Algorithms for Markov Binomial Chains
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915357699080192 |
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| author | Gonzalez, Alejandro Alarcón Hens, Niel Leys, Tim Pérez, Guillermo A. |
| author_facet | Gonzalez, Alejandro Alarcón Hens, Niel Leys, Tim Pérez, Guillermo A. |
| contents | We study algorithms to analyze a particular class of Markov population processes that is often used in epidemiology. More specifically, Markov binomial chains are the model that arises from stochastic time-discretizations of classical compartmental models. In this work we formalize this class of Markov population processes and focus on the problem of computing the expected time to termination in a given such model. Our theoretical contributions include proving that Markov binomial chains whose flow of individuals through compartments is acyclic almost surely terminate. We give a PSPACE algorithm for the problem of approximating the time to termination and a direct algorithm for the exact problem in the Blum-Shub-Smale model of computation. Finally, we provide a natural encoding of Markov binomial chains into a common input language for probabilistic model checkers. We implemented the latter encoding and present some initial empirical results showcasing what formal methods can do for practicing epidemiologists. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04902 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algorithms for Markov Binomial Chains Gonzalez, Alejandro Alarcón Hens, Niel Leys, Tim Pérez, Guillermo A. Logic in Computer Science We study algorithms to analyze a particular class of Markov population processes that is often used in epidemiology. More specifically, Markov binomial chains are the model that arises from stochastic time-discretizations of classical compartmental models. In this work we formalize this class of Markov population processes and focus on the problem of computing the expected time to termination in a given such model. Our theoretical contributions include proving that Markov binomial chains whose flow of individuals through compartments is acyclic almost surely terminate. We give a PSPACE algorithm for the problem of approximating the time to termination and a direct algorithm for the exact problem in the Blum-Shub-Smale model of computation. Finally, we provide a natural encoding of Markov binomial chains into a common input language for probabilistic model checkers. We implemented the latter encoding and present some initial empirical results showcasing what formal methods can do for practicing epidemiologists. |
| title | Algorithms for Markov Binomial Chains |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2408.04902 |