors in conjunction with a Markov model of cancer development. We evaluate Artificial Neural Network (ANN) survival time prediction (which was done on this data set in a previous study) via a simulation study.
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