@article{GerlachGlueckKunze2023,
  author    = {Gerlach, Moritz and Gl{\"u}ck, Jochen and Kunze, Markus},
  title     = {Stability of transition semigroups and applications to parabolic equations},
  series = {Transactions of the American Mathematical Society},
  volume    = {376},
  journal   = {Transactions of the American Mathematical Society},
  number    = {1},
  publisher = {American Mathematical Soc.},
  address   = {Providence},
  issn      = {0002-9947},
  doi       = {10.1090/tran/8620},
  pages     = {153 -- 180},
  year      = {2023},
  abstract  = {This paper deals with the long-term behavior of positive operator semigroups on spaces of bounded functions and of signed measures, which have applications to parabolic equations with unbounded coefficients and to stochas-tic analysis. The main results are a Tauberian type theorem characterizing the convergence to equilibrium of strongly Feller semigroups and a generalization of a classical convergence theorem of Doob. None of these results requires any kind of time regularity of the semigroup.},
  language  = {en}
}
@article{DimitrovaKoppitz2022,
  author    = {Dimitrova, Ilinka and Koppitz, J{\"o}rg},
  title     = {On relative ranks of the semigroup of orientation-preserving transformations on infinite chain with restricted range},
  series = {Communications in algebra},
  volume    = {50},
  journal   = {Communications in algebra},
  number    = {5},
  publisher = {Taylor \& Francis Group},
  address   = {Philadelphia},
  issn      = {0092-7872},
  doi       = {10.1080/00927872.2021.2000998},
  pages     = {2157 -- 2168},
  year      = {2022},
  abstract  = {Let X be an infinite linearly ordered set and let Y be a nonempty subset of X. We calculate the relative rank of the semigroup OP(X,Y) of all orientation-preserving transformations on X with restricted range Y modulo the semigroup O(X,Y) of all order-preserving transformations on X with restricted range Y. For Y = X, we characterize the relative generating sets of minimal size.},
  language  = {en}
}
@article{DimitrovaKoppitz2020,
  author    = {Dimitrova, Ilinka and Koppitz, J{\"o}rg},
  title     = {On relative ranks of the semigroup of orientation-preserving transformations on infinite chains},
  series = {Asian-European journal of mathematics},
  volume    = {14},
  journal   = {Asian-European journal of mathematics},
  number    = {08},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {1793-5571},
  doi       = {10.1142/S1793557121501461},
  pages     = {15},
  year      = {2020},
  abstract  = {In this paper, we determine the relative rank of the semigroup OP(X) of all orientation-preserving transformations on infinite chains modulo the semigroup O(X) of all order-preserving transformations.},
  language  = {en}
}
@article{KretzschmarAshbyFearonetal.2022,
  author    = {Kretzschmar, Mirjam E. and Ashby, Ben and Fearon, Elizabeth and Overton, Christopher E. and Panovska-Griffiths, Jasmina and Pellis, Lorenzo and Quaife, Matthew and Rozhnova, Ganna and Scarabel, Francesca and Stage, Helena B. and Swallow, Ben and Thompson, Robin N. and Tildesley, Michael J. and Villela, Daniel Campos},
  title     = {Challenges for modelling interventions for future pandemics},
  series = {Epidemics},
  volume    = {38},
  journal   = {Epidemics},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {1755-4365},
  doi       = {10.1016/j.epidem.2022.100546},
  pages     = {13},
  year      = {2022},
  abstract  = {Mathematical modelling and statistical inference provide a framework to evaluate different non-pharmaceutical and pharmaceutical interventions for the control of epidemics that has been widely used during the COVID-19 pandemic. In this paper, lessons learned from this and previous epidemics are used to highlight the challenges for future pandemic control. We consider the availability and use of data, as well as the need for correct parameterisation and calibration for different model frameworks. We discuss challenges that arise in describing and distinguishing between different interventions, within different modelling structures, and allowing both within and between host dynamics. We also highlight challenges in modelling the health economic and political aspects of interventions. Given the diversity of these challenges, a broad variety of interdisciplinary expertise is needed to address them, combining mathematical knowledge with biological and social insights, and including health economics and communication skills. Addressing these challenges for the future requires strong cross disciplinary collaboration together with close communication between scientists and policy makers.},
  language  = {en}
}