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.

@article{paperbot3404,
  title = {Algorithms for Markov Binomial Chains},
  author = {Alejandro Alarcón Gonzalez and Niel Hens and Tim Leys and Guillermo A. Pérez},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 21, Issue 2},
  year = {2025},
  doi = {10.46298/lmcs-21(2:28)2025}
}